Archive ouverte UNIGE | last documents for author 'Markus Buttiker'https://archive-ouverte.unige.ch/Latest objects deposited in the Archive ouverte UNIGE for author 'Markus Buttiker'engDynamic mesoscopic conductors: single electron sources, full counting statistics, and thermal machineshttps://archive-ouverte.unige.ch/unige:88977https://archive-ouverte.unige.ch/unige:88977We theoretically investigate questions regarding the controlled emission and entanglement of individual electrons in mesoscopic circuits, the statistics of current fluctuations and electron waiting times for phase-coherent quantum transport, and thermal machines such as heat engines and refrigerators at the nano-scale. Chapter 2 focuses on dynamic single-electron sources, specifically on the generation of ac spin currents in topological insulators, Mach-Zehnder interferometry with periodic voltage pulses, and the on-demand entanglement of few-electron excitations. In Chapter 3, we present a novel theory for joint electron waiting times and we connect the occurence of negative values in the full counting statistics to a peculiar interference effect. Chapter 4 discusses a heat engine based on the interference in a Mach-Zehnder interferometer as well as implementations for the arguably smallest thermal machines making use of a Josephson junction coupled to harmonic oscillators.Wed, 16 Nov 2016 11:07:47 +0100Topological origin of subgap conductance in insulating bilayer graphenehttps://archive-ouverte.unige.ch/unige:35115https://archive-ouverte.unige.ch/unige:35115The edges of graphene-based systems possess unusual electronic properties, originating from the non-trivial topological structure associated with the pseudospinorial character of the electron wavefunctions. These properties, which have no analogue for electrons described by the Schrödinger equation in conventional systems, have led to the prediction of many striking phenomena, such as gate-tunable ferromagnetism and valley-selective transport1, 2, 3. In most cases, however, the predicted phenomena are not expected to survive the strong structural and chemical disorder that unavoidably affects the edges of real graphene devices. Here, we present a theoretical investigation of the intrinsic low-energy states at the edges of electrostatically gapped bilayer graphene, and find that the contribution of edge modes to the linear conductance of realistic devices remains sizable even for highly imperfect edges. This contribution may dominate over that of the bulk for sufficiently clean devices, such as those based on suspended bilayer graphene samples. Our results illustrate the robustness of those phenomena whose origin is rooted in the topology of the electronic band structure, even in the absence of specific protection mechanisms.Mon, 31 Mar 2014 09:57:59 +0200Marginal topological properties of graphene: a comparison with topological insulatorshttps://archive-ouverte.unige.ch/unige:34970https://archive-ouverte.unige.ch/unige:34970The electronic structures of graphene systems and topological insulators have closely related features, such as a quantized Berry phase and zero-energy edge states. The reason for these similarities is that in both systems there are two relevant orbital bands, which generate the pseudo-spin degree of freedom and, less obviously, there is a correspondence between the valley degree of freedom in graphene and electron spin in topological insulators. Despite the similarities, there are also several important differences, both for the bulk topological properties and for their implications for the edge states—primarily due to the fundamental difference between valley and spin. In view of their peculiar band structure features, gapped graphene systems should be properly characterized as marginal topological insulators, distinct from either the trivial insulators or the true topological insulators.Tue, 25 Mar 2014 10:42:59 +0100Marginality of bulk-edge correspondence for single-valley Hamiltonianshttps://archive-ouverte.unige.ch/unige:34967https://archive-ouverte.unige.ch/unige:34967We study the correspondence between the nontrivial topological properties associated with the individual valleys of gapped bilayer graphene (BLG), as a prototypical multivalley system, and the gapless modes at its edges and other interfaces. We find that the exact connection between the valley-specific Hall conductivity and the number of gapless edge modes does not hold in general, but is dependent on the boundary conditions, even in the absence of intervalley coupling. This nonuniversality is attributed to the absence of a well-defined topological invariant within a given valley of BLG; yet, a more general topological invariant may be defined in certain cases, which explains the distinction between the BLG-vacuum and BLG-BLG interfaces.Tue, 25 Mar 2014 10:38:01 +0100Counting statistics in interacting nano-scale conductorshttps://archive-ouverte.unige.ch/unige:34909https://archive-ouverte.unige.ch/unige:34909Counting statistics investigates the probability P(n,t) that a number n of electrons traverse a nano-scale conductor during a time span t. It is equivalent to consider the zero frequency charge or current correlators, the so-called moments and cumulants, in principle up to infinite order. In this thesis we investigate several aspects of electronic correlations due to interactions. First we investigate the influence of interactions on the counting statistics, considering a generic two-terminal conductor. We show that if the factorial cumulants oscillate as functions of any system parameter or time, then the electrons must be interacting. This statement may be verified in Coulomb blockaded quantum dots, where it is possible to monitor the traversal of electrons in real-time. Moreover, we use a Markovian master equation to describe the first experiment on counting statistics of Andreev events, where two electrons tunnel accross a tunnel barrier between a superconducting lead and a normal metallic island. The statistics are strongly super-Poissonian, reflecting that Andreev events occur in avalanches of different sizes. Finally, we consider finite frequency current noise and show that the noise spectra are in general asymmetric in the applied bias voltage. Using a higher order fluctuation relation, which is an extension of the fluctuation dissipation relation to the non-equilibrium transport regime, we show that this asymmetry is due to a broken electron-hole symmetry, resulting in a finite rectification. We point out that this can occur either due to an asymmetrically applied bias, but more importantly, due to interactions and an inherent chirality of the conductor.Mon, 24 Mar 2014 11:14:32 +0100Coherence of single and many-particle states in mesoscopic systemshttps://archive-ouverte.unige.ch/unige:22610https://archive-ouverte.unige.ch/unige:22610Cette thèse est consacrée à l'étude des propriétés de cohérence d'états à électron unique ou à plusieurs électrons dans des systèmes mésoscopiques. Nous avons tout d'abord utiliser les propriétés de cohérence d'électrons émis par une source dc pour proposer une mesure de parité à l'aide d'un interféromètre de Mach-Zehnder qui crée de l'intrication entre deux qubits. Nous nous sommes ensuite intéressés aux électrons émis par une source qui permet d'injecter des états à particule unique de manière quasi-déterministe. Nous avons caractérisé leurs propriétés de cohérence à l'aide de leur fonction de corrélation au 1er ordre, dérivée à partir de la matrice de diffusion de la source. Enfin, nous avons développé une théorie quantique de la distribution des temps d'attente entre deux électrons consécutifs dans un conducteur mésoscopique. Contrairement à la mesure des fluctuations du courant moyen à travers un canal quantique parfait, cela a permis de mettre en évidence, entre autres, le fait que les électrons ne sont pas séparés en temps de manière uniforme du fait des interactions à courte distance induites par le principe de Pauli.Mon, 27 Aug 2012 10:48:06 +0200Gap theory of rectification in ballistic three-terminal conductorshttps://archive-ouverte.unige.ch/unige:5186https://archive-ouverte.unige.ch/unige:5186abstract not availableMon, 15 Feb 2010 16:28:26 +0100Quantum to classical transition of the charge relaxation resistance of a mesoscopic capacitorhttps://archive-ouverte.unige.ch/unige:4669https://archive-ouverte.unige.ch/unige:4669We present an analysis of the effect of dephasing on the single channel charge relaxation resistance of a mesoscopic capacitor in the linear low frequency regime. The capacitor consists of a cavity which is via a quantum point contact connected to an electron reservoir and Coulomb coupled to a gate. The capacitor is in a perpendicular high magnetic field such that only one (spin polarized) edge state is (partially) transmitted through the contact. In the coherent limit the charge relaxation resistance for a single channel contact is independent of the transmission probability of the contact and given by half a resistance quantum. The loss of coherence in the conductor is modeled by attaching to it a fictitious probe, which draws no net current. In the incoherent limit one could expect a charge relaxation resistance that is inversely proportional to the transmission probability of the quantum point contact. However, such a two terminal result requires that scattering is between two electron reservoirs which provide full inelastic relaxation. We find that dephasing of a single edge state in the cavity is not sufficient to generate an interface resistance. As a consequence the charge relaxation resistance is given by the sum of one constant interface resistance and the (original) Landauer resistance. The same result is obtained in the high temperature regime due to energy averaging over many occupied states in the cavity. Only for a large number of open dephasing channels, describing spatially homogenous dephasing in the cavity, do we recover the two terminal resistance, which is inversely proportional to the transmission probability of the QPC. We compare different dephasing models and discuss the relation of our results to a recent experiment.Tue, 15 Dec 2009 13:57:06 +0100Orbital Entanglement In Mesoscopic Conductorshttps://archive-ouverte.unige.ch/unige:4490https://archive-ouverte.unige.ch/unige:4490We present an investigation of orbital entanglement in mesoscopic conductors. Several schemes for generation of orbital entanglement are discussed, such as normal-superconducting, electron-hole and dynamic orbital entanglers. The generated, orbitally entangled state is investigated with the focus on the state emitted in an electronic analog of the optical Hanbury Brown Twiss experiment. The one and two particle properties of the emitted state are described in terms of reduced density matrices. Approaches to detect and characterize the entanglement based on zero frequency shot noise are discussed, with the focus on a complete reconstruction of the emitted state via quantum state tomography.Tue, 01 Dec 2009 16:27:44 +0100Basic Elements of Electrical Conductionhttps://archive-ouverte.unige.ch/unige:4489https://archive-ouverte.unige.ch/unige:4489A theory of the dynamical conductance of mesoscopic conductors is presented. It is applied to mesoscopic capacitors, resonant double barriers, ballistic wires, metallic diffusive wires, and to the Corbino disk and the Hall bar in quantizing magnetic fields. Central to this approach is a discussion of the charge and potential distribution in mesoscopic conductors. It is necessary to take into account the implications of the long-range Coulomb interaction in order to obtain a charge and current conserving theory. We emphasize the low-frequency response. This has the advantage that the approach is of considerable generality. The theory can be used to discuss the self-consistency of the dc-conductance formula. The theory can also be applied to discuss the rectifying (nonlinear) behavior of mesoscopic conductors.Tue, 01 Dec 2009 16:27:43 +0100Dynamic Conductance in Quantum Hall Systemshttps://archive-ouverte.unige.ch/unige:4488https://archive-ouverte.unige.ch/unige:4488In the framework of the edge-channel picture and the scattering approach to conduction, we discuss the low frequency admittance of quantized Hall samples up to second order in frequency. The first-order term