Study of the Hall effect in two different strongly correlated fermion systems

TL;DR

This paper explores the Hall effect in two strongly correlated fermion systems, revealing temperature-dependent behaviors and corrections to classical models, with implications for experimental observations in organic compounds and cobaltates.

Contribution

It provides a detailed theoretical analysis of the Hall effect in weakly coupled Luttinger liquids and 2D triangular lattices, including temperature, frequency, and doping dependencies, using novel analytical and numerical methods.

Findings

Power-law correction to Hall coefficient in Luttinger liquids

High-temperature Hall coefficient approaches band value

Striking T-linear behavior of Hall coefficient at high T

Abstract

We investigate the Hall effect in two different theoretical models of strongly correlated systems: a system made of weakly coupled Luttinger liquids, in the presence of umklapp scattering, and the 2D triangular lattice, with nearest-neighbor hopping and a local Hubbard interaction. In the first model we use a memory function approach to compute the Hall coefficient as a function of temperature and frequency in the presence of umklapp scattering. We find a power-law correction to the free-fermion value (band value), with an exponent depending on the Luttinger parameter $K_{\rho}$. At sufficiently high temperature or frequency the Hall coefficient approaches the band value. We discuss the applications to Hall experiments made in quasi 1D organic compounds. In the second model, the complete temperature and doping dependencies of the high-frequency Hall coefficient $\RH$ are evaluated analytically and numerically for small, intermediate, and strong interactions using various approximation schemes. We find that $\RH$ follows the semiclassical $1/qn^*$ law near T=0, but exhibits a striking $T$-linear behavior with an interaction- and doping-dependent slope at high temperature. We compare our results with Hall measurements performed in cobaltates.