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Thermoelectric transport properties of a chain of quantum dots with self-consistent reservoirs

Contributors

Jacquet, Philippe

Published in

Journal of statistical physics, vol. 134, p. 709-748

Publication date

2009

Abstract

We introduce a model for charge and heat transport based on the Landauer-Büttiker scattering approach. The system consists of a chain of N quantum dots, each of them being coupled to a particle reservoir. Additionally, the left and right ends of the chain are coupled to two particle reservoirs. All these reservoirs are independent and can be described by any of the standard physical distributions: Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein. In the linear response regime, and under some assumptions, we first describe the general transport properties of the system. Then we impose the self-consistency condition, i.e. we fix the boundary values (T L,μ L) and (T R,μ R), and adjust the parameters (T i,μ i ), for i=1,…,N, so that the net average electric and heat currents into all the intermediate reservoirs vanish. This condition leads to expressions for the temperature and chemical potential profiles along the system, which turn out to be independent of the distribution describing the reservoirs. We also determine the average electric and heat currents flowing through the system and present some numerical results, using random matrix theory, showing that these currents are typically governed by Ohm and Fourier laws.

Keywords

  • Quantum transport
  • Quantum dots
  • Landauer-Büttiker scattering approach
  • Onsager relations
  • Entropy production
  • Random matrix theory
  • Ohm and Fourier laws

UNIGE affiliation entities

Citation (ISO format)

JACQUET, Philippe. Thermoelectric transport properties of a chain of quantum dots with self-consistent reservoirs. In: Journal of statistical physics, 2009, vol. 134, p. 709–748. doi: 10.1007/s10955-009-9697-1

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Article (Published version)

Identifiers

Journal ISSN

0022-4715
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Technical informations

Creation

20/04/2010 15:03:00

First validation

20/04/2010 15:03:00

Update

14/03/2023 15:28:10

Status update

14/03/2023 15:28:10

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