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

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.