gives the leading order phase-shift between current and voltage and is associated with the displacement current. It is determined by the emittance which is a capacitance in a capacitive arrangement of edge channels but which is inductive-like if edge channels predominate which transmit charge between different reservoirs. The second-order term is associated with the charge relaxation. We apply our results to a Corbino disc and to two- and four-terminal quantum Hall bars, and we discuss the symmetry properties of the current response. In particular, we calculate the longitudinal resistance and the Hall resistance as a function of frequency.Tue, 01 Dec 2009 16:27:42 +0100Admittance and Nonlinear Transport in Quantum Wires, Point Contacts, and Resonant Tunneling Barriershttps://archive-ouverte.unige.ch/unige:4487https://archive-ouverte.unige.ch/unige:4487We present a discussion of the admittance (ac-conductance) and nonlinear I-V-characteristic for a number of mesoscopic conductors. Our approach is based on a generalization of the scattering approach which now includes the effects of the (long-range) Coulomb interaction. We discuss the admittance of a wire with an impurity and with a nearby gate. We extend a discussion of the low-frequency admittance of a quantum point contact to investigate the effects of the gates used to form the contact. We discuss the nonlinear I-V characteristic of a resonant double barrier structure and discuss the admittance for the double barrier for a large range of frequencies. Our approach emphasizes the overall conservation of charge (gauge invariance) and current conservation and the resulting sum rules for the admittance matrix and nonlinear transport coefficients.Tue, 01 Dec 2009 16:27:41 +0100Charge Relaxation in the Presence of Shot Noise in Coulomb Coupled Mesoscopic Systemshttps://archive-ouverte.unige.ch/unige:4486https://archive-ouverte.unige.ch/unige:4486In the presence of shot noise the charge on a mesoscopic conductor fluctuates. We are interested in the charge fluctuations which arise if the conductor is in the proximity of a gate to which it is coupled by long range Coulomb forces only. Specifically we consider a gate coupled to the edge of a Hall bar subject to a quantizing magnetic field which contains a quantum point contact. The gate is located away from the quantum point contact. We evaluate the charge relaxation resistance for this geometry. The charge relaxation resistance determines the current fluctuations and potential fluctuations induced into the gate. If there is only one edge channel the charge relaxation resistance is determined by transmission and reflection probabilities alone, but in the presence of many channels the density of states of all edge states determines this resistance.Tue, 01 Dec 2009 16:27:40 +0100Shot-Noise-Induced Charge and Potential Fluctuations of Edge States in Proximity of a Gatehttps://archive-ouverte.unige.ch/unige:4485https://archive-ouverte.unige.ch/unige:4485We evaluate the RC-time of edge states capacitively coupled to a gate located away from a QPC which allows for partial transmission of an edge channel. At long times or low frequencies the RC-time governs the relaxation of charge and current and governs the fluctuations of the equilibrium electrostatic potential. The RC-time in mesoscopic structures is determined by an electrochemical capacitance which depends on the density of states of the edge states and a charge relaxation resistance. In the non-equilibrium case, in the presence of transport, the shot noise leads to charge fluctuations in proximity of the gate which are again determined by the equilibrium electrochemical capacitance but with a novel resistance. The case of multiple edge states is discussed and the effect of a dephasing voltage probe on these resistances is investigated. The potential fluctuations characterized by these capacitances and resistances are of interest since they determine the dephasing rate in Coulomb coupled mesoscopic conductors.Tue, 01 Dec 2009 16:27:39 +0100Charge Fluctuations and Dephasing in Coulomb Coupled Conductorshttps://archive-ouverte.unige.ch/unige:4484https://archive-ouverte.unige.ch/unige:4484It is shown that the dephasing rate in Coulomb coupled mesoscopic structures is determined by charge relaxation resistances. The charge relaxation resistance together with the capacitance determines the RC-time of the mesoscopic structure and at small frequencies determines the voltage fluctuation spectrum. Self-consistent expressions are presented which give the charge relaxation resistance and consequently the dephasing rate in terms of the diagonal and off-diagonal elements of a generalized Wigner-Smith delay-time matrix. Dephasing rates are discussed both for the equilibrium state and in the transport state in which charge fluctuations are generated by shot noise. A number of different geometries are discussed. This article is to appear in {\it Quantum Mesoscopic Phenomena and Mesoscopic Devices}, edited by I. O. Kulik and R. Ellialtioglu, (Kluwer, unpublished).Tue, 01 Dec 2009 16:27:38 +0100Traversal, reflection and dwell time for quantum tunnelinghttps://archive-ouverte.unige.ch/unige:4483https://archive-ouverte.unige.ch/unige:4483abstract not availableTue, 01 Dec 2009 16:27:37 +0100Capacitance, Charge Fluctuations and Dephasing In Coulomb Coupled Conductorshttps://archive-ouverte.unige.ch/unige:4482https://archive-ouverte.unige.ch/unige:4482The charge fluctuations of two nearby mesoscopic conductors coupled only via the long range Coulomb force are discussed and used to find the dephasing rate which one conductor exerts on the other. The discussion is based on a formulation of the scattering approach for charge densities and the density response to a fluctuating potential. Coupling to the Poisson equation results in an electrically self-consistent description of charge fluctuations. At equilibrium the low-frequency noise power can be expressed with the help of a charge relaxation resistance (which together with the capacitance determines the RC-time of the structure). In the presence of transport the low frequency charge noise power is determined by a resistance which reflects the presence of shot noise. We use these results to derive expressions for the dephasing rates of Coulomb coupled conductors and to find a self-consistent expression for the measurement time.Tue, 01 Dec 2009 16:27:36 +0100The Local Larmor Clock, Partial Densities of States, and Mesoscopic Physicshttps://archive-ouverte.unige.ch/unige:4481https://archive-ouverte.unige.ch/unige:4481The local Larmor clock is used to derive a hierarchy of local densities of states. At the bottom of this hierarchy are the partial density of states for which represent the contribution to the local density of states if both the incident and outgoing scattering channel are prescribed. On the next higher level is the injectivity which represents the contribution to the local density of states if only the incident channel is prescribed regardless of the final scattering channel. The injectivity is related by reciprocity to the emissivity of a point into a quantum channel. The sum of all partial density of states or the sum of all injectivities or the sum of all emissivities is equal to the local density of states. The use of the partial density of states is illustrated for a number of different electron transport problems in mesoscopic physics: The transmission from a tunneling tip into a mesoscopic conductor, the discussion of inelastic or phase breaking scattering with a voltage probe, and the ac-conductance of mesoscopic conductors. The transition from a capacitive response (positive time-delay) to an inductive response (negative time-delay) for a quantum point contact is used to illustrate the difficulty in associating time-scales with a linear response analysis. A brief discussion of the off-diagonal elements of a partial density of states matrix is presented. The off-diagonal elements permit to investigate carrier fluctuations away from the average carrier density. The work concludes with a discussion of the relation between the partial density of states matrix and the Wigner-Smith delay time matrix.Tue, 01 Dec 2009 16:27:35 +0100Decoherence from Vacuum Fluctuationshttps://archive-ouverte.unige.ch/unige:4480https://archive-ouverte.unige.ch/unige:4480Vacuum fluctuations are a source of irreversibility and decoherence. We investigate the persistent current and its fluctuations in a ring with an in-line quantum dot with an Aharonov-Bohm flux through the hole of the ring. The Coulomb blockade leads to persistent current peaks at values of the gate voltage at which two charge states of the dot have the same free energy. We couple the structure to an external circuit and investigate the effect of the zero-temperature (vacuum fluctuations) on the ground state of the ring. We find that the ground state of the ring undergoes a crossover from a state with an average persistent current much larger than the (time-dependent) mean squared fluctuations to a state with a small average persistent current and large mean squared fluctuations. We discuss the spectral density of charge fluctuations and discuss diffusion rates for angle variables characterizing the ground state in Bloch representation.Tue, 01 Dec 2009 16:27:34 +0100Irreversibility and Dephasing from Vacuum Fluctuationshttps://archive-ouverte.unige.ch/unige:4479https://archive-ouverte.unige.ch/unige:4479We investigate the role of vacuum (zero-point) fluctuations in generating decoherence in a number of simple models. First we discuss a harmonic oscillator coupled to a semi-infinite elastic string and discuss the irreversible nature of such a bath. We investigate the fluctuations in energy of the oscillator and discuss the trace the oscillator leaves in the bath. Most of the work deals with two-level systems coupled to a bosonic bath (a transmission line). For two-level systems with a Hamiltonian that commutes with the total Hamiltonian (system plus coupling plus bath) the ground state is a pure state. The energy of the system is a constant of motion. For the general case, the energy of the two-level system fluctuates, and the ground state is only partially coherent. A particular realization of such a two level system consists of a mesoscopic ring with a quantum dot coupled capacitively to a transmission line. In the presence of an Aharonov-Bohm flux this system exhibits a persistent current. This current is a measure of the coherence of the ground state. As a function of the coupling strength the ground state undergoes a crossover from a state characterized by a time-averaged persistent current which is much larger than its time-averaged mean squared fluctuations to a state characterized by a persistent current with an average amplitude that is much smaller than its mean squared fluctuations.Tue, 01 Dec 2009 16:27:32 +0100Reversing the sign of current-current correlationshttps://archive-ouverte.unige.ch/unige:4478https://archive-ouverte.unige.ch/unige:4478Current-correlations are a very sensitive probe of the fluctuations of small conductors. For non-interacting particles injected from thermal sources there is a simple connection between the sign of correlations and statistics: current-current correlations of Fermions are negative, intensity-intensity correlations of Bosons can be positive. In contrast to photons, electrons are interacting entities, and we can expect the simple connection between statistics and the sign of current-current correlations to be broken, if interactions play a crucial role. We present a number of examples in which interactions are important. At a voltage probe the potential fluctuates to maintain zero current. It is shown that there are geometries for which these fluctuations lead to positive correlations. Displacement currents at capacitively coupled contacts are also positively correlated if both contacts contribute to screening of the same excess charge fluctuation. Hybrid normal superconducting systems provide another example which permits positive correlations. The conditions for positive correlations differ strongly depending on whether the normal conductor is open and well coupled to the superconductor or is only weakly coupled via a barrier to the superconductor. In latter case, positive correlations result if the partition