Chiral orbital current and anomalous magnetic moment in gapped graphene

TL;DR

This paper develops a low-energy theory for chiral orbital currents and magnetic moments in gapped graphene, revealing valley-dependent effects and implications for magnetic susceptibility and topological insulators.

Contribution

It introduces a novel effective-mass framework capturing inter-band effects and valley-dependent magnetic phenomena in gapped graphene and related materials.

Findings

Chiral current circulation is linked to magnetic moments and varies between valleys.

Valley-dependent magnetic moments cause Landau level splitting and susceptibility divergence.

The theory applies to topological insulator surface states, connecting to magneto-electric responses.

Abstract

We present a low-energy effective-mass theory to describe chiral orbital current and anomalous magnetic moment in graphenes with band gap and related materials. We show that a Bloch electron generally contains an anomalous current density due to inter-band matrix elements, which describes a chiral current circulation associated with magnetic moment. In gapped graphenes, the chiral current is opposite between different valleys, and corresponding magnetic moment accounts for valley splitting of Landau levels. In gapped bilayer graphene, in particular, the valley-dependent magnetic moment is responsible for divergence of paramagnetic susceptibility at the band bottom, and full valley polarization is achieved in relatively small magnetic field range. The formulation also applies to the gapped surface states of three-dimensional topological insulator, where the anomalous current is related to the magneto-electric response in spatially-modulated potential.