  The Josephson-like interband couplings in multi-band superconductivity
exhibit degenerate energy minima, which support states with kinks in phase of
superconductivity. When the interband couplings in systems of three or more
components are frustrated, the time-reversal symmetry (TRS) can be broken,
which generates another type of phase kink between the two
time-reversal-symmetry breaking (TRSB) pair states. In this work, we focus on
these novel states of phase kinks, and investigate their stability, similarity,
differences and physical consequences. Main results are summarized as follows:
(1) We find a new type of phase slip when the kink becomes unstable. (2) In the
kink region, TRS is broken and spontaneous magnetic fields are induced. (3) In
superconductors with TRSB, composite topological excitations associated with
variations of both superconductivity phase and amplitude can be created by
local perturbations, or due to proximity effect between normal metals.
