Geometry-induced topological superconductivity

TL;DR

This paper demonstrates that the geometry and size of topological insulators can induce topological superconductivity with p ± ip pairing symmetry, supporting Majorana zero modes without magnetic fields.

Contribution

It reveals how surface curvature and size of topological insulators can be used to control electron pairing and induce topological superconductivity.

Findings

Topological superconductivity can be induced by geometry and size of TIs.

Vortices with Majorana zero modes can form spontaneously on TI surfaces.

Topological superconductivity arises with p ± ip pairing in nanoscale TIs.

Abstract

Intrinsic topological superconductors with p-wave pairing are rare in nature. Its underlying reason is due to the fact that it is usually difficult to change the relative strength between the singlet and triplet channels for the electron-electron interaction in material. Here we show that by considering superconductivity occurring on surfaces of topological insulators (TIs), the relative strength between the singlet and triplet channels can be changed by geometry and sizes of TIs. Specifically, we show that pairing of electrons at different locations on the surface of a topological insulator generally tends to favor the triplet pairing and can induce topological superconductivity by controlling the surface curvature and size of the topological insulator. We illustrate the effects in two configurations, thin film geometry and the spherical geometry with a sphere or a hemisphere, and find that topological superconductivity arises with the $p \pm ip$ pairing symmetry dominated in nanoscale size of the TI. As a consequence, vortices can spontaneously form on surfaces of topological insulators with roughness of appropriate curvature. These vortices support a Majorana zero mode inside each core and can be used as a platform to host Majorana zero modes without invoking real magnetic fields. Our theoretical discovery opens a new route to realize topological superconductivity in material.