Superconductivity is associated with spontaneously broken gauge symmetry. In some exotic superconductors the time-reversal symmetry is broken as well, accompanied with internal magnetic field. A time-reversal symmetry broken (TRSB) superconductivity without internal magnetic field involved can be induced by frustrated inter-component couplings, which becomes a realistic issue recently due to the discovery of iron-pnictide superconductors. Here we derive stability condition for this novel TRSB state using the Ginzburg-Landau (GL) theory. We find that there are multiple divergent coherence lengths, and that this novel superconductivity cannot be categorized by the GL number into type I or type II. We reveal that the critical Josephson current of a constriction junction between two bulk superconductors of different chiralities is suppressed significantly from that for same chirality. This effect provides a unique way to verify experimentally this brand new superconductivity.Comment: 4 pages, 4 figure
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