Magnetic oscillations of the anomalous Hall conductivity

TL;DR

This paper demonstrates that in a model of 2D massive Dirac fermions, the oscillations of the anomalous Hall conductivity have the same amplitude as the diagonal conductivity, suggesting new ways to observe these effects.

Contribution

It shows that the amplitude of Shubnikov--de Haas oscillations in anomalous Hall conductivity matches that of diagonal conductivity in a Dirac fermion model, a novel insight.

Findings

Oscillations of anomalous Hall conductivity can be as strong as diagonal conductivity oscillations.

Potential observation of these oscillations via valley and spin Hall effects in specific materials.

Provides a theoretical basis for experimental detection of anomalous Hall oscillations.

Abstract

It is known that the Shubnikov--de Haas oscillations can be observed in the Hall resistivity, although their amplitude is much weaker than the amplitude of the diagonal resistivity oscillations. Employing a model of two-dimensional massive Dirac fermions that exhibits anomalous Hall effect, we demonstrate that the amplitude of the Shubnikov--de Haas oscillations of the anomalous Hall conductivity is the same as that of the diagonal conductivity. We argue that the oscillations of the anomalous Hall conductivity can be observed by studying the valley Hall effect in graphene superlattices and the spin Hall effect in the low-buckled Dirac materials.