Abstract
We investigate excitation modes in multi-gap superconductors. Multi-gap superconductors have multiple excitation modes. In particular, the Nambu-Goldstone mode , Leggett mode and Higgs modes are important and play an important role in multi-gap superconductors. The multiple-phase invariance in a multi-gap system is partially or totally spontaneously broken in a superconductor. We evaluate the dispersion relation and the mass formulas of these modes by using the functional-integral method. The broken multiple-phase invariance leads to a new quantum phase such as the time-reversal symmetry breaking , the emergence of massless modes and fractionally quantized-flux vortices. There is a possibility that half-flux vortices exist in a two-component superconductor in magnetic field .
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