Index theorem for topological heterostructure systems

TL;DR

This paper applies the Niemi-Semenoff index theorem to a topological insulator-superconductor junction with magnetic insulators, revealing how both gapless and massive modes influence Majorana zero modes and their topological protection.

Contribution

It extends the index theorem application to heterostructure systems, showing that massive modes can affect Majorana zero mode protection in topological insulator junctions.

Findings

Majorana zero modes are influenced by both gapless and massive interface modes.

Topological protection of Majorana modes can be compromised under realistic conditions.

The index theorem provides a comprehensive framework for understanding zero-energy states in heterostructures.

Abstract

We apply the Niemi-Semenoff index theorem to an s-wave superconductor junction system attached with a magnetic insulator on the surface of a three-dimensional topological insulator. We find that the total number of the Majorana zero energy bound states is governed not only by the gapless helical mode but also by the massive modes localized at the junction interface. The result implies that the topological protection for Majorana zero modes in class D heterostructure junctions may be broken down under a particular but realistic condition.