Disorder and quantum transport of the helical quantum Hall phase in graphene

Recently, an exotic quantum Hall ferromagnet with spin-filtered helical edge modes was observed in monolayer graphene on a high-dielectric constant substrate at moderate magnetic fields, withstanding temperatures of up to 110 Kelvin [L. Veyrat et al., Science 367, 781 (2020)]. However, the characteristic quantized longitudinal resistance mediated by these edge modes departs from quantization with decreasing temperature. In this work, we investigate the transport properties of helical edge modes in a graphene nanoribbon under a perpendicular magnetic field using the Landauer-B\"uttiker transport formalism. We find that the departure of quantization of longitudinal conductance is due to the helical-edge gap opened by the Rashba spin-orbital coupling. The quantization can be restored by weak nonmagnetic Anderson disorder at low temperature, increasing the localization length, or by raising temperature at weak disorder, through thermal broadening. The resulted conductance is very close to the quantized value $2{e}^{2}/h$, which is qualitatively consistent with the experimental results. Furthermore, we suggest that the helical quantum Hall phase in graphene could be a promising platform for creating Majorana zero modes by introducing superconductivity.