  We show that finite current in superconductors can induce topological phase
transitions, as a result of the deformation of the quasiparticle spectrum by a
finite center-of-mass (COM) momentum of the Cooper pairs. To show the wide
applicability of this mechanism, we examine the topological properties of three
prototypical systems, the Kitaev chain, $s$-wave superconductors, and $d$-wave
superconductors. We introduce a finite COM momentum as an external field
corresponding to supercurrent and show that all the models exhibit
current-induced topological phase transitions. We also discuss the possibility
of observing the phase transitions in experiments and the relation to the other
finite COM momentum pairing states.
