Momentum relaxation in a semiconductor proximity-coupled to a disordered s-wave superconductor: effect of scattering on topological superconductivity

TL;DR

This paper investigates how disorder in a superconductor affects the proximity-induced topological superconductivity in a semiconductor, finding that topological phases can be robust despite superconductor impurities due to quantum interference effects.

Contribution

It demonstrates that static disorder in the superconductor does not necessarily suppress topological superconductivity in the semiconductor, highlighting the role of quantum interference in mitigating disorder effects.

Findings

Effective impurity scattering rate is suppressed by quantum interference.

Topological superconductivity remains stable in a large parameter regime.

Disorder in the superconductor does not eliminate proximity-induced topological phases.

Abstract

We study the superconducting proximity effect between a conventional semiconductor and a disordered s-wave superconductor. We calculate the effective momentum relaxation rate in the semiconductor due to processes involving electron tunneling into a disordered superconductor and scattering off impurities. The magnitude of the effective disorder scattering rate is important for understanding the stability of the topological (chiral p-wave) superconducting state that emerges in the semiconductor, since disorder scattering has a detrimental effect and can drive the system into a non-topological state. We find that the effective impurity scattering rate involves higher-order tunneling processes and is suppressed due to the destructive quantum interference of quasi-particle and quasi-hole trajectories. We show that, despite the fact that both the proximity-induced gap and the effective impurity scattering rate depend on interface transparency, there is a large parameter regime where the topological superconducting phase is robust against disorder in the superconductor. Thus, we establish that the static disorder in the superconductor does not suppress the proximity induced topological superconductivity in the semiconductor.