# Fermion pairing in mixed-dimensional atomic mixtures

## TL;DR

This paper explores how mixed-dimensional cold atom mixtures can be tuned to favor various superconducting orders, revealing that certain induced pairings can achieve higher critical temperatures than traditional models.

## Contribution

It demonstrates the control of multiple superconducting pairing symmetries in mixed-dimensional systems using functional renormalization group analysis.

## Key findings

- Control over s-, p-, d-, and g-wave pairing symmetries.
- Induced d-wave pairing can have a critical temperature an order of magnitude higher.
- Charge-density wave order can also emerge in the system.

## Abstract

We investigate the quantum phases of mixed-dimensional cold atom mixtures. In particular, we consider a mixture of a Fermi gas in a two-dimensional lattice, interacting with a bulk Fermi gas or a Bose-Einstein condensate in a three-dimensional lattice. The effective interaction of the two-dimensional system mediated by the bulk system is determined. We perform a functional renormalization group analysis, and demonstrate that by tuning the properties of the bulk system, a subtle competition of several superconducting orders can be controlled among $s$-wave, $p$-wave, $d_{x^2-y^2}$-wave, and $g_{xy(x^2-y^2)}$-wave pairing symmetries. Other instabilities such as a charge-density wave order are also demonstrated to occur. In particular, we find that the critical temperature of the $d$-wave pairing induced by the next-nearest-neighbor interactions can be an order of magnitude larger than that of the same pairing induced by doping in the simple Hubbard model. We expect that by combining the nearest-neighbor interaction with the next-nearest-neighbor hopping (known to enhance $d$-wave pairing), an even higher critical temperature may be achieved.