Time-Reversal-Symmetry-Broken State in the BCS Formalism for a Multi-Band Superconductor

In three-band BCS superconductors with repulsive interband 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 {\pi}. 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 interband coupling strength and show how a new phase transition appears between the TRSB and conventional BCS states.