Quantum Hall effect in gapped graphene heterojunctions

We model the quantum Hall effect in heterostructures made of two gapped graphene stripes with different gaps, $Δ_1$ and $Δ_2$. We consider two main situations, $Δ_1=0,Δ_2\neq0$ and $Δ_1=-Δ_2$. They are different in a fundamental aspect: only the latter feature kink states that, when intervalley coupling is absent, are protected against backscattering. We compute the two terminal conductance of heterostructures with channel length up to 430 nm, in two transport configurations, parallel and perpendicular to the interface. By studying the effect of disorder on the transport along the boundary, we quantify the robustness of kink states with respect to backscattering. Transport perpendicular to the boundary shows how interface states open a backscattering channel for the conducting edge states, spoiling the perfect conductance quantization featured by the homogeneously gapped graphene Hall bars. Our results can be relevant for the study of graphene deposited on hexagonal Boron-Nitride as well as to model graphene with an interaction-driven gapped phase with two equivalent phases separated by a domain wall.

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