Collective Edge Modes near the onset of a graphene quantum spin Hall state

TL;DR

This paper models the evolution of edge modes in graphene under a tilted magnetic field, revealing a transition from gapped to gapless charged edge modes as the system shifts from a canted antiferromagnetic to a ferromagnetic state.

Contribution

It provides a theoretical framework describing how spin and valley edge textures evolve during the CAF to FM transition in graphene.

Findings

CAF has gapless neutral bulk modes but gapped charged edge modes.

At the transition, charged edge modes become gapless.

Gapless charged edge modes connect smoothly to FM helical edge modes.

Abstract

Graphene subject to a strong, tilted magnetic field exhibits an insulator-metal transition tunable by tilt-angle, attributed to the transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) bulk state at filling factor zero. We develop a theoretical description for the spin and valley edge textures in the two phases, and the implied evolution in the nature of edge modes through the transition. In particular, we show that the CAF has gapless neutral modes in the bulk, but supports gapped charged edge modes. At the transition to the FM state the charged edge modes become gapless and are smoothly connected to the helical edge modes of the FM state. Possible experimental consequences are discussed.