Intrinsic Hall conductivities induced by the orbital magnetic moment

TL;DR

This paper predicts a purely quantum, intrinsic contribution to Hall conductivities arising from the geometric properties of electronic wave-functions, independent of scattering, and dominant near band edges and crossings.

Contribution

It introduces a new scattering time-independent component of Hall conductivity linked to the orbital magnetic moment and wave-function geometry.

Findings

Intrinsic Hall conductivity is scattering time-independent.

The effect influences thermo-electric and thermal conductivities.

It causes negative magneto-resistance and underestimates charge carrier density.

Abstract

The intrinsic anomalous Hall effect is one of the most exciting manifestations of the geometric properties of the electronic wave-function. Here, we predict that the electronic wave-function's geometric nature also gives rise to a purely quantum mechanical, {\it intrinsic} (scattering time-independent) component of the Hall conductivities in the presence of a magnetic field. We show that the orbital magnetic moment and the anomalous Hall velocity combine to generate a scattering time-independent contribution to the Hall effect, in addition to the Lorentz force induced scattering time-dependent `classical' Hall effect. This dissipation-less Hall effect also manifests in the thermo-electric and thermal conductivities and is dominant near the band edges and band-crossings. It gives rise to negative magneto-resistance and it also leads to an underestimation in the charge carrier density measured in Hall experiments.