noise generated by Cooper pairs is overcome by pairs which are broken up and emit one electron into the contacts of interest.Tue, 01 Dec 2009 16:27:30 +0100Low frequency admittance of quantized Hall conductorshttps://archive-ouverte.unige.ch/unige:4281https://archive-ouverte.unige.ch/unige:4281We present a current and charge conserving theory for the low frequency admittance of a two-dimensional electron gas connected to ideal metallic contacts and subject to a quantizing magnetic field. In the framework of the edge-channel picture, we calculate the admittance up to first order with respect to frequency. The transport coefficients in first order with respect to frequency, which are called emittances, determine the charge emitted into a contact of the sample or a gate in response to an oscillating voltage applied to a contact of the sample or a nearby gate. The emittances depend on the potential distribution inside the sample which is established in response to the oscillation of the potential at a contact. We show that the emittances can be related to the elements of an electro-chemical capacitance matrix which describes a (fictitious) geometry in which each edge channel is coupled to its own reservoir. The particular relation of the emittance matrix to this electro-chemical capacitance matrix depends strongly on the topology of the edge channels: We show that edge channels which connect different reservoirs contribute with a negative capacitance to the emittance. For example, while the emittance of a two-terminal Corbino disc is a capacitance, the emittance of a two-terminal quantum Hall bar is a negative capacitance. The geometry of the edge-channel arrangement in a many-terminal setup is reflected by symmetry properties of the emittance matrix. We investigate the effect of voltage probes and calculate the longitudinal and the Hall resistances of an ideal four-terminal Hall bar for low frequencies.Mon, 30 Nov 2009 16:08:47 +0100Partial Densities of States, Scattering Matrices, and Green's Functionshttps://archive-ouverte.unige.ch/unige:4280https://archive-ouverte.unige.ch/unige:4280The response of an arbitrary scattering problem to quasi-static perturbations in the scattering potential is naturally expressed in terms of a set of local partial densities of states and a set of sensitivities each associated with one element of the scattering matrix. We define the local partial densities of states and the sensitivities in terms of functional derivatives of the scattering matrix and discuss their relation to the Green's function. Certain combinations of the local partial densities of states represent the injectivity of a scattering channel into the system and the emissivity into a scattering channel. It is shown that the injectivities and emissivities are simply related to the absolute square of the scattering wave-function. We discuss also the connection of the partial densities of states and the sensitivities to characteristic times. We apply these concepts to a delta-barrier and to the local Larmor clock.Mon, 30 Nov 2009 16:08:45 +0100Gauge Invariant Nonlinear Electric Transport in Mesoscopic Conductorshttps://archive-ouverte.unige.ch/unige:4279https://archive-ouverte.unige.ch/unige:4279We use the scattering approach to investigate the nonlinear current-voltage characteristic of mesoscopic conductors. We discuss the leading nonlinearity by taking into account the self-consistent nonequilibrium potential. We emphasize conservation of the overall charge and current which are connected to the invariance under a global voltage shift (gauge invariance). As examples, we discuss the rectification coefficient of a quantum point contact and the nonlinear current-voltage characteristic of a resonant level in a double barrier structure.Mon, 30 Nov 2009 16:08:44 +0100Magnetic Field Symmetry of Dynamic Capacitanceshttps://archive-ouverte.unige.ch/unige:4278https://archive-ouverte.unige.ch/unige:4278While the static capacitance matrix is always symmetric and thus an even function of the magnetic field, the dynamic capacitance matrix of multi-terminal samples obeys in general only the weaker Onsager-Casimir symmetry relations. Our results are in accordance with recent experimental observations of asymmetric dynamic capacitances in quantized Hall systems. We predict quantization of the four-terminal resistances of an insulating Hall sample.Mon, 30 Nov 2009 16:08:43 +0100Charge-Relaxation and Dwell Time in the Fluctuating Admittance of a Chaotic Cavityhttps://archive-ouverte.unige.ch/unige:4277https://archive-ouverte.unige.ch/unige:4277We consider the admittance of a chaotic quantum dot, capacitively coupled to a gate and connected to two electron reservoirs by multichannel ballistic point contacts. For a dot in the regime of weak-localization and universal conductance fluctuations, we calculate the average and variance of the admittance using random-matrix theory. We find that the admittance is governed by two time-scales: the classical admittance depends on the RC-time of the quantum dot, but the relevant time scale for the weak-localization correction and the admittance fluctuations is the dwell time. An extension of the circular ensemble is used for a statistical description of the energy dependence of the scattering matrix.Mon, 30 Nov 2009 16:08:42 +0100Quantum-Statistical Current Correlations in Multilead Chaotic Cavitieshttps://archive-ouverte.unige.ch/unige:4276https://archive-ouverte.unige.ch/unige:4276Quantum mechanics requires that identical particles are treated as indistinguishable. This requirement leads to correlations in the fluctuating properties of a system. Theoretical predictions are made for an experiment on a multi-lead chaotic quantum dot which can identify exchange effects in electronic current-current correlations. Interestingly, we find that the ensemble averaged exchange effects are of the order of the channel number, and are insensitive to dephasing.Mon, 30 Nov 2009 16:08:41 +0100Distribution of Parametric Conductance Derivatives of a Quantum Dothttps://archive-ouverte.unige.ch/unige:4275https://archive-ouverte.unige.ch/unige:4275The conductance G of a quantum dot with single-mode ballistic point contacts depends sensitively on external parameters X, such as gate voltage and magnetic field. We calculate the joint distribution of G and dG/dX by relating it to the distribution of the Wigner-Smith time-delay matrix of a chaotic system. The distribution of dG/dX has a singularity at zero and algebraic tails. While G and dG/dX are correlated, the ratio of dG/dX andMon, 30 Nov 2009 16:08:40 +0100Nanoscopic Tunneling Contacts on Mesoscopic Multiprobe Conductorshttps://archive-ouverte.unige.ch/unige:4274https://archive-ouverte.unige.ch/unige:4274We derive Bardeen-like expressions for the transmission probabilities between two multi-probe mesoscopic conductors coupled by a weak tunneling contact. We emphasize especially the dual role of a weak coupling contact as a current source and sink and analyze the magnetic field symmetry. In the limit of a point-like tunneling contact the transmission probability becomes a product of local, partial density of states of the two mesoscopic conductors. We present expressions for the partial density of states in terms of functional derivatives of the scattering matrix with respect to the local potential and in terms of wave functions. We discuss voltage measurements and resistance measurements in the transport state of conductors. We illustrate the theory for the simple case of a scatterer in an otherwise perfect wire. In particular, we investigate the development of the Hall-resistance as measured with weak coupling probes.Mon, 30 Nov 2009 16:08:39 +0100Front Propagation in Evanescent Mediahttps://archive-ouverte.unige.ch/unige:4272https://archive-ouverte.unige.ch/unige:4272We investigate the time evolution of waves in evanescent media generated by a source within this medium and observed at some distance away from the location of the source. The aim is to find a velocity which describes a causal process and is thus, for a medium with relativistic dispersion, limited by the velocity of light. For a source with a sharp onset in time, the wave function consists of a forerunner generated by the onset of the source, and of a monochromatic front. The forerunner is dominated by a frequency which decreases with time, and the monochromatic front carries the oscillation frequency of the source into the evanescent medium. For a medium with Schrödinger-like dispersion the velocity of the front is infinite and the monochromatic front propagates with a velocity which is in agreement with the traversal time for tunneling. In the relativistic case the forerunners travel with the velocity of light and the velocity the monochromatic front is smaller than the velocity of light and only for special energies equal to the velocity of light. For sources with a sharp onset, the forerunners are not attenuated and in magnitude far exceed the monochromatic front. This renders the detection of the monochromatic front difficult. To avoid the different behavior of forerunners and monochromatic fronts, sources which are frequency-band limited can be considered or a short-time Fourier transform of the field at the observation point can be taken. Both discussions suggest that the traversal time can be determined only up to a factor of (1).Mon, 30 Nov 2009 16:08:37 +0100Charge Fluctuations in Quantum Point Contacts and Chaotic Cavities in the Presence of Transporthttps://archive-ouverte.unige.ch/unige:4273https://archive-ouverte.unige.ch/unige:4273We analyze the frequency-dependent current fluctuations induced into a gate near a quantum point contact or a quantum chaotic cavity. We use a current and charge conserving, effective scattering approach in which interactions are treated in random phase approximation. The current fluctuations measured at a nearby gate, coupled capacitively to the conductor, are determined by the screened charge fluctuations of the conductor. Both the equilibrium and the non-equilibrium current noise at the gate can be expressed with the help of resistances which are related to the charge dynamics on the conductor. We evaluate these resistances for a point contact and determine their distributions for an ensemble of chaotic cavities. For a quantum point contact these resistances exhibit pronounced oscillations with the opening of new channels. For a chaotic cavity coupled to one channel point contacts the charge relaxation resistance shows a broad distribution between 1/4 and 1/2 of a resistance quantum. The non-equilibrium resistance exhibits a broad distribution between zero and 1/4 of a resistance quantum.Mon, 30 Nov 2009 16:08:37 +0100Front Propagation in Evanescent Mediahttps://archive-ouverte.unige.ch/unige:4271https://archive-ouverte.unige.ch/unige:4271We investigate the time evolution of waves in evanescent media generated by a source within this medium and observed at some distance away from the location of the source. The aim is to find a velocity which describes a causal process and is thus, for a medium with relativistic dispersion, limited by the velocity of light. The wave function consists of a broad frequency forerunner generated by the onset of the source, and of a monochromatic front which carries the oscillation frequency of the source. For a medium with Schrödinger-like dispersion the monochromatic front propagates with a velocity which is in agreement with the traversal time, and in the relativistic case the velocity of the fronts is limited by the velocity of light. For sources with a sharp onset, the forerunners are not attenuated and in magnitude far exceed the monochromatic front. In contrast, for sources which are frequency-band limited, the forerunners are also attenuated and become comparable to the monochromatic front: like in the propagating case, there exists a time at which a broad frequency forerunner is augmented by a monochromatic wave.Mon, 30 Nov 2009 16:08:35 +0100Scattering Theory of Photon-Assisted Electron Transporthttps://archive-ouverte.unige.ch/unige:4270https://archive-ouverte.unige.ch/unige:4270The scattering matrix approach to phase-coherent transport is generalized to nonlinear ac-transport. In photon-assisted electron transport it is often only the dc-component of the current that is of experimental