Distribution of Conductances in Chiral Topological Superconductor Junctions

TL;DR

This paper investigates the conductance distribution in heterojunctions of chiral topological superconductors and quantum Hall insulators, revealing non-quantized conductance in weak disorder and quantized conductance in strong disorder regimes.

Contribution

It introduces a model for conductance distribution in TSC-QHI junctions considering disorder effects, highlighting the role of Majorana modes and random rotations.

Findings

Conductance follows a distribution determined by C and N in weak disorder.

Strong disorder leads to quantized conductance values.

Discussion on fractionally quantized thermal conductances.

Abstract

We study the electronic transport of heterojunctions made of chiral topological superconductors (TSCs) with $N$ 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 $\sigma_{12}$ of a QHI-TSC-QHI junction is generically non-quantized, but obeys a certain distribution determined by $C$ and $N$, which is induced by random SO($N$) rotations of chiral Majorana fermion mode basis on the TSC edges. Oppositely, in the strong disorder regime, $\sigma_{12}$ tends to be a quantized value. We conclude with a brief discussion on the fractionally quantized thermal conductances of the junction.