Inspired by recent experiments on ${}^3\mathrm{He}$ films between one and two atoms thick, we consider a bilayer Hubbard model on a triangular lattice. Our results are obtained in the framework of a cluster dynamical mean-field calculation with a quantum Monte Carlo impurity solver. For appropriate model parameters, we observe an enhancement of the effective mass as the first layer approaches integer filling and the second remains only partially filled. At finite temperatures, this increase of the effective mass—or, equivalently, the decrease of the coherence temperature—leads to a crossover to a state where the first-layer fermions localize, drop out of the Luttinger volume, and generate essentially free local moments. This finite temperature behavior is shown to be robust against the cluster size above some critical temperature. The zero-temperature phase diagram, however, depends on the cluster topology. In particular, for clusters with an even number of unit cells, the growth of the effective mass is cut off by a first-order, orbital-selective Mott transition.

• Received 4 October 2010

DOI:https://doi.org/10.1103/PhysRevB.83.045103