Emergence of helical edge conduction in graphene at the ν=0 quantum Hall state

Abstract

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 back-scattering. 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.

16 pages, 1 figure

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• Spin-Valley Coherent Phases of the $\nu =0$ Quantum Hall State in Bilayer Graphene
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• Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride
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• Symmetry characterization of the collective modes of the phase diagram of the $\nu =0$ quantum Hall state in graphene: Mean-field and spontaneously broken symmetries
• Interacting quantum Hall states in a finite graphene flake and at finite temperature
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