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 ${\ensuremath{\sigma}}₁₂$ 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 $\mathrm{SO}(N)$ rotations of chiral Majorana fermion modes during propagation along the TSC edges. Oppositely, in the strong disorder regime, ${\ensuremath{\sigma}}₁₂$ 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.