H–T Phase Diagram of Multi-component Superconductors with Frustrated Inter-component Couplings

Multi-band superconductors in which frustrated inter-band couplings yield a time-reversal-symmetry breaking (TRSB) state are investigated. Stability condition for the TRSB state are derived based on the Bardeen–Cooper–Schrieffer (BCS) theory. With the time-dependent Ginzburg–Landau (GL) method, vortex states are investigated first at the vicinity of critical temperature Tc where the GL theory is valid, and the results are extended to compose the H–T phase diagram. When material parameters satisfy the condition that the nucleation field is slightly larger than the thermodynamic field (\(H_{\text{n}} \gtrsim H_{\text{tc}}\)) derived in a previous work [X. Hu and Z. Wang, Phys. Rev. B 85, 064516 (2012)], an unconventional intermediate state characterized by clustering vortices appears. Calculation of interface energy reveals that the clustering vortices are associated with positive interface energy.