Broken time-reversal symmetry in Josephson junction involving two-band superconductors

A novel time-reversal symmetry breaking state is found theoretically in the Josephson junction between the two-gap superconductor and the conventional s-wave superconductor. This occurs due to the frustration between the three order parameters analogous to the two antiferromagnetically coupled XY-spins put under a magnetic field. This leads to the interface states with the energies inside the superconducting gap. Possible experimental observations of this state with broken time-reversal symmetry are discussed.