# Fermi-Bose mixture in mixed dimensions

## TL;DR

This paper proposes a novel method to realize a topological p-wave superfluid in a 2D fermionic gas mediated by a 3D BEC, overcoming previous instability issues and predicting achievable critical temperatures.

## Contribution

It introduces a phonon-mediated pairing mechanism in mixed dimensions, calculating the critical temperature with advanced diagrammatic corrections, and outlines an experimental implementation.

## Key findings

- Critical temperature is significantly boosted by higher-order corrections.
- The proposed scheme makes p-wave superfluidity experimentally feasible.
- The approach overcomes instability issues of previous p-wave superfluid attempts.

## Abstract

One of the challenging goals in the studies of many-body physics with ultracold atoms is the creation of a topological $p_{x} + ip_{y}$ 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 Bethe-Salpeter formalism, and show that it is significantly boosted by higher-order diagramatic 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.