Majorana modes at the ends of superconductor vortices in doped topological insulators

TL;DR

This paper investigates the existence of vortex Majorana zero modes in doped topological insulators with bulk superconductivity, revealing they can survive doping below a critical level linked to a topological phase transition.

Contribution

It demonstrates that vortex Majorana modes can exist in doped topological insulators and identifies the conditions and material properties influencing their presence.

Findings

Majorana modes appear below a critical doping level.

The critical doping depends on vortex orientation and Fermi surface Berry phase.

Certain doped materials like p-doped Bi2Te3 support Majorana modes.

Abstract

Recent experiments have observed bulk superconductivity in doped topological insulators. Here we ask whether vortex Majorana zero modes, previously predicted to occur when superconductivity is induced on the surface of topological insulators, survive even in these doped systems with metallic normal states. Assuming inversion symmetry, we find that Majorana zero modes indeed appear but only below a critical doping. The critical doping is associated with a topological phase transition of the vortex line, where it supports gapless excitations along its length. The critical point depends only on the orientation of the vortex line, and a Berry phase property, the SU(2) Berry phase of the Fermi surface in the metallic normal state. By calculating this phase for available band structures we determine that materials candidates like $p$-doped Bi$_{2}$Te$_{3}$ under pressure supports vortex end Majorana modes. Surprisingly, even superconductors derived from topologically trivial band structures can support Majorana modes, providing a promising route to realizing them.