# Pairing in two-dimensional Fermi gases with a coordinate-space potential

## TL;DR

This paper investigates pairing phenomena in two-dimensional Fermi gases with finite-range interactions, deriving a mean-field gap equation, numerically solving it, and using Monte Carlo simulations to evaluate energies and pairing gaps, providing benchmarks for future theories.

## Contribution

It introduces a mean-field pairing gap equation for finite-range potentials in 2D Fermi gases and uses Monte Carlo methods to evaluate energies and pairing gaps, offering new benchmarks.

## Key findings

- Short effective ranges yield results identical to zero-range models.
- Numerical solutions of the gap equation across interaction strengths.
- Monte Carlo energies used to extract pairing gaps via odd-even staggering.

## Abstract

In this work we theoretically study pairing in two-dimensional Fermi gases, a system which is experimentally accessible using cold atoms. We start by deriving the mean-field pairing gap equation for a coordinate-space potential with a finite interaction range, and proceed to solve this numerically. We find that for sufficiently short effective ranges the answer is identical to the zero-range one. We then use Diffusion Monte Carlo to evaluate the total energy for many distinct particle numbers; we employ several variational parameters to produce a good ground-state energy and then use these results to extract the pairing gap across a number of interaction strengths in the strongly interacting two-dimensional crossover. Extracting the gap via the odd-even energy staggering, our microscopic results can be used as benchmarks for other theoretical approaches.