Memory function approach to the Hall constant in strongly correlated electron systems

TL;DR

This paper uses the memory function formalism within the Hubbard model to analyze the Hall constant in high-temperature superconductors, revealing how strong correlations influence its doping and temperature dependence.

Contribution

It introduces a memory function approach to study the Hall constant, emphasizing the importance of resistivity-focused Mori theory in strongly correlated systems.

Findings

Memory function causes sign change of Hall constant with doping

Hall constant decreases with increasing temperature

Strong correlations significantly affect Hall behavior

Abstract

The anomalous properties of the Hall constant in the normal state of high-$T_c$ superconductors are investigated within the single-band Hubbard model. We argue that the Mori theory is the appropriate formalism to address the Hall constant, since it aims directly at resistivities rather than conductivities. More specifically, the frequency dependent Hall constant decomposes into its infinite frequency limit and a memory function contribution. As a first step, both terms are calculated perturbatively in $U$ and on an infinite dimensional lattice, where $U$ is the correlation strength. If we allow $U$ to be of the order of twice the bare band width, the memory function contribution causes the Hall constant to change sign as a function of doping and to decrease as a function of temperature.