Superconducting proximity effect in an SSH-superconductor junction

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.