interest. But ac-currents at all frequencies exist independently of whether they are measured or not. We present a theory of photon-assisted electron transport which is charge and current conserving for all Fourier components of the current. We find that the photo-current can be considered as an up- and down-conversion of the harmonic potentials associated with the displacement currents. As an example explicit calculations are presented for a resonant double barrier coupled to two reservoirs and capacitively coupled to a gate. Two experimental situations are considered: in the first case the ac-field is applied via a gate, and in the second case one of the contact potentials is modulated. For the first case we show that the relative weight of the conduction sidebands varies with the screening properties of the system. In contrast to the non-interacting case the relative weights are not determined by Bessel functions. Moreover, interactions can give rise to an asymmetry between absorption and emission peaks. In the contact driven case, the theory predicts a zero-bias current proportional to the asymmetry of the double barrier. This is in contrast to the discussion of Tien and Gordon which, in violation of basic symmetry principles, predicts a zero-bias current also for a symmetric double barrier.Mon, 30 Nov 2009 16:08:34 +0100Quantum Shot Noise at Local-Tunneling Contacts on Mesoscopic Multiprobe Conductorshttps://archive-ouverte.unige.ch/unige:4269https://archive-ouverte.unige.ch/unige:4269New experiments that measure the low-frequency shot-noise spectrum at local tunneling contacts on mesoscopic structures are proposed. The current fluctuation spectrum at a single tunneling tip is determined by local partial densities of states. The current-correlation spectrum between two tunneling tips is sensitive to non-diagonal density of states elements which are expressed in terms of products of scattering states of the conductor. Thus such an experiment permits to investigate correlations of electronic wave functions. We present specific results for a clean wire with a single barrier and for metallic diffusive conductors.Mon, 30 Nov 2009 16:08:33 +0100Local Non-equilibrium Distribution of Charge Carriers in a Phase-Coherent Conductorhttps://archive-ouverte.unige.ch/unige:4268https://archive-ouverte.unige.ch/unige:4268We use the scattering matrix approach to derive generalized Bardeen-like formulae for the conductances between the contacts of a phase-coherent multiprobe conductor and a tunneling tip which probes its surface. These conductances are proportional to local partial densities of states, called injectivities and emissivities. The current and the current fluctuations measured at the tip are related to an effective local non-equilibrium distribution function. This distribution function contains the quantum-mechanical phase-coherence of the charge carriers in the conductor and is given as products of injectivities and the Fermi distribution functions in the electron reservoirs. The results are illustrated for measurements on ballistic conductors with barriers and for diffusive conductors.Mon, 30 Nov 2009 16:08:32 +0100Charge Relaxation and Dephasing in Coulomb Coupled Conductorshttps://archive-ouverte.unige.ch/unige:4267https://archive-ouverte.unige.ch/unige:4267The dephasing time in coupled mesoscopic conductors is caused by the fluctuations of the dipolar charge permitted by the long range Coulomb interaction. We relate the phase breaking time to elementary transport coefficients which describe the dynamics of this dipole: the capacitance, an equilibrium charge relaxation resistance and in the presence of transport through one of the conductors a non-equilibrium charge relaxation resistance. The discussion is illustrated for a quantum point contact in a high magnetic field in proximity to a quantum dot.Mon, 30 Nov 2009 16:08:31 +0100Distribution Functions and Current-Correlations in Normal-Metal-Superconductor Heterostructureshttps://archive-ouverte.unige.ch/unige:4266https://archive-ouverte.unige.ch/unige:4266We introduce electron-like and hole-like distribution functions, which determine the currents and the fluctuation spectra of the currents measured at a normal-conductor--superconductor hetero-structure. These distribution functions are expressed with the help of newly defined partial densities of states for hetero-structures. Voltage measurements using a weakly coupled contact on such a structure show the absence of a contact resistance to the superconducting reservoir and illustrate how the interface to the superconductor acts as an Andreev mirror. We also discuss the current-current correlations measured at two normal contacts and argue that the appearance of positive correlations is a purely mesoscopic effect, which vanishes in the limit of a large number of channels and in the average over an ensemble.Mon, 30 Nov 2009 16:08:30 +0100Shot Noise in Mesoscopic Conductorshttps://archive-ouverte.unige.ch/unige:4265https://archive-ouverte.unige.ch/unige:4265Theoretical and experimental work concerned with dynamic fluctuations has developed into a very active and fascinating subfield of mesoscopic physics. We present a review of this development focusing on shot noise in small electric conductors. Shot noise is a consequence of the quantization of charge. It can be used to obtain information on a system which is not available through conductance measurements. In particular, shot noise experiments can determine the charge and statistics of the quasiparticles relevant for transport, and reveal information on the potential profile and internal energy scales of mesoscopic systems. Shot noise is generally more sensitive to the effects of electron-electron interactions than the average conductance. We present a discussion based on the conceptually transparent scattering approach and on the classical Langevin and Boltzmann-Langevin methods; in addition a discussion of results which cannot be obtained by these methods is provided. We conclude the review by pointing out a number of unsolved problems and an outlook on the likely future development of the field.Mon, 30 Nov 2009 16:08:26 +0100Traversal Time for Tunnelinghttps://archive-ouverte.unige.ch/unige:4264https://archive-ouverte.unige.ch/unige:4264The time required for decay of a metastable state, through tunneling, is a well settled subject. During this lifetime of the initial state, the particle oscillates within its initial well. By contrast, questions about the duration of the actual tunneling process, when it finally occurs, have led to widely divergent answers. In recent years, Jonson, Stevens, and we, have, through independent approaches, pointed out that there is an effective barrier traversal velocity obtained by dividing the magnitude of the imaginary momentum, under the barrier, by the particle mass. Here we present a fourth approach to this earlier answer, by considering a time modulated stream incident on the barrier. At low modulation frequencies the transmitted beam reproduces the incident modulation without lag, and without change in modulation depth. As the modulation frequency is increased we eventually depart from this simple behavior, and that is taken as a measure of the transversal time. We also provide some of the details omitted in our earlier analysis.Mon, 30 Nov 2009 16:08:25 +0100Traversal Time for Tunnelinghttps://archive-ouverte.unige.ch/unige:4263https://archive-ouverte.unige.ch/unige:4263One of several contradictory existing results for the time a tunneling particle interacts with its barrier is confirmed, by considering tunneling through a time-modulated barrier. At low modulation frequencies the traversing particle sees a static barrier. At high frequencies the particle tunnels through the time-averaged potential, but can do it inelastically, losing or gaining modulation quanta. The transition between the two regimes yields ?dx[m / 2(V-E)]1 / 2 for the traversal time.Mon, 30 Nov 2009 16:08:25 +0100Coulomb Induced Positive Current-Current Correlations in Normal Conductorshttps://archive-ouverte.unige.ch/unige:4262https://archive-ouverte.unige.ch/unige:4262In the white-noise limit current correlations measured at different contacts of a mesoscopic conductor are negative due to the antisymmetry of the wave function (Pauli principle). We show that current fluctuations at capacitive contacts induced via the long range Coulomb interaction as consequence of charge fluctuations in the mesoscopic sample can be {\it positively} correlated. The positive correlations are a consequence of the extension of the wave-functions into areas near both contacts. As an example we investigate in detail a quantum point contact in a high magnetic field under conditions in which transport is along an edge state.Mon, 30 Nov 2009 16:08:24 +0100Time Dependence of Evanescent Quantum Waveshttps://archive-ouverte.unige.ch/unige:4261https://archive-ouverte.unige.ch/unige:4261The time dependence of quantum evanescent waves generated by a point source with an infinite or a limited frequency band is analyzed. The evanescent wave is characterized by a forerunner (transient) related to the precise way the source is switched on. It is followed by an asymptotic, monochromatic wave which at long times reveals the oscillation frequency of the source. For a source with a sharp onset the forerunner is exponentially larger than the monochromatic solution and a transition from the transient regime to the asymtotic regime occurs only at asymptotically large times. In this case, the traversal time for tunneling plays already a role only in the transient regime. To enhance the monochromatic solution compared to the forerunner we investigate (a) frequency band limited sources and (b) the short time Fourier analysis (the spectrogram) corresponding to a detector which is frequency band limited. Neither of these two methods leads to a precise determination of the traversal time. However, if they are limited to determine the traversal time only with a precision of the traversal time itself both methods are successful: In this case the transient behavior of the evanescent waves is at a time of the order of the traversal time followed by a monochromatic wave which reveals the frequency of the source.Mon, 30 Nov 2009 16:08:23 +0100Effect of Incoherent Scattering on Shot Noise Correlations in the Quantum Hall Regimehttps://archive-ouverte.unige.ch/unige:4260https://archive-ouverte.unige.ch/unige:4260We investigate the effect of incoherent scattering in a Hanbury Brown and Twiss situation with electrons in edge states of a three-terminal conductor submitted to a strong perpendicular magnetic field. The modelization of incoherent scattering is performed by introducing an additional voltage probe through which the current is kept equal to zero which causes voltage fluctuations at this probe. It is shown that inelastic scattering can lead in this framework to positive correlations, whereas correlations remain always negative for quasi-elastic scattering.Mon, 30 Nov 2009 16:08:21 +0100Zero-point fluctuations in the ground state of a mesoscopic normal ringhttps://archive-ouverte.unige.ch/unige:4259https://archive-ouverte.unige.ch/unige:4259We investigate the persistent current of a ring with an in-line quantum dot capacitively coupled to an external circuit. Of special interest is the magnitude of the persistent current as a function of the external impedance in the zero temperature limit when the only fluctuations in the external circuit are zero-point fluctuations. These are time-dependent fluctuations which polarize the ring-dot structure and we discuss in detail the contribution of displacement currents to the persistent current. We have earlier discussed an exact solution for the persistent current and its fluctuations based on a Bethe ansatz. In this work, we emphasize a physically more intuitive approach using a Langevin description of the external circuit. This approach is limited to weak coupling between the ring and the external circuit. We show that the zero temperature persistent current obtained in this approach is consistent with the persistent current calculated from a Bethe ansatz solution. In the absence of coupling our system is a two level system consisting of the ground state and the first excited state. In the presence of coupling we investigate the