Edge states, mass and spin gaps, and quantum Hall effect in graphene

TL;DR

This paper investigates how Dirac masses and spin gaps influence edge states and quantum Hall effects in graphene under strong magnetic fields, linking experimental observations with theoretical models.

Contribution

It introduces a theoretical framework connecting Dirac mass and spin gap generation to edge state behavior in graphene with different boundary conditions.

Findings

Gapless edge states occur only when the spin gap dominates for zigzag edges.

The existence of edge states depends on the type of mass gaps for armchair edges.

The scenario explains the removal of degeneracies observed experimentally.

Abstract

Motivated by recent experiments and a theoretical analysis of the gap equation for the propagator of Dirac quasiparticles, we assume that the physics underlying the recently observed removal of sublattice and spin degeneracies in graphene in a strong magnetic field is connected with the generation of both Dirac masses and spin gaps. The consequences of such a scenario for the existence of the gapless edge states with zigzag and armchair boundary conditions are discussed. In the case of graphene on a half-plane with a zigzag edge, there are gapless edge states in the spectrum only when the spin gap dominates over the mass gap. In the case of an armchair edge, however, the existence of the gapless edge states depends on the specific type of mass gaps.