Superconducting Proximity Effect in an SSH-Superconductor Junction

TL;DR

This paper models the microscopic interaction between a superconductor and a one-dimensional topological insulator (SSH chain), analyzing how tunneling and phase fluctuations affect the quasiparticle spectrum.

Contribution

It derives the effective interaction action and examines the stability and lifetime of states in the SSH chain influenced by different superconducting environments.

Findings

States are stable inside the gap for bulk superconductors.

Phase fluctuations cause finite lifetime effects in lower-dimensional superconductors.

The results suggest possible phenomenological reproductions.

Abstract

A model of microscopic interaction between a superconductor and a one-dimensional topological insulator, an SSH chain, is considered. Using the functional integration method, the effective action of the interaction between a superconductor and a topological insulator is obtained. We obtain corrections to the quasiparticle excitation spectrum of the SSH chain due to tunneling in various limits and discuss the influence of phase fluctuations. We find that for bulk superconductors, the states of the chain are stable for energies lying inside the superconducting gap while in lower-dimensional superconductors phase fluctuations yield finite temperature-dependent lifetimes even inside the gap. We also discuss whether these results can be reproduced within a simple phenomenological approach.