Time-reversal-symmetry-broken state in the BCS formalism for a multi-band superconductor

In three-band BCS superconductors with repulsive inter-band interactions, frustration between the bands can lead to an inherently complex gap function, arising out of a phase difference between the bands in the range 0 and π. Since the complex conjugate of this state is also a solution, the ground state is degenerate, and there appears a time-reversal-symmetry-broken state. In this paper we investigate the existence of this state as a function of inter-band coupling strength and show how a new phase transition appears between the TRSB and conventional BCS states.