| Summary: | One of the challenging goals in the studies of many-body physics with ultracold atoms is the creation of a topological ${p}_{x}+{{\rm{i}}{p}}_{y}$ superfluid for identical fermions in two dimensions (2D). The expectations of reaching the critical temperature T _c through p -wave Feshbach resonance in spin-polarized fermionic gases have soon faded away because on approaching the resonance, the system becomes unstable due to inelastic-collision processes. Here, we consider an alternative scenario in which a single-component degenerate gas of fermions in 2D is paired via phonon-mediated interactions provided by a 3D BEC background. Within the weak-coupling regime, we calculate the critical temperature T _c for the fermionic pair formation using the Bethe–Salpeter formalism, and show that it is significantly boosted by higher-order diagrammatic terms, such as phonon dressing and vertex corrections. We describe in detail an experimental scheme to implement our proposal, and show that the long-sought p -wave superfluid is at reach with state-of-the-art experiments.
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