Dynamical mean-field study of the Mott transition in thin films

The correlation-driven transition from a paramagnetic metal to a paramagnet ic Mott-Hubbard insulator is studied within the half-filled Hubbard model f or a thin-film geometry. We consider simple-cubic films with different low- index surfaces and film thickness d ranging from d = 1