Phase fluctuation in multi-band superconductors

The positive interband Josephson interaction leads to emergence of non-trivial order parameters such as a sign-reversal one for a two-band superconductor, a frustrated superconductivity for a three-band superconductor. The frustrated superconductivity appears on the way to fully incoherent state due to the Coulomb interaction. The physical background of the frustrated superconductivity is transparent and the effect can be directly examined in the fluctuation of the interband phase difference. To understand the relationship between the phase fluctuation and an emergence of the chiral superconductivity, we examine a simple situation, which is almost degenerated system using Ginzburg-Landau theory. The frustration retains the interband phase difference fluctuation and this fluctuation becomes a seed of a chiral domain.