Absence of Perfect Conductance Quantization of Helical-edge Transport in Graphene under a Strong, Tilted Magnetic Field

In a recent experiment, Young et al. [Nature {\bf 505}, 528 (2014)] observed a metal to insulator transition as well as transport through helical edge states in monolayer graphene under a strong, tilted magnetic field. Under such conditions, the bulk is a magnetic insulator which can exhibit metallic conduction through helical edges. It was found that two-terminal conductance of the helical channels deviates from the expected quantized value at low-temperatures ($=e^2/h$ per edge, at zero temperature). Motivated by this observation, we study the effect of disorder on the conduction through the edge channels. We show that, unlike the situation in semiconducting quantum wells, a disorder Rashba spin-orbit coupling does not lead to backscattering, at least to leading order. Instead we find the lack of perfect anti-alignment of the electron spins in the helical channels to be the most likely source for backscattering arising from scalar (i.e. spin-independent) impurities. The intrinsic spin-orbit coupling and other time-reversal symmetry breaking and/or sublattice-parity breaking potentials also lead to (sub-leading) corrections to the channel conductance.