Fermi-Bose mixture in mixed dimensions

One of the challenging goals in the studies of many-body physics with ultracold atoms is the creationof a topological px + ipysuperfluid for identical fermions in two dimensions (2D). The expectationsof reaching the critical temperature Tc through p-wave Feshbach resonance in spin-polarizedfermionic 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 3DBEC background. Within the weak-coupling regime, we calculate the critical temperature Tc for the fermionic pair formation using the BetheSalpeter formalism, and show that it is significantly boosted by higher-order diagrammatic terms, such as phonon dressing and vertexcorrections.Wedescribe in detail an experimental scheme to implement our proposal, and show thatthe long-sought p-wave superfluid is at reach with state-of-the-art experiments.