Multi-gap superconductors exhibit interesting
properties. In an N-gap superconductor, we have in general
U(1)N phase invariance. This multiple-phase invariance
is partially or totally spontaneously broken in a superconductor.
The Nambu-Goldstone modes, as well as
Higgs modes, are important and will play an important
role in multi-condensate superconductors. The additional
phase invariance leads to a new quantum phase, with help
of frustrated Josephson effects, 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 two-component superconductors
in a magnetic field. The half-quantum flux vortex
can be interpreted as a monopole, and two half-flux
vortices form a bound state connected by a domain wall.
There is an interesting analogy between quarks and fractionally
quantized-flux vortices in superconductors.