Time-reversal-invariant topological superfluids in Bose-Fermi mixtures

A mixed dimensional system of fermions in two layers immersed in a Bose-Einstein condensate (BEC) is shown to be a promising setup to realize topological superfluids with time-reversal symmetry (TRS). The induced interaction between the fermions mediated by the BEC gives rise to a competition between p-wave pairing within each layer and s-wave pairing between the layers. When the layers are far apart, intralayer pairing dominates and the system forms a topological superfluid either with or without TRS. With decreasing layer separation or increasing BEC coherence length, interlayer pairing sets in. We show that this leads either to a second-order transition breaking TRS where the edge modes gradually become gapped or to a first-order transition to a topologically trivial s-wave superfluid. Our results provide a realistic road map for experimentally realizing a topological superfluid with TRS in a cold atomic system.