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Recently, an exotic quantum Hall ferromagnet with spin-filtered helical edgemodes was observed in monolayer graphene on a high-dielectric constantsubstrate at moderate magnetic fields, withstanding temperatures of up to 110Kelvin [L. Veyrat et al., Science 367, 781 (2020)]. However, the characteristicquantized longitudinal resistance mediated by these edge modes departs fromquantization with decreasing temperature. In this work, we investigate thetransport properties of helical edge modes in a graphene nanoribbon under aperpendicular magnetic field using the Landauer-Buttiker transport formalism.We find that the departure of quantization of longitudinal conductance is dueto the helical-edge gap opened by the Rashba spin-orbital coupling. Thequantization can be restored by weak nonmagnetic Anderson disorder at lowtemperature, increasing the localization length, or by raising temperature atweak disorder, through thermal broadening. The resulted conductance is veryclose to the quantized value 2e2/h, which is in qualitatively consistent withthe experimental results. Furthermore, we suggest that the helical quantum Hallphase in graphene could be a promising platform for creating Majorana zeromodes by introducing superconductivity.

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