Multi-band superconductors in which frustrated inter-band couplings yield a time-reyersal-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 T_c 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_n greater, similar H_(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.
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机译：研究了多频带超导体，其中受阻的带间耦合产生了时空对称对称断裂（TRSB）状态。基于Bardeen-Cooper-Schrieffer（BCS）理论推导了TRSB状态的稳定性条件。使用时变的Ginzburg-Landau（GL）方法，首先在GL理论有效的临界温度T_c附近研究涡旋态，并将结果扩展为H-T相图。当材料参数满足成核场略大于先前工作中得出的热力学场（H_n较大，相似的H_（tc））的条件时[X.胡和Z.王，物理。 Rev. B 85，064516（2012）]，出现了一个以聚集涡旋为特征的非常规中间状态。界面能的计算表明聚类涡旋与正界面能有关。
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