projection of the actual state on the ground state and the first exited state of the decoupled ring. With each of these projections we can associate a phase diffusion time. In the zero temperature limit we find that the phase diffusion time of the excited state projection saturates, whereas the phase diffusion time of the ground state projection diverges.Mon, 30 Nov 2009 16:08:19 +0100Quantum Coherence of the Ground State of a Mesoscopic Ringhttps://archive-ouverte.unige.ch/unige:4258https://archive-ouverte.unige.ch/unige:4258We discuss the phase coherence properties of a mesoscopic normal ring coupled to an electric environment via Coulomb interactions. This system can be mapped onto the Caldeira-Leggett model with a flux dependent tunneling amplitude. We show that depending on the strength of the coupling between the ring and the environment the free energy can be obtained either by a Bethe ansatz approch (for weak coupling) or by using a perturbative expression which we derive here (in the case of strong coupling). We demonstrate that the zero-point fluctuations of the environment can strongly suppress the persistent current of the ring below its value in the absence of the environment. This is an indication that the equilibrium fluctuations in the environment disturb the coherence of the wave functions in the ring. Moreover the influence of quantum fluctuations can induce symmetry breaking seen in the polarization of the ring and in the flux induced capacitance.Mon, 30 Nov 2009 16:08:18 +0100Semiclassical theory of shot noise in disordered SN contactshttps://archive-ouverte.unige.ch/unige:4257https://archive-ouverte.unige.ch/unige:4257We present a semiclassical theory of shot noise in diffusive superconductor - normal metal contacts. At subgap voltages, we reproduce the doubling of shot noise with respect to conventional normal-metal contacts, which is interpreted in terms of an energy balance of electrons. Above the gap, the voltage dependence of the noise crosses over to the standard one with a voltage-independent excess noise. The semiclassical description of noise leads to correlations between currents at different electrodes of multiterminal SN contacts which are always of fermionic type, i.e. negative. Using a quantum extension of the Boltzmann - Langevin method, we reproduce the peculiarity of noise at the Josephson frequency and obtain an analytical frequency dependence of noise at above-gap voltages.Mon, 30 Nov 2009 16:08:16 +0100Charge fluctuation induced dephasing in a gated mesoscopic interferometerhttps://archive-ouverte.unige.ch/unige:4256https://archive-ouverte.unige.ch/unige:4256The reduction of the amplitude of Aharonov-Bohm oscillations in a ballistic one-channel mesoscopic interferometer due to charge fluctuations is investigated. In the arrangement considered the interferometer has four terminals and is coupled to macroscopic metallic side-gates. The Aharonov-Bohm oscillation amplitude is calculated as a function of temperature and the strength of coupling between the ring and the side-gates. The resulting dephasing rate is linear in temperature in agreement with recent experiments. Our derivation emphasizes the relationship between dephasing, ac-transport and charge fluctuations.Mon, 30 Nov 2009 16:08:15 +0100Effect of inelastic scattering on parametric pumpinghttps://archive-ouverte.unige.ch/unige:4255https://archive-ouverte.unige.ch/unige:4255Pumping of charge in phase-coherent mesoscopic systems due to the out-of-phase modulation of two parameters has recently found considerable interest. We investigate the effect of inelastic processes on the adiabatically pumped current through a two terminal mesoscopic sample. We find that the loss of coherence does not suppress the pumped charge but rather an additional physical mechanism for an incoherent pump effect comes into play. In a fully phase incoherent system the pump effect is similar to a rectification effect.Mon, 30 Nov 2009 16:08:14 +0100Ground State Energy Fluctuations of a System Coupled to a Bathhttps://archive-ouverte.unige.ch/unige:4254https://archive-ouverte.unige.ch/unige:4254It is often argued that a small non-degenerate quantum system system coupled to a bath has a fixed energy in its ground state since a fluctuation in energy would require an energy supply from the bath. We consider a simple model of a harmonic oscillator (the system) coupled to a linear string and determine the mean squared energy fluctuations. We also analyze the two time correlator of the energy and discuss its behavior for a finite string.Mon, 30 Nov 2009 16:08:13 +0100Charge densities and charge noise in mesoscopic conductorshttps://archive-ouverte.unige.ch/unige:4253https://archive-ouverte.unige.ch/unige:4253We introduce a hierarchy of density of states to characterize the charge distribution in a mesoscopic conductor. At the bottom of this hierarchy are the partial density of states which represent the contribution to the local density of states if both the incident and the out-going scattering channel is prescribed. The partial density of states play a prominent role in measurements with a scanning tunneling microscope on multiprobe conductors in the presence of current flow. The partial density of states determine the degree of dephasing generated by a weakly coupled voltage probe. In addition the partial density of states determine the frequency-dependent response of mesoscopic conductors in the presence of slowly oscillating voltages applied to the contacts of the sample. The partial density of states permit the formulation of a Friedel sum rule which can be applied locally. We introduce the off-diagonal elements of the partial density of states matrix to describe charge fluctuation processes. This generalization leads to a local Wigner-Smith life-time matrix.Mon, 30 Nov 2009 16:08:11 +0100Dissipation and noise in adiabatic quantum pumpshttps://archive-ouverte.unige.ch/unige:4252https://archive-ouverte.unige.ch/unige:4252We investigate the distribution function, the heat flow and the noise properties of an adiabatic quantum pump for an arbitrary relation of pump frequencyMon, 30 Nov 2009 16:08:10 +0100Chaotic dot-superconductor analog of the Hanbury Brown Twiss effecthttps://archive-ouverte.unige.ch/unige:4251https://archive-ouverte.unige.ch/unige:4251As an electrical analog of the optical Hanbury Brown Twiss effect, we study current cross-correlations in a chaotic quantum dot-superconductor junction. One superconducting and two normal reservoirs are connected via point contacts to a chaotic quantum dot. For a wide range of contact widths and transparencies, we find large positive current correlations. The positive correlations are generally enhanced by normal backscattering in the contacts. Moreover, for normal backscattering in the contacts, the positive correlations survive when suppressing the proximity effect in the dot with a weak magnetic field.Mon, 30 Nov 2009 16:08:09 +0100Efficiency of Mesoscopic Detectorshttps://archive-ouverte.unige.ch/unige:4250https://archive-ouverte.unige.ch/unige:4250We consider a mesoscopic measuring device whose conductance is sensitive to the state of a two-level system. The detector is described with the help of its scattering matrix. Its elements can be used to calculate the relaxation and decoherence time of the system, and determine the characteristic time for a reliable measurement. We derive conditions needed for an efficient ratio of decoherence and measurement time. To illustrate the theory we discuss the distribution function of the efficiency of an ensemble of open chaotic cavities.Mon, 30 Nov 2009 16:08:08 +0100Noise-assisted classical adiabatic pumping in a symmetric periodic potentialhttps://archive-ouverte.unige.ch/unige:4249https://archive-ouverte.unige.ch/unige:4249We consider a classical overdamped Brownian particle moving in a symmetric periodic potential. We show that a net particle flow can be produced by adiabatically changing two external periodic potentials with a spatial and a temporal phase difference. The classical pumped current is found to be independent of the friction and to vanish both in the limit of low and high temperature. Below a critical temperature, adiabatic pumping appears to be more efficient than transport due to a constant external force.Mon, 30 Nov 2009 16:08:06 +0100Floquet states and persistent currents transitions in a mesoscopic ringhttps://archive-ouverte.unige.ch/unige:4248https://archive-ouverte.unige.ch/unige:4248We consider the effect of an oscillating potential on the single-particle spectrum and the time-averaged persistent current of a one-dimensional phase-coherent mesoscopic ring with a magnetic flux. We show that in a ring with an even number of spinless electrons the oscillating potential has a strong effect on the persistent current when the excited side bands are close to the eigen levels of a pure ring. Resonant enhancement of side bands of the Floquet state generates a sign change of the persistent current.Mon, 30 Nov 2009 16:08:05 +0100Semiclassical theory of current correlations in chaotic dot-superconductor systemshttps://archive-ouverte.unige.ch/unige:4247https://archive-ouverte.unige.ch/unige:4247We present a semiclassical theory of current correlations in multiterminal chaotic dot-superconductor junctions, valid in the absence of the proximity effect in the dot. For a dominating coupling of the dot to the normal terminals and a nonperfect dot-superconductor interface, positive cross correlations are found between currents in the normal terminals. This demonstrates that positive cross correlations can be described within a semiclassical approach. We show that the semiclassical approach is equivalent to a quantum mechanical Green's function approach with suppressed proximity effect in the dot.Mon, 30 Nov 2009 16:08:03 +0100Floquet scattering theory of quantum pumpshttps://archive-ouverte.unige.ch/unige:4246https://archive-ouverte.unige.ch/unige:4246We develop the Floquet scattering theory for quantum mechanical pumping in mesoscopic conductors. The nonequilibrium distribution function, the dc charge and heat currents are investigated at arbitrary pumping amplitude and frequency. For mesoscopic samples with discrete spectrum we predict a sign reversal of the pumped current when the pump frequency is equal to the level spacing in the sample. This effect allows to measure the phase of the transmission coefficient through the mesoscopic sample. We discuss the necessary symmetry conditions (both spatial and temporal) for pumping.Mon, 30 Nov 2009 16:08:02 +0100Hanbury Brown Twiss effects in channel mixing normal-superconducting systemshttps://archive-ouverte.unige.ch/unige:4245https://archive-ouverte.unige.ch/unige:4245An investigation of the role of the proximity effect in current cross correlations in multiterminal, channel-mixing, normal-superconducting systems is presented. The proposed experiment is an electrical analog of the optical Hanbury Brown Twiss intensity cross correlation experiment. A chaotic quantum dot is connected via quantum point contacts to two normal and one superconducting reservoir. For dominating coupling of the dot to the superconducting reservoir, a magnetic flux of the order of a flux quantum in the dot suppresses the proximity effect and reverses the sign of the cross correlations, from positive to negative. In the opposite limit, for a dominating coupling to the normal reservoirs, the proximity effect is weak and the cross correlation are positive for a nonideal contact between the dot and the superconducting reservoir. We show that in this limit the correlations can be explained with particle counting arguments.Mon, 30 Nov 2009 16:08:01 +0100Scattering Theory of Mesoscopic Detectorshttps://archive-ouverte.unige.ch/unige:4244https://archive-ouverte.unige.ch/unige:4244We consider a two-level system coupled to a mesoscopic two-terminal conductor that acts as measuring device. As a convenient description of the conductor we introduce its scattering matrix. We show how its elements can be used to calculate the relaxation and decoherence rates of the two-level system. Special emphasis is laid on the charge screening in the conductor that becomes important in the many-channel limit. Finally we give some examples that illustrate charge screening in different limits.Mon, 30 Nov 2009 16:08:00 +0100Local