Long-range triplet Josephson current driven by the bias voltage

We study the long-range triplet Josephson current in a clean junction composed of two s-wave superconductors and a normal-metal/ferromagnet/normal-metal trilayer. Through applying the bias voltages on the metal regions by two antiparallel half-metal electrodes, we show that the amplitude and direction of this long-range current can be controlled flexibly. Such current arises from the fact that the applied voltage can produce a nonequilibrium spin-dependent quasiparticle distribution in the metal regions so that the Cooper pairs entering these regions acquire extra momenta, which will lead to a spin-transition process in the metal regions. This process can produce the parallel spin-triplet pairs in the central ferromagnet layer. In particular, if the voltage is applied only to one metal region, we further find that the recently discovered long-range superharmonic Josephson current will appear because of the transport of an even number of parallel spin-triplet pairs.