Complex systems exhibit emergent properties characterized by fascinating phenomena. These are a direct consequence of the interplay among different constituents and cannot simply be reduced to independent contributions.
In the study of materials, the number of particles that have to be considered is on the order of 1023 (Avogadro number). Thus, materials generally belong to the category of complex systems. Understanding and explaining the properties of materials with simple models is one of the key challenges addressed by condensed matter physicists.
Surprisingly, certain materials can be described in terms of independent particles, whose behaviors can be simply modeled. There are, however, materials where such approximations do not hold and particles cannot be considered as independent. The interactions – correlations– among all these particles are at the heart of many striking phenomena. We can define these class of materials as correlated materials.
Particularly interesting is the manifestation of phase transitions. A phase transition occurs when the system switches to a new ground state, which is more energetically favorable. Some examples in condensed matter are the transition from insulating to metallic behavior, the appearance of superconducting or magnetically ordered states.
The microscopic origin of phase transition often relies into the net balance between different attractive and repulsive terms, which fundamentally derive from Coulomb interaction and quantum mechanics principles.
In the following, I will focus on experimental studies of correlated crystals. Crystalline materials have a special characteristic: translational symmetry with unit cell periodicity. This allows to describe the system focusing on the repeated unit cell instead of modelling the full macroscopic material. As a consequence, all the main observable quantities can be written in terms of momentum (spatial frequency), which is the axis of the reciprocal space (the Fourier transform of the real space).
Experimentally, different techniques are able to probe various materials responses in different regimes. The investigations of momentum-resolved properties can be performed only with a limited number of approaches. On the other hand, to thoroughly understand materials’ behaviors, it is essential to combine information provided by a variety of experimental probes.
In this thesis, I show how momentum-resolved measurements can provide valuable insights that help to understand microscopic correlations. More specifically, I investigate how the high energy response changes when a superconducting material crosses the phase transition. Moreover, I develop a novel experimental approach which can explore momentum-resolved properties in out-of-equilibrium systems.
