Theory of edge states in a quantum anomalous Hall insulator/ spin-singlet s-wave superconductor hybrid system

TL;DR

This paper investigates the topological edge states in a hybrid system combining a quantum anomalous Hall insulator with a spin-singlet s-wave superconductor, revealing the conditions for Majorana modes and their degeneracy lifting.

Contribution

It provides a detailed analysis of the topological phases and edge states in the hybrid system, including how Zeeman fields and doping affect Majorana mode degeneracy.

Findings

Identification of topological phases with Chern numbers 1 and 2.

Observation of chiral Majorana edge modes in the system.

Degeneracy lifting of Majorana modes under magnetic field or doping.

Abstract

We study the edge states for a quantum anomalous Hall system (QAHS) coupled with a spin-singlet s-wave superconductor through the proximity effect, and clarify the topological nature of them. When we consider a superconducting pair potential induced in the QAHS, there appear topological phases with nonzero Chern numbers, $i.e.$, ${\cal N}=1$ and ${\cal N}=2$, where Andreev bound states appear as chiral Majorana edge modes. We calculate the energy spectrum of the edge modes and the resulting local density of states. It is found that the degenerate chiral Majorana edge modes for ${\cal N}=2$ are lifted off by applying Zeeman magnetic field along the parallel to the interface or the shift of the chemical potential by doping. The degeneracy of the chiral Majorana edge modes and its lifting are explained by two different winding numbers defined at the time-reversal invariant point of the edge momentum.