Absence of binding of heavy fermions by two light atoms in two dimensions

TL;DR

This paper uses mean-field theory to show that in two dimensions, two light fermions cannot form a bound state with heavy fermions, instead splitting into single-light-atom droplets, unlike the one-dimensional case.

Contribution

The study provides the first mean-field analysis of heavy-light fermion interactions in two dimensions, revealing the absence of binding and droplet formation.

Findings

Two light fermions do not bind with heavy fermions in 2D.

System always splits into droplets with a single light atom.

Contrasts with 1D case where binding is possible.

Abstract

By developing the mean-field theory valid for large $N$, we investigate the problem of two light fermions interacting via a zero-range potential with $N$ heavy fermions in two dimensions. We obtain numerical evidence that this system is never fully bound. It always splits into droplets containing a single light atom. This is in contrast to the one-dimensional case where any number of heavy and light fermions can be bound together.