  We study binding of $N$ identical heavy fermions by a light atom in two
dimensions assuming zero-range attractive heavy-light interactions. By using
the mean-field theory valid for large $N$ we show that the $N+1$ cluster is
bound when the mass ratio exceeds $1.074N^2$. The mean-field theory, being
scale invariant in two dimensions, predicts only the shapes of the clusters
leaving their sizes and energies undefined. By taking into account
beyond-mean-field effects we find closed-form expressions for these quantities.
We also discuss differences between the Thomas-Fermi and Hartree-Fock
approaches for treating the heavy fermions.
