A mixed dimensional system of fermions in two layers immersed in a Bose-Einstein condensate (BEC) is shown to be a promising setup to realise 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, intra-layer pairing dominates and the system forms a topological superfluid either with or without TRS. With decreasing layer separation or increasing BEC coherence length, inter-layer 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 roadmap for experimentally realising a topological superfluid with TRS in a cold atomic system.
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