Time-reversal symmetry breaking surface states of d-wave superconductors induced by an additional order parameter with negative T_c

TL;DR

This paper explores how surface states in d-wave superconductors can break time-reversal symmetry through an induced s-wave order parameter, even when its bare transition temperature is negative, especially at small GL parameters.

Contribution

It demonstrates that coupling to magnetic fields can induce T-breaking surface states in d-wave superconductors with negative T_c s-wave components, expanding understanding of surface phenomena.

Findings

T-breaking surface states can occur with negative T_c s-wave order parameter.

Magnetic field coupling can induce s-wave OP even if T_c is negative.

T-breaking states are favored at small GL parameter (kappa).

Abstract

Surface states of d_{x^2-y^2}-wave superconductors are studied using the Ginzburg-Landau (GL) theory. For a [110] surface it has been known that the time-reversal symmetry (T) breaking surface state, (d+-is)-wave state, can occur if the bare transition temperature of the s-wave order parameter (OP) is positive. We show that even if this bare T_c is negative, it is possible to break T because the coupling to the spontaneously generated magnetic field may induce the s-wave OP. The T-breaking state is favored when the GL parameter (kappa) is small.