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

## TL;DR

This paper proposes a realistic cold atomic system setup using Bose-Fermi mixtures to realize time-reversal invariant topological superfluids, analyzing phase transitions driven by inter- and intra-layer pairing interactions.

## Contribution

It introduces a mixed dimensional Bose-Fermi system as a platform for topological superfluids with TRS and explores the phase transitions involved.

## Key findings

- Intra-layer p-wave pairing dominates at large layer separation.
- Decreasing layer separation induces inter-layer pairing, leading to TRS breaking or trivial phases.
- The system provides a feasible experimental route to realize topological superfluids with TRS.

## Abstract

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.