No-go theorem for a time-reversal invariant topological phase in noninteracting systems coupled to conventional superconductors

TL;DR

This paper proves that non-interacting electron systems coupled to conventional s-wave superconductors cannot host time-reversal invariant topological phases, implying that Majorana states require interactions or unconventional superconductors.

Contribution

It establishes a no-go theorem for realizing time-reversal invariant topological phases in non-interacting systems with conventional superconductors.

Findings

Topological invariant is always trivial in such systems

Time-reversal invariant topological phases require interactions or unconventional superconductors

Results apply to both one- and two-dimensional systems

Abstract

We prove that a system of non-interacting electrons proximity coupled to a conventional s-wave superconductor cannot realize a time reversal invariant topological phase. This is done by showing that for such a system, in either one or two dimensions, the topological invariant of the corresponding symmetry class (DIII) is always trivial. Our results suggest that the pursuit of Majorana bound states in time-reversal invariant systems should be aimed at interacting systems or at proximity to unconventional superconductors.