Friedel sum rule on graphshttps://archive-ouverte.unige.ch/unige:4243https://archive-ouverte.unige.ch/unige:4243We consider graphs made of one-dimensional wires connected at vertices and on which may live a scalar potential. We are interested in a scattering situation where the graph is connected to infinite leads. We investigate relations between the scattering matrix and the continuous part of the local density of states, the injectivities, emissivities and partial local density of states. Those latter quantities can be obtained by attaching an extra lead at the point of interest and by investigating the transport in the limit of zero transmission into the additional lead. In addition to the continuous part related to the scattering states, the spectrum of graphs may present a discrete part related to states that remain uncoupled to the external leads. The theory is illustrated with the help of a few simple examples.Mon, 30 Nov 2009 16:07:58 +0100Stochastic Path Integral Formulation of Full Counting Statisticshttps://archive-ouverte.unige.ch/unige:4242https://archive-ouverte.unige.ch/unige:4242We derive a stochastic path integral representation of counting statistics in semi-classical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to find the propagator for charge distributions with an arbitrary number of counting fields and generalized charges. The counting statistics is given by the saddle point approximation to the path integral, and fluctuations around the saddle point are suppressed in the semi-classical approximation. We use this approach to derive the current cumulants of a chaotic cavity in the hot-electron regime.Mon, 30 Nov 2009 16:07:56 +0100Statistics of Charge Fluctuations in Chaotic Cavitieshttps://archive-ouverte.unige.ch/unige:4241https://archive-ouverte.unige.ch/unige:4241We consider the zero frequency fluctuations of charge inside a mesoscopic conductor in the large capacitance limit. In analogy to current counting statistics we derive the characteristic function of charge fluctuations in terms of the scattering matrix of the conductor. Using random matrix theory we evaluate the characteristic function semi-analytically for chaotic cavities. Our result is universal in the sense that it describes not only the fluctuations of charge, but of any observable quantity inside the cavity. We discuss equilibrium and non-equilibrium fluctuations and extend our theory to the case of contacts with arbitrary transparency. Finally we investigate the suppression of fluctuations in the small capacitance limit due to charge screening.Mon, 30 Nov 2009 16:07:55 +0100Hidden quantum pump effects in quantum coherent ringshttps://archive-ouverte.unige.ch/unige:4240https://archive-ouverte.unige.ch/unige:4240Time periodic perturbations of an electron system on a ring are examined. For small frequencies periodic small amplitude perturbations give rise to side band currents which in leading order are inversely proportional to the frequency. These side band currents compensate the current of the central band such that to leading order no net pumped current is generated. In the non-adiabatic limit, larger pump frequencies can lead to resonant excitations: as a consequence a net pumped current arises. We illustrate our results for a one channel ring with a quantum dot whose barriers are modulated parametrically.Mon, 30 Nov 2009 16:07:54 +0100Orbital entanglement and violation of Bell inequalities in mesoscopic conductorshttps://archive-ouverte.unige.ch/unige:4239https://archive-ouverte.unige.ch/unige:4239We propose a spin-independent scheme to generate and detect two-particle entanglement in a mesoscopic normal-superconductor system. A superconductor, weakly coupled to the normal conductor, generates an orbitally entangled state by injecting pairs of electrons into different leads of the normal conductor. The entanglement is detected via violation of a Bell inequality, formulated in terms of zero-frequency current cross-correlators. It is shown that the Bell inequality can be violated for arbitrary strong dephasing in the normal conductor.Mon, 30 Nov 2009 16:07:53 +0100Probe-configuration dependent dephasing in a mesoscopic interferometerhttps://archive-ouverte.unige.ch/unige:4238https://archive-ouverte.unige.ch/unige:4238Dephasing in a ballistic four-terminal Aharonov-Bohm geometry due to charge and voltage fluctuations is investigated. Treating two terminals as voltage probes, we find a strong dependence of the dephasing rate on the probe configuration in agreement with a recent experiment by Kobayashi et al. (J. Phys. Soc. Jpn. 71, 2094 (2002)). Voltage fluctuations in the measurement circuit are shown to be the source of the configuration dependence.Mon, 30 Nov 2009 16:07:51 +0100Orbital entanglement and violation of Bell inequalities in the presence of dephasinghttps://archive-ouverte.unige.ch/unige:4237https://archive-ouverte.unige.ch/unige:4237We discuss orbital entanglement in mesoscopic conductors, focusing on the effect of dephasing. The entanglement is detected via violation of a Bell Inequality formulated in terms of zero-frequency current correlations. Following closely the recent work by Samuelsson, Sukhorukov and Buttiker, we investigate how the dephasing affects the possibility to violate the Bell Inequality and how system parameters can be adjusted for optimal violation.Mon, 30 Nov 2009 16:07:50 +0100Entangled Hanbury Brown Twiss effects with edge stateshttps://archive-ouverte.unige.ch/unige:4236https://archive-ouverte.unige.ch/unige:4236Electronic Hanbury Brown Twiss correlations are discussed for geometries in which transport is along adiabatically guided edge channels. We briefly discuss partition noise experiments and discuss the effect of inelastic scattering and dephasing on current correlations. We then consider a two-source Hanbury Brown Twiss experiment which demonstrates strikingly that even in geometries without an Aharonov-Bohm effect in the conductance matrix (second-order interference), correlation functions can (due to fourth-order interference) be sensitive to a flux. Interestingly we find that this fourth-order interference effect is closely related to orbital entanglement. The entanglement can be detected via violation of a Bell Inequality in this geometry even so particles emanate from uncorrelated sources.Mon, 30 Nov 2009 16:07:48 +0100Reduced and projected two-particle entanglement at finite temperatureshttps://archive-ouverte.unige.ch/unige:4235https://archive-ouverte.unige.ch/unige:4235We present a theory for two-particle entanglement production and detection in mesoscopic conductors at finite temperature. In contrast to the zero temperature limit, the entanglement of the density matrix projected out of the emitted many-body state is different from the entanglement of the reduced density matrix, detectable by current correlation measurements. We show that under very general conditions the reduced entanglement constitutes a lower bound for the projected entanglement. Applying the theory to the recent experiment [Neder et al, Nature 448 333 (2007)] on a fermionic Hanbury Brown Twiss two-particle interferometer we find that despite an appreciable entanglement production in the experiment, the detectable entanglement is close to zero.Mon, 30 Nov 2009 16:07:46 +0100Entanglement at finite temperatures in the electronic two-particle interferometerhttps://archive-ouverte.unige.ch/unige:4234https://archive-ouverte.unige.ch/unige:4234In this work we discuss a theory for entanglement generation, characterization and detection in fermionic two-particle interferometers at finite temperature. The motivation for our work is provided by the recent experiment by the Heiblum group, Neder et al, Nature 448, 333 (2007), realizing the two particle interferometer proposed by Samuelsson, Sukhorukov, and Buttiker, Physical Review Letters 92, 026805 (2004). The experiment displayed a clear two-particle Aharonov-Bohm effect, however with an amplitude suppressed due to finite temperature and dephasing. This raised qualitative as well quantitative questions about entanglement production and detection in mesoscopic conductors at finite temperature. As a response to these questions, in our recent work, Samuelsson, Neder, and Buttiker, Physical Review Letters 102, 106804 (2009) we presented a general theory for finite temperature entanglement in mesoscopic conductors. Applied to the two-particle interferometer we showed that the emitted two-particle state in the experiment was clearly entangled. Moreover, we demonstrated that the entanglement of the reduced two-particle state, reconstructed from measurements of average currents and current cross correlations, constitutes a lower bound to the entanglement of the emitted state. The present work provides an extended and more detailed discussion of these findings.Mon, 30 Nov 2009 16:07:44 +0100Charge fluctuations in the edge states of normal-superconducting hybrid nano-structureshttps://archive-ouverte.unige.ch/unige:4233https://archive-ouverte.unige.ch/unige:4233In this work we show how to calculate the equilibrium and non-equilibrium charge fluctuations in a gated normal mesoscopic conductor which is attached to one normal lead and one superconducting lead. We then consider an example where the structure is placed in a high magnetic field, such that the transport is dominated by edge states. We calculate the equilibrium and non-equilibrium charge fluctuations in the gate, for a single edge state, comparing our results to those for the same system, but with two normal leads. We then consider the specific example of a quantum point contact and calculate the charge fluctuations in the gate for more than one edge state.Mon, 30 Nov 2009 16:07:43 +0100Bunches of photons : antibunches of electronshttps://archive-ouverte.unige.ch/unige:4232https://archive-ouverte.unige.ch/unige:4232When a photon beam from a light source is split in two, with one part transmitted and the other reflected at a half-silvered mirror, it is found that the intensities of these beams are correlated: the photons exhibit "bunching," that is, they tend to come in clusters of identical particles occupying the same state. In contrast, electrons are expected to exhibit "antibunching" and therefore a negative intensity correlation. Büttiker (page 275) discusses two successful measurements of such antibunching of fermions in mesoscopic conductors (Henny et al., page 296, and Oliver et al., page 299) and explains why their approach is important for investigating a range of subjects from superconductivity to noise suppression in quantum computing.Mon, 30 Nov 2009 16:07:42 +0100Charge relaxation resistances and charge fluctuations in mesoscopic conductorshttps://archive-ouverte.unige.ch/unige:4231https://archive-ouverte.unige.ch/unige:4231A brief overview is presented of recent work which investigates the time-dependent relaxation of charge and its spontaneous fluctuations on mesoscopic conductors in the proximity of gates. The leading terms of the low frequency conductance are determined by a capacitive or inductive emittance and a dissipative charge relaxation resistance. The charge relaxation resistance is determined by the ratio of the mean square dwell time of the carriers in the conductor and the square of the mean dwell time. The contribution of each scattering channel is proportional to half a resistance quantum. We discuss the charge relaxation resistance for mesoscopic capacitors, quantum point contacts, chaotic cavities, ballistic wires and for transport along edge channels in the quantized Hall regime. At equilibrium the charge relaxation resistance also determines via the fluctuation-dissipation theorem the spontaneous fluctuations of charge on the conductor. Of particular interest are the charge fluctuations in the presence of transport in a regime where the conductor exhibits shot noise. At low frequencies and voltages charge relaxation is determined by a nonequilibrium charge relaxation resistance.Mon, 30 Nov 2009 16:07:41 +0100Multi-terminal scattering approach to conductance and noise at scanning tunnelling microscope tipshttps://archive-ouverte.unige.ch/unige:4230https://archive-ouverte.unige.ch/unige:4230Experiments that measure the average current and current fluctuations at one or two local tunnelling contacts on a mesoscopic multiprobe conductor are