Highly tunable time-reversal-invariant topological superconductivity in topological insulator thin films

TL;DR

This paper explores how topological superconductivity in topological insulator thin films can be tuned via electric fields and doping, revealing conditions for nontrivial phases with potential Majorana modes.

Contribution

It identifies multiple configurations for time-reversal-invariant topological superconductivity in TI thin films and demonstrates their high tunability through electric fields and chemical potential adjustments.

Findings

Topological phases depend on intra- or inter-surface pairing configurations.

Electric field and doping can tune the topological state.

Spin-triplet inter-surface pairing always yields a topological phase.

Abstract

We study time-reversal-invariant topological superconductivity in topological insulator (TI) thin films including both intra- and inter-surface pairing. We find a nontrivial topology for multiple different configurations. For intra-surface pairing a $\pi$-phase difference between the intra-surface pairing states is required. We show that in this case the resulting topological phase is highly tunable by both an applied electric field and varied chemical potential. For spin-singlet inter-surface pairing, a sign-changing tunnel coupling present in many TI thin films is needed, and again, the topology can be tuned by electric field or doping. Notably, we find that the required inter-surface pairing strength for achieving nontrivial topology can still be subdominant compared to the intra-surface pairing. Finally, for spin-triplet inter-surface pairing we prove that the superconducting state is always topological nontrivial. We show that thin films of Cu-doped Bi$_2$Se$_3$ will likely host such spin-triplet inter-surface pairing. Taken together, these results show that time-reversal-invariant topological superconductivity is common in superconducting TI thin films and that the topological phase and its Kramers pair of Majorana edge modes is highly tunable with an applied electric field and varied chemical potential.