Quantum phase transition of chiral Majorana fermion in the presence of disorder

TL;DR

This paper investigates the quantum phase transitions in disordered 2D quantum anomalous Hall insulators with superconductivity, revealing two distinct transitions and analyzing the critical behavior of conductance plateaus related to chiral Majorana fermions.

Contribution

It provides a theoretical framework for understanding the phase transitions and conductance behavior in disordered topological superconductors with Majorana fermions, supported by symmetry and renormalization group analysis.

Findings

Identifies two phase transitions from to
and then to  in the system.

Analyzes the critical scaling of the .5h conductance plateau.

Distinguishes between different mechanisms for the half plateau in experiments.

Abstract

We study the quantum phase transitions of a disordered two-dimensional quantum anomalous Hall insulator with $s$-wave superconducting proximity, which are governed by the percolation theory of chiral Majorana fermions. Based on symmetry arguments and a renormalization group analysis, we show there are generically two phase transitions from Bogoliubov-de Gennes Chern number $\mathcal{N}=0$ to $\mathcal{N}=1$ ($p+ip$ chiral topological superconductor) and then to $\mathcal{N}=2$, in agreement with the conclusion from the band theory without disorders. Further, we discuss the critical scaling behavior of the $e^2/2h$ conductance half plateau induced by $\mathcal{N}=1$ chiral topological superconductor recently observed in the experiment. In particular, we compare the critical behavior of the half plateau induced by topological superconductor with that predicted recently by alternative explanations of the half plateau, and show that they can be distinguished in experiments.