proposed and theoretically investigated. The average current and the current fluctuations at a single tunnelling tip are determined by an effective local distribution function, which is given as the product of local partial densities of states (injectivities) and the Fermi distribution functions in the electron reservoirs. The current correlations at two tips connected to a phase-coherent conductor are determined by spatially non-diagonal density of states elements and can give information about the phase and correlations of wavefunctions. All results are illustrated for measurements on a ballistic wire and on a metallic diffusive wire.Mon, 30 Nov 2009 16:07:40 +0100Local densities, distribution functions, and wave-function correlations for spatially resolved shot noise at nanocontactshttps://archive-ouverte.unige.ch/unige:4229https://archive-ouverte.unige.ch/unige:4229We consider a current-carrying, phase-coherent multi-probe conductor to which a small tunneling contact is attached. We treat the conductor and the tunneling contact as a phase-coherent entity and use a Green's function formulation of the scattering approach. We show that the average current and the current fluctuations at the tunneling contact are determined by an effective local non-equilibrium distribution function. This function characterizes the distribution of charge-carriers (or quasi-particles) inside the conductor. It is an exact quantum-mechanical expression and contains the phase-coherence of the particles via local partial densities of states, called injectivities. The distribution function is analyzed for different systems in the zero-temperature limit as well as at finite temperature. Furthermore, we investigate in detail the correlations of the currents measured at two different contacts of a four-probe sample, where two of the probes are only weakly coupled contacts. In particular, we show that the correlations of the currents are at zero-temperature given by spatially non-diagonal injectivities and emissivities. These non-diagonal densities are sensitive to correlations of wave functions and the phase of the wave functions. We consider ballistic conductors and metallic diffusive conductors. We also analyze the Aharonov-Bohm oscillations in the shot noise correlations of a conductor which in the absence of the nano-contacts exhibits no flux-sensitivity in the conductance.Mon, 30 Nov 2009 16:07:39 +0100Transition from sub-Poissonian to super-Poissonian shot noise in resonant quantum wellshttps://archive-ouverte.unige.ch/unige:4228https://archive-ouverte.unige.ch/unige:4228We investigate the transition from sub-Poissonian to super-Poissonian values of the zero-temperature shot noise power of a resonant double barrier of macroscopic cross-section. This transition occurs for driving voltages which are sufficiently strong to bring the system near an instability threshold. It is shown that interactions in combination with the energy dependence of the tunneling rates dramatically affect the noise level in such a system. Interaction-induced fluctuations of the band bottom of the well contribute to the noise and lead to a new energy in the Fano factor. They can enhance the noise to super-Poissonian values in a voltage range preceding the instability threshold of the system. At low voltages, interactions may either enhance or suppress the noise compared to the the non-interacting case.Mon, 30 Nov 2009 16:07:38 +0100Charge fluctuations in a quantum point contact attached to a superconducting leadhttps://archive-ouverte.unige.ch/unige:4227https://archive-ouverte.unige.ch/unige:4227We show how to calculate the charge noise spectrum in a normal mesoscopic conductor, which is capacitively coupled to a macroscopic gate, when this conductor is attached to L normal leads and M superconducting leads, the only restriction being that the superconducting leads must be at the same chemical potential. We then proceed to examine results for a quantum point contact (QPC) in a normal lead connecting to a superconductor. Of interest is the fluctuating current in a gate capacitively coupled to a QPC. The results are compared with the case when all leads are normal. We find a doubling of the equilibrium charge fluctuations and a large enhancement (>2) in the current noise spectrum to first order in \|eV\|, when a channel in the QPC is opening.Mon, 30 Nov 2009 16:07:37 +0100Friedel phases and phases of transmission amplitudes in quantum scattering systemshttps://archive-ouverte.unige.ch/unige:4226https://archive-ouverte.unige.ch/unige:4226We illustrate the relation between the scattering phase appearing in the Friedel sum rule and the phase of the transmission amplitude for quantum scatterers connected to two one-dimensional leads. Transmission zero points cause abrupt phase changes +/-π of the phase of the transmission amplitude. In contrast, the Friedel phase is a continuous function of energy. We investigate these scattering phases for simple scattering problems and illustrate the behavior of these models by following the path of the transmission amplitude in the complex plane as a function of energy. We verify the Friedel sum rule for these models by direct calculation of the scattering phases and by direct calculation of the density of states.Mon, 30 Nov 2009 16:07:35 +0100Characteristic potentials for mesoscopic rings threaded by an Aharonov-Bohm fluxhttps://archive-ouverte.unige.ch/unige:4225https://archive-ouverte.unige.ch/unige:4225Electro-static potentials for samples with the topology of a ring and penetrated by an Aharonov-Bohm flux are discussed. The sensitivity of the electron-density distribution to small variations in the flux generates an effective electro-static potential which is itself a periodic function of flux. We investigate a simple model in which the flux sensitive potential leads to a persistent current which is enhanced compared to that of a loop of non-interacting electrons. For sample geometries with contacts the sensitivity of the electro-static potential to flux leads to a flux-induced capacitance. This capacitance gives the variation in charge due to an increment in flux. The flux-induced capacitance is contrasted with the electro-chemical capacitance which gives the variation in charge due to an increment in an electro-chemical potential. The discussion is formulated in terms of characteristic functions which give the variation of the electro-static potential in the interior of the conductor due to an increment in the external control parameters (flux, electro-chemical potentials).Mon, 30 Nov 2009 16:07:34 +0100Time-dependent current partition in mesoscopic conductorshttps://archive-ouverte.unige.ch/unige:4224https://archive-ouverte.unige.ch/unige:4224The currents at the terminals of a mesoscopic conductor are evaluated in the presence of slowly oscillating potentials applied to the contacts of the sample. The need to find a charge- and current-conserving solution to this dynamic current partition problem is emphasized. We present results for the electrochemical admittance describing the long-range Coulomb interaction in a Hartree approach. For multiply connected samples we discuss the symmetry of the admittance under the reversal of an Aharonov-Bohm flux.Mon, 30 Nov 2009 16:07:32 +0100Adiabatic charge transport in mesoscopic and nanoscopic conductorshttps://archive-ouverte.unige.ch/unige:4223https://archive-ouverte.unige.ch/unige:4223Transport coefficients are derived which govern the current response of phase coherent conductors in the presence of slowly oscillating external perturbations. We derive the low-frequency admittance if oscillating voltages are applied to the contacts of the sample and discuss the response to an oscillating magnetic flux. Whereas the dc-conductance is determined only by the equilibrium electrostatic potential, the adiabatic transport coefficients discussed here depend on the electrostatic potential that is established in the presence of transport. The symmetry of the transport coefficients under flux reversal is discussed. Novel experiments to find Aharonov-Bohm oscillations in capacitance coeffcients are suggested.Mon, 30 Nov 2009 16:07:32 +0100Aharonov-Bohm oscillations in a mesoscopic ring with a quantum dothttps://archive-ouverte.unige.ch/unige:4222https://archive-ouverte.unige.ch/unige:4222We present an analysis of the Aharonov-Bohm oscillations for a mesoscopic ring with a quantum dot inserted in one of its arms. It is shown that microreversibility demands that the phase of the Aharonov-Bohm oscillations changes {\it abruptly} when a resonant level crosses the Fermi energy. We use the Friedel sum rule to discuss the conservation of the parity of the oscillations at different conductance peaks. Our predictions are illustrated with the help of a simple one channel model that permits the variation of the potential landscape along the ring.Mon, 30 Nov 2009 16:07:30 +0100Suppression of level hybridization due to Coulomb interactionshttps://archive-ouverte.unige.ch/unige:4221https://archive-ouverte.unige.ch/unige:4221We investigate an ensemble of systems formed by a ring enclosing a magnetic flux. The ring is coupled to a side stub via a tunnelling junction and via Coulomb interaction. We generalize the notion of level hybridization due to the hopping, which is naturally defined only for one-particle problems, to the many-particle case, and we discuss the competition between the level hybridization and the Coulomb interaction. It is shown that strong enough Coulomb interactions can isolate the ring from the stub, thereby increasing the persistent current. Our model describes a strictly canonical system (the number of carriers is the same for all ensemble members). Nevertheless for small Coulomb interactions and a long side stub the model exhibits a persistent current typically associated with a grand canonical ensemble of rings and only if the Coulomb interactions are sufficiently strong does the model exhibit a persistent current which one expects from a canonical ensemble.Mon, 30 Nov 2009 16:07:29 +0100Diffusion controlled initial recombinationhttps://archive-ouverte.unige.ch/unige:4220https://archive-ouverte.unige.ch/unige:4220This work addresses nucleation rates in systems with strong initial recombination. Initial (or `geminate') recombination is a process where a dissociated structure (anion, vortex, kink etc.) recombines with its twin brother (cation, anti-vortex, anti-kink) generated in the same nucleation event. Initial recombination is important if there is an asymptotically vanishing interaction force instead of a generic saddle-type activation barrier. At low temperatures, initial recombination strongly dominates homogeneous recombination. In a first part, we discuss the effect in one-, two-, and three-dimensional diffusion controlled systems with spherical symmetry. Since there is no well-defined saddle, we introduce a threshold which is to some extent arbitrary but which is restricted by physically reasonable conditions. We show that the dependence of the nucleation rate on the specific choice of this threshold is strongest for one-dimensional systems and decreases in higher dimensions. We discuss also the influence of a weak driving force and show that the transport current is directly determined by the imbalance of the activation rate in the direction of the field and the rate against this direction. In a second part, we apply the results to the overdamped sine-Gordon system at equilibrium. It turns out that diffusive initial recombination is the essential mechanism which governs the equilibrium kink nucleation rate. We emphasize analogies between the single particle problem with initial recombination and the multi-dimensional kink-antikink nucleation problem.Mon, 30 Nov 2009 16:07:27 +0100Interaction constants and dynamic conductance of a gated wirehttps://archive-ouverte.unige.ch/unige:4219https://archive-ouverte.unige.ch/unige:4219We show that the interaction constant governing the long-range electron-electron interaction in a quantum wire coupled to two reservoirs and capacitively coupled to a gate can be determined by a low-frequency measurement. We present a self-consistent, charge and current conserving, theory of the full conductance matrix. The collective excitation spectrum consists of plasma modes with a relaxation rate which increases with the