Hall Coefficient in an Interacting Electron Gas

Abstract

The Hall conductivity in a weak homogeneous magnetic field, $ω_{c}τ\ll 1$, is calculated. We have shown that to leading order in $1/ε_{F}τ$ 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.