We just published on the arXiv our latest manuscript, in collaboration with the group of Thierry Giamarchi. We develop the Kubo formalism equations of the Hall response in a 2d conductor, which allows us to go to study correlated electron liquids at low densities. Surprisingly, we found an enormous enhancement of the Hall response.
Title: Hall response of locally-correlated two-dimensional electrons at low density
Authors: Giacomo Morpurgo, Louk Rademaker, Christophe Berthod, Thierry Giamarchi
Abstract: We study the Hall constant in a homogeneous two-dimensional fluid of correlated electrons immersed in a perpendicular magnetic field, with special focus on the regime of low carrier density. The model consists of a one-band tight-binding model and a momentum-independent causal self-energy, representing interaction-induced correlations effects that are restricted to be local in space. We write general gauge-invariant equations for the conductivity tensor at first order in the magnetic field and solve them numerically (analytically when possible) in a minimal model of anisotropic square lattice with constant self-energy. Our results show that deviations from the universal behavior of the Hall constant, as observed in the semiclassical regime, appear upon entering the quantum regime, where the Fermi energy and interaction are comparable energy scales.
Reference: arXiv:2310.10466 (2023)