Time-reversal symmetry breaking phase and gapped surface states in d-wave nanoscale superconductors

TL;DR

This paper demonstrates that d-wave superconductors with [110] surfaces can spontaneously break time-reversal symmetry, leading to complex order parameters and vortex-antivortex pairs, which are detectable experimentally.

Contribution

It reveals the spontaneous TRS breaking and complex order parameters in d-wave nanoscale superconductors with [110] surfaces, a novel phenomenon in this context.

Findings

Spontaneous TRS breaking occurs with complex order parameters.

Vortex-antivortex pairs can form along the surfaces.

Surface-sensitive probes can detect these phenomena.

Abstract

We solve the Bogoliubov-de Gennes equations self-consistently for d-wave superconductors with [110] surfaces. We find spontaneous breaking of time-reversal symmetry (TRS) caused by the spontaneous occurrence of a complex order parameter with an extended s-wave symmetry along the [110] surfaces. In the TRS-breaking phase, the d-wave order parameter itself becomes complex. We also show that vortex-antivortex pairs can appear along the [110] surfaces of nanoribbons. These pairs are detectable with surface sensitive probes.