interaction strength and is inversely proportional to the length of the wire.Mon, 30 Nov 2009 16:07:26 +0100Die Admittanz mesoskopischer Leiterhttps://archive-ouverte.unige.ch/unige:4217https://archive-ouverte.unige.ch/unige:4217Elektrische Strukturen im Submikrometerbereich haben bei tiefen Temperaturen Eigenschaften, die sich stark von denen makroskopischer Leiter unterscheiden. Auch elektrotechnische Größen wie Widerstand, Kapazität und Induktivität von elektronischen Nanometer-Bauelementen werden durch Quanteneigenschaften verändert.Mon, 30 Nov 2009 16:07:25 +0100Effect of interactions on the admittance of ballistic wireshttps://archive-ouverte.unige.ch/unige:4218https://archive-ouverte.unige.ch/unige:4218A self-consistent theory of the admittance of a perfect ballistic, locally charge neutral wire is proposed. Compared to a non-interacting theory, screening effects drastically change the frequency behavior of the conductance. In the single-channel case the frequency dependence of the admittance is monotonic, while for two or more channels collective interchannel excitations lead to resonant structures in the admittance. The imaginary part of the admittance is typically positive, but can become negative near resonances.Mon, 30 Nov 2009 16:07:25 +0100Rectification of fluctuations in an underdamped ratchethttps://archive-ouverte.unige.ch/unige:4216https://archive-ouverte.unige.ch/unige:4216We investigate analytically the motion of underdamped particles subject to a deterministic periodic potential and a periodic temperature. Despite the fact that an underamped particle experiences the temperature oscillation many times in its escape out of a well and in its motion along the potential, a net directed current linear in the friction constant is found. If both the potential and the temperature modulation are sinusoidal with a phase lagMon, 30 Nov 2009 16:07:24 +0100Reply to the comment on "Breathers and kink-antikink nucleation"https://archive-ouverte.unige.ch/unige:4214https://archive-ouverte.unige.ch/unige:4214A Reply to the Comment by P. Hänggi and F. Marchesoni.Mon, 30 Nov 2009 16:07:22 +0100Shot-noise current-current correlations in multiterminal diffusive conductorshttps://archive-ouverte.unige.ch/unige:4215https://archive-ouverte.unige.ch/unige:4215We investigate the correlations in the current fluctuations at different terminals of metallic diffusive conductors. We start from scattering matrix expressions for the shot noise and use the Fisher-Lee relation in combination with diagram technique to evaluate the noise correlations. Of particular interest are exchange (interference) effects analogous to the Hanbury Brown--Twiss effect in optics. We find that the exchange effect exists in the ensemble averaged current correlations. Depending on the geometry, it might have the same magnitude as the mean square current fluctuations of the shot noise. The approach which we use is first applied to present a novel derivation of the 1/3-suppression of shot noise in a two-terminal geometry, valid for an arbitrary relation between the length and wire width. We find that in all geometries correlations are insensitive to dephasing.Mon, 30 Nov 2009 16:07:22 +0100Dynamic conductance and quantum noise in mesoscopic conductorshttps://archive-ouverte.unige.ch/unige:4213https://archive-ouverte.unige.ch/unige:4213We present results for the dc conductance, the ac conductance, and the current–current fluctuation spectra of mesoscopic, phase-coherent conductors based on a second quantization approach to scattering and a self-consistent potential approach. A second quantization approach permits an investigation of statistical effects due to the symmetry of the wave functions under exchange of particles. A self-consistent approach is needed to enforce overall charge conservation and to obtain current conserving expressions for frequency-dependent conductances and fluctuation spectra. For the particular example of a mesoscopic capacitor we present microscopic expressions for the electrochemical capacitance and the charge relaxation resistance.Mon, 30 Nov 2009 16:07:21 +0100Mesoscopic capacitors : a statistical analysishttps://archive-ouverte.unige.ch/unige:4212https://archive-ouverte.unige.ch/unige:4212The capacitance of mesoscopic samples depends on their geometry and physical properties, described in terms of characteristic times scales. The resulting ac admittance shows sample to sample fluctuations. Their distribution is studied here -through a random-matrix model- for a chaotic cavity capacitively coupled to a backgate: it is observed from the distribution of scattering time delays for the cavity, which is found analytically for the orthogonal, unitary, and symplectic universality classes, one mode in the lead connecting the cavity to the reservoir and no direct scattering. The results agree with numerical simulations.Mon, 30 Nov 2009 16:07:20 +0100Low frequency admittance of a quantum point contacthttps://archive-ouverte.unige.ch/unige:4211https://archive-ouverte.unige.ch/unige:4211We present a current and charge conserving theory for the low frequency admittance of a quantum point contact. We derive expressions for the electrochemical capacitance and the displacement current. The latter is determined by the emittance which equals the capacitance only in the limit of vanishing transmission. With the opening of channels the capacitance and the emittance decrease in a steplike manner in synchronism with the conductance steps. For vanishing reflection, the capacitance vanishes and the emittance is negative.Mon, 30 Nov 2009 16:07:19 +0100Charge transfer induced persistent current and capacitance oscillationshttps://archive-ouverte.unige.ch/unige:4210https://archive-ouverte.unige.ch/unige:4210The transfer of charge between different regions of a phase-coherent mesoscopic sample is investigated. Charge transfer from a side branch quantum dot into a ring changes the persistent current through a sequence of plateaus of diamagnetic and paramagnetic states. In contrast, a quantum dot embedded in a ring exhibits sharp resonances in the persistent current, whose sign is independent of the number of electrons in the dot if the total number of electrons in the system is even. It is shown that such a mesoscopic system can be polarized appreciably not only by the application of an external voltage, but also via an Aharonov-Bohm flux.Mon, 30 Nov 2009 16:07:17 +0100Nucleation of weakly driven kinkshttps://archive-ouverte.unige.ch/unige:4209https://archive-ouverte.unige.ch/unige:4209We study nucleation of kink-antikink pairs under weak nonequilibrium conditions and in the strong friction limit. We introduce an effective critical nucleus of size s0, which is small compared to the inverse kink density but large compared to a kink size. We evaluate independently the nucleation rate and the kink lifetime from a multidimensional Kramers theory and by studying kink-antikink annihilation processes. We find a kink density which is independent of s0 and of the driving force in this regime. The result is in accordance with the equilibrium kink density obtained from statistical mechanics.Mon, 30 Nov 2009 16:07:17 +0100Voltage and dephasing probes in mesoscopic conductors : a study of full-counting statisticshttps://archive-ouverte.unige.ch/unige:4208https://archive-ouverte.unige.ch/unige:4208Voltage and dephasing probes introduce incoherent inelastic and incoherent quasielastic scattering into a coherent mesoscopic conductor. We discuss in detail the concepts of voltage and dephasing probes and develop a full-counting statistics approach to investigate their effect on the transport statistics. The formalism is applied to several experimentally relevant examples. A comparison of different probe models and with procedures like phase averaging over an appropriate phase distribution shows that there is a perfect equivalence between the models for the case of one single-channel probe. Interestingly, the appropriate phase-distribution function is found to be uniform. A uniform distribution is provided by a chaotic cavity with a long dwell time. The dwell time of a chaotic cavity plays a role similar to the charge response time of a voltage or dephasing probe. For multichannel or multiple probes the transport statistics of voltage and dephasing probes differs and the equivalence with phase averaging is similarly lost.Mon, 30 Nov 2009 16:07:14 +0100Two-particle scattering matrix of two interacting mesoscopic conductorshttps://archive-ouverte.unige.ch/unige:4207https://archive-ouverte.unige.ch/unige:4207We consider two quantum coherent conductors interacting weakly via long range Coulomb forces. We describe the interaction in terms of two-particle collisions described by a two-particle scattering matrix. As an example we determine the transmission probability and correlations in a two-particle scattering experiment and find that the results can be expressed in terms of the density-of-states matrices of the non-interacting scatterers.Mon, 30 Nov 2009 16:07:13 +0100Time-resolved noise of adiabatic quantum pumpshttps://archive-ouverte.unige.ch/unige:4206https://archive-ouverte.unige.ch/unige:4206We investigate quantum-statistical correlation properties of a periodically driven mesoscopic scatterer on a time scale shorter than the period of a drive. In this limit the intrinsic quantum fluctuations in the system of fermions are the main source of a noise. Nevertheless the effect of a slow periodic drive is clearly visible in a two-time current-current correlation function as a specific periodic in time modulation. In the limit of a strong drive such a modulation can change the sign of a current correlation function.Mon, 30 Nov 2009 16:07:12 +0100Relaxation time of a chiral quantum R-L circuithttps://archive-ouverte.unige.ch/unige:4205https://archive-ouverte.unige.ch/unige:4205We report on the GHz complex admittance of a chiral one dimensional ballistic conductor formed by edge states in the quantum Hall regime. The circuit consists of a wide Hall bar (the inductor L) in series with a tunable resistor (R) formed by a quantum point contact. Electron interactions between edges are screened by a pair of side gates. Conductance steps are observed on both real and imaginary parts of the admittance. Remarkably, the phase of the admittance is transmission-independent. This shows that the relaxation time of a chiral R-L circuit is resistance independent. A current and charge conserving scattering theory is presented that accounts for this observation with a relaxation time given by the electronic transit time in the circuit.Mon, 30 Nov 2009 16:07:10 +0100Mesoscopic capacitance oscillationshttps://archive-ouverte.unige.ch/unige:4204https://archive-ouverte.unige.ch/unige:4204We examine oscillations as a function of Fermi energy in the capacitance of a mesoscopic cavity connected via a single quantum channel to a metallic contact and capacitively coupled to a back gate. The oscillations depend on the distribution of single levels in the cavity, the interaction strength and the transmission probability through the quantum channel. We use a Hartree-Fock approach to exclude self-interaction. The sample specific capacitance oscillations are in marked contrast to the charge relaxation resistance, which together with the capacitance defines the RC-time, and which for spin polarized electrons is quantized at half a resistance quantum. Both the capacitance oscillations and the quantized charge relaxation resistance are seen in a strikingly clear manner in a recent experiment.Mon, 30 Nov 2009 16:07:09 +0100Magnetic-field symmetries of mesoscopic non-linear conductancehttps://archive-ouverte.unige.ch/unige:4203https://archive-ouverte.unige.ch/unige:4203We examine contributions to the dc-current of mesoscopic samples which are non-linear in applied voltage. In the presence of a magnetic field, the current can be decomposed into components which are odd (antisymmetric) and even (symmetric) under flux reversal. For a two-terminal chaotic cavity, these components turn out to be very sensitive to the strength of the Coulomb interaction and the asymmetry of the contact conductances. For both two- and multi-terminal quantum dots we discuss correlations of current non-linearity in voltage measured at different magnetic fields and temperatures.Mon, 30 Nov 2009 16:07:08 +0100