The conductance of graphene subject to a strong, tilted magnetic field exhibits a dramatic change from insulating to conducting behavior with tilt angle, regarded as evidence for the transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) ν = 0 quantum Hall state. We develop a theory for the electric transport in this system based on the spin-charge connection, whereby the evolution in the nature of collective spin excitations is reflected in the charge-carrying modes. To this end, we derive an effective field-theoretical description of the low-energy excitations, associated with quantum fluctuations of the spin-valley domain-wall ground-state configuration which characterizes the two-dimensional (2D) system with an edge. This analysis yields a model describing a one-dimensional charged edge mode coupled to charge-neutral spin-wave excitations in the 2D bulk. Focusing particularly on the FM phase, naively expected to exhibit perfect conductance, we study a mechanism whereby the coupling to these bulk excitations assists in generating backscattering. Our theory yields the conductance as a function of temperature and the Zeeman energy—the parameter that tunes the transition between the FM and CAF phases—with behavior in qualitative agreement with experiment.
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The authors thank the Aspen Center for Physics (NSF Grant No. 1066293) for its hospitality. This work was supported by the US-Israel Binational Science Foundation (BSF) Grant No. 2012120 (E.S., G.M., H.A.F.), the Israel Science Foundation (ISF) Grant No. 231/14 (E.S.), and NSF Grants No. DMR 1306897 (G.M.), No. DMR-1506263 (H.A.F.), and No. DMR-1506460 (H.A.F.).
Tikhonov, Pavel; Shimshoni, Efrat; Fertig, H. A.; and Murthy, Ganpathy, "Emergence of Helical Edge Conduction in Graphene at the ν = 0 Quantum Hall State" (2016). Physics and Astronomy Faculty Publications. 442.