Distribution of conductances in chiral topological superconductor junctions

We study the electronic transport of heterojunctions made of chiral topological superconductors (TSCs) with integer N chiral Majorana fermion modes and quantum Hall insulators (QHIs) with integer Chern number C. In the weak disorder regime, we show the two-terminal conductance σ12 of a QHI-TSC-QHI junction for most N>1 is nonquantized but obeys a certain distribution determined by C and N, which is induced by random SO(N) rotations of chiral Majorana fermion modes during propagation along the TSC edges. Oppositely, in the strong disorder regime, σ12 tends to a quantized value. This provides a unique electrical signature for chiral TSC with N>1, which is significantly different from the extensively studied N=1 case. We conclude with a brief discussion on the fractionally quantized thermal conductances of the junction.