Majorana zero modes bound to a vortex line in a topological superconductor

TL;DR

This paper investigates Majorana zero modes in a 3D topological superconductor, confirming the validity of an index theorem for line defects by analytical and topological index comparisons.

Contribution

It demonstrates that the index theorem for point defects extends to line defects in topological superconductors, validated through analytical solutions and topological calculations.

Findings

Index theorem holds for line defects in 3D topological superconductors.

Analytical zero-energy solutions match topological index calculations.

The validity of the index theorem is confirmed beyond point-like defects.

Abstract

We explore Majorana zero modes bound to a vortex line in a three dimensional topological superconductor model, focusing our attention on the validity of the index theorem previously derived. We first solve the Bogoliubov-de Gennes equation at the zero energy to obtain the analytical index. We next calculate the topological index given by the order parameters. It turns out that they indeed coincide and that index theorem, which has been derived on the implicit assumption that a defect is point-like, is also valid for a line defect.