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

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.

7 pages, v2: references added, typos corrected, almost final version

References in corpus (8)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• On the $Z_2$ classification of Quantum Spin Hall Models
• Splitting of Majorana modes due to intervortex tunneling in a p + ip superconductor
• Zero modes of two-dimensional chiral p-wave superconductors
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• Near zero modes in condensate phases of the Dirac theory on the honeycomb lattice

Cited by in corpus (3)

• Topological Defects and Gapless Modes in Insulators and Superconductors
• Topological superconductors as nonrelativistic limits of Jackiw-Rossi and Jackiw-Rebbi models
• Z${}_2$ index theorem for Majorana zero modes in a class D topological superconductor