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 ν=0. 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.
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We would like to thank the Aspen Center for Physics (NSF Grant No. 1066293) for its hospitality. This work was partly supported by the US-Israel Binational Science Foundation via Grant No. 2012120 (E.S., G.M., H.A.F). E.S. acknowledges support by the Israel Science Foundation via Grant No. 231/14 and also travel support by the Simons Foundation. G.M. acknowledges support by the National Science Foundation via Grants No. NSF-PHY 0970069 and No. NSF-DMR 1306897. H.A.F. acknowledges support by the National Science Foundation via Grant No. NSF-DMR 1005035.
Murthy, Gunpathy; Shimshoni, Efrat; and Fertig, H. A., "Collective Edge Modes Near the Onset of a Graphene Quantum Spin Hall State" (2014). Physics and Astronomy Faculty Publications. 286.