Odd-frequency superconducting pairing in topological insulators

TL;DR

This paper demonstrates the emergence of disorder-robust odd-frequency spin-triplet s-wave superconductivity on topological insulator surfaces when coupled to a conventional superconductor, driven by in-surface gap gradients.

Contribution

It provides analytical and numerical evidence that odd-frequency pairing appears under in-surface gap gradients, expanding understanding of unconventional superconductivity in topological materials.

Findings

Odd-frequency pairing is present with in-surface gap gradients.

The odd-frequency order parameter is proportional to the gap gradient.

No low-energy states are induced by the odd-frequency component.

Abstract

We discuss the appearance of odd-frequency spin-triplet s-wave superconductivity, first proposed by Berezinskii [{\it JETP} {\bf 20}, 287 (1974)], on the surface of a topological insulator proximity coupled to a conventional spin-singlet s-wave superconductor. Using both analytical and numerical methods we show that this disorder robust odd-frequency state is present whenever there is an in-surface gradient in the proximity induced gap, including superconductor-normal state (SN) junctions. The time-independent order parameter for the odd-frequency superconductor is proportional to the in-surface gap gradient. The induced odd-frequency component does not produce any low-energy states.