Hall Coefficient in an Interacting Electron Gas

TL;DR

This paper calculates the Hall conductivity in a weak magnetic field for an interacting electron gas, showing that the Hall coefficient remains unrenormalized by electron-electron interactions to leading order, explaining experimental stability.

Contribution

It provides a new formulation of the Hall effect calculation that avoids artificial field modulation and emphasizes magnetic flux during scattering.

Findings

Hall coefficient not renormalized by electron interactions to leading order

Explains experimental stability of Hall coefficient in dilute gases

Reformulates the problem focusing on magnetic flux in scattering

Abstract

The Hall conductivity in a weak homogeneous magnetic field, $\omega_{c}\tau \ll 1$, is calculated. We have shown that to leading order in $1/\epsilon_{F}\tau$ the Hall coefficient $R_{H}$ is not renormalized by the electron-electron interaction. Our result explains the experimentally observed stability of the Hall coefficient in a dilute electron gas not too close to the metal-insulator transition. We avoid the currently used procedure that introduces an artificial spatial modulation of the magnetic field. The problem of the Hall effect is reformulated in a way such that the magnetic flux associated with the scattering process becomes the central element of the calculation.