Spontaneous edge corner currents in $s+is$ superconductors and time reversal symmetry breaking surface states

TL;DR

This paper investigates $s+is$ superconductors, revealing that they can host spontaneous boundary currents and magnetic fields at corners, even without topological or chiral properties, due to surface states breaking time reversal symmetry.

Contribution

It uncovers the existence of time reversal symmetry breaking surface states and spontaneous boundary currents in $s+is$ superconductors, expanding understanding beyond topological classifications.

Findings

Spontaneous boundary currents and magnetic fields occur at corners.

Surface states can break time reversal symmetry independently of the bulk.

Boundary effects arise in non-topological, non-chiral superconducting states.

Abstract

We present a study of the basic microscopic model of an $s$-wave superconductor with frustrated interband interaction. When frustration is strong, such an interaction gives raise to a $s+is$ state. This is a $s$-wave superconductor that spontaneously breaks time reversal symmetry. We show that, in addition to the known $s+is$ state, there is additional phase, where the system's bulk is a conventional $s$-wave state, but superconducting surface states break time reversal symmetry. Furthermore, we show that $s+is$ superconductors can have spontaneous boundary currents and spontaneous magnetic fields. These arise at lower-dimensional boundaries, namely, the corners, in two-dimensional samples. This demonstrates that boundary currents effects in superconductors can arise in states which are not topological and not chiral according to the modern classification.