Stabilization of Majorana modes in vortices in the superconducting phase of topological insulators using topologically trivial bands

TL;DR

This paper investigates how hybridization with trivial bands can extend the doping range for Majorana modes in topological insulators, potentially stabilizing topological phenomena over broader doping levels.

Contribution

It demonstrates that hybridization with trivial bands can significantly extend the doping range for Majorana modes in topological insulators, especially in materials like HgTe.

Findings

Hybridization with trivial bands extends the doping range for Majorana modes.

The doping range is increased for p-doping and decreased for n-doping.

Implication for stabilizing topological phenomena over wider doping ranges.

Abstract

If superconductivity is induced in the metallic surface states of topological insulators via proximity, Majorana modes will be trapped on the vortex cores. The same effects hold for doped topological insulators which become bulk s-wave superconductors as long as the doping does not exceed a critical values $ \mu^{\pm}_c.$ It is this critical chemical potential at which the material forgets it arose from a band-inverted topological insulator; it loses its topological \emph{imprint.} For the most common classes of topological insulators, which can be modeled with a minimal 4-band Dirac model the values of $\mu^{\pm}_c$ can be easily calculated, but for materials with more complicated electronic structures such as HgTe or ScPtBi the result is unknown. We show that due to the hybridization with an additional Kramers' pair of topologically trivial bands the topological imprint of HgTe-like electronic structures (which includes the ternary Heusler compounds) can be widely extended for p-doping. As a practical consequence we consider the effects of such hybridization on the range of doping over which Majorana modes will be bound to vortices in superconducting topological insulators and show that the range is strongly extended for p-doping, and reduced for n-doping. This leaves open the possibility that other topological phenomena may be stabilized over a wider range of doping.