  Topological insulator edges and spin-orbit-coupled quantum wires in proximity
to s-wave super- conductors can be tuned through a topological quantum phase
transition by a Zeeman field. Here we show that a supercurrent flowing in the
s-wave superconductor also drives such a transition. We propose to use this new
mechanism to generate and manipulate Majorana fermions that localize at domain
walls between topological and nontopological regions of an edge or wire. In
quantum wires, this method carries the added benefit that a supercurrent
reduces the critical Zeeman field at which the topological phase appears.
