Induced topological order at the boundary of 3D topological superconductors

TL;DR

This paper models 3D topological superconductors in class DIII, demonstrating that their boundary states exhibit induced topological order and support Majorana zero modes, with potential applications in quantum computing.

Contribution

It introduces tight-binding models showing how boundary topological order in 3D superconductors is induced by the bulk, enabling robust Majorana zero modes.

Findings

Gapless Majorana surface states emerge at the boundary.

Surface states become gapped under Zeeman field, behaving as 2D superconductors.

Boundary topological order matches the bulk's winding number.

Abstract

We present tight-binding models of 3D topological superconductors in class DIII that support a variety of winding numbers. We show that gapless Majorana surface states emerge at their boundary in agreement with the bulk-boundary correspondence. At the presence of a Zeeman field the surface states become gapped and the boundary behaves as a 2D superconductor in class D. Importantly, the 2D and 3D winding numbers are in agreement signifying that the topological order of the boundary is induced by the order of the 3D bulk. Hence, the boundary of a 3D topological superconductor in class DIII can be used for the robust realisation of localised Majorana zero modes.