Unconventional superfluid in a two-leg fermonic ladder

We show that a novel unconventional superfluid triggered by a spin-orbit coupling is realized in a repulsively interacting fermonic ladder system. A competition between spin singlet and triplet pairings occurs due to the breaking of inversion symmetry. We show that both superfluid orders decay algebraically with the same exponent except for the special coupling constants for which a dominant superfluid is determined solely by the spin-orbit coupling. We also propose an experiment to observe such phases with cold atoms.