  We address the problem of a single "spin-down" impurity atom interacting
attractively with a spin-up Fermi gas in two dimensions (2D). We consider the
case where the mass of the impurity is greater than or equal to the mass of a
spin-up fermion. Using a variational approach, we resolve the questions raised
by previous studies and we show that there is, in fact, a transition between
polaron and molecule (dimer) ground states in 2D. For the molecule state, we
use a variational wave function with a single particle-hole excitation on the
Fermi sea and we find that its energy matches that of the exact solution in the
limit of infinite impurity mass. Thus, we expect the variational approach to
provide a reliable tool for investigating 2D systems.
