Superconducting proximity effect in semiconductor thin films with spin-splitting and spin-orbit interaction

TL;DR

This paper develops a microscopic model to analyze the band structure and topological phases of semiconductor thin films with spin-orbit and exchange interactions in proximity to superconductors, highlighting conditions for Majorana states.

Contribution

It provides analytical expressions for proximity-induced gaps and topological invariants in finite-thickness semiconductor films, advancing understanding of topological superconductivity in heterostructures.

Findings

Finite film thickness causes resonant states affecting topological phases.

Proximity effect and topological invariant depend on semiconductor parameters.

Complex band structure with alternating trivial and non-trivial phases.

Abstract

Superconducting heterostructures with spin-active materials have emerged as promising platforms for engineering topological superconductors featuring Majorana bound states at surfaces, edges and vortices. Here we present a method for evaluating, from a microscopic model, the band structure of a semiconductor film of finite thickness deposited on top of a conventional superconductor. Analytical expressions for the proximity induced gap openings are presented in terms of microscopic parameters and the proximity effect in presence of spin-orbit and exchange splitting is visualized in terms of Andreev reflection processes. An expression for the topological invariant, associated with the existence of Majorana bound states, is shown to depend only on parameters of the semiconductor film. The finite thickness of the film leads to resonant states in the film giving rise to a complex band structure with the topological phase alternating between trivial and non-trivial as the parameters of the film are tuned.