Interplay between snake and quantum edge states in a graphene Hall bar with a pn-junction

Abstract

The magneto- and Hall resistance of a locally gated cross shaped graphene Hall bar is calculated. The edge of the top gate is placed diagonally across the center of the Hall cross. Four-probe resistance is calculated using the Landauer-B\"uttiker formalism, while the transmission coefficients are obtained using the non-equilibrium Green's function approach. The interplay between transport due to edge channels and snake states is investigated. When two edge channels are occupied we predict oscillations in the Hall and the bend resistance as function of the magnetic field which are a consequence of quantum interference between the occupied snake states.