Odd-frequency superconducting pairing and subgap density of states at the edge of a two-dimensional topological insulator without magnetism

TL;DR

This paper explores how odd-frequency spin-triplet pairing arises at the edges of 2D topological insulators without magnetism and links it to observable features in the local density of states, especially at phase differences.

Contribution

It analytically demonstrates the emergence of odd-frequency pairing due to spin-momentum locking and connects it to LDOS features in various hybrid junctions at the topological insulator edge.

Findings

Odd-frequency pairing is linked to LDOS enhancements at interfaces.

Zero-energy LDOS peak at phase π is due to odd-frequency pairing.

Analytical results apply to NS, NSN, and SNS junctions.

Abstract

We investigate the emergence and consequences of odd-frequency spin-triplet s-wave pairing in superconducting hybrid junctions at the edge of a two-dimensional topological insulator without any magnetism. More specifically, we consider several different normal-superconductor hybrid systems at the topological insulator edge, where spin-singlet s-wave superconducting pairing is proximity-induced from an external conventional superconductor. We perform fully analytical calculations and show that odd-frequency mixed spin-triplet s-wave pairing arises due to the unique spin-momentum locking in the topological insulator edge state and the naturally non-constant pairing potential profile in hybrid systems. Importantly, we establish a one-to-one correspondence between the local density of states (LDOS) at low energies and the odd-frequency spin-triplet pairing in NS, NSN and SNS junctions along the topological insulator edge; at interfaces the enhancement in the LDOS can directly be attributed to the contribution of odd-frequency pairing. Furthermore, in SNS junctions we show that the emergence of the zero-energy LDOS peak at the superconducting phase $\phi=\pi$ is associated purely with odd-frequency pairing in the middle of the junction.