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

TL;DR

This paper develops a memory function approach within strongly correlated electron models to explain the frequency and doping dependence of the Hall constant in high-T_c superconductors, linking it to spinon relaxation and high-energy scales.

Contribution

It introduces a memory function framework to analyze the Hall constant's behavior, connecting frequency dependence to spinon relaxation and high-energy scale projection in the Hubbard model.

Findings

Hall constant decreases by (1+δ)/2 when frequency drops into the Mott-Hubbard gap.

Memory function describes transition from infinite to zero frequency for the Hall constant.

The approach links the Hall effect to spinon relaxation time in the t-J model.

Abstract

The anomalous frequency and doping dependence of the Hall constant in the normal state of high-T_c superconductors are investigated within models of strongly correlated electron systems. In Mori theory, the transition of the Hall constant from infinite to zero frequency is described by a memory function. It naturally introduces a second time scale, that, within the t-J model, is identified with the spinon relaxation time of Anderson. This provides us with a phenomenological understanding of the interplay between the frequency and temperature dependence of the Hall constant for frequencies below the Mott-Hubbard gap. Within the single-band Hubbard model in the limit $U\gg t$, the memory function is calculated via its moments and shown to project out the high-energy scale U. This causes the Hall constant to decrease by a factor $(1+\delta)/2$ ($\delta$: doping), when the frequency is lowered from infinity to values within the Mott-Hubbard gap. Finally, it is outlined, how the Hall constant may be calculated in the low frequency regime.