  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-Buttiker 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 2e2/h, which is in 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.
