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

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.