Role of disorder in superconducting Chern insulator

Motivated by a recent experiment in which a half-integer quantized conductance plateau ($0.5e^2/h$) has been observed on a superconducting quantum anomalous Hall insulator film, we carry out a simulation of a two-dimensional disordered Chern insulator coupled with superconductor. In particular we calculate the magnetic field dependence of the longitudinal and Hall conductance in the Hall bar geometry of a disordered Chern insulator both with a superconductor and without. Our specific focus is on the behavior of this conductance near the transition between topological phase ($\nu$=0) and trivial phase ($\nu$=1), where we expect to reproduce the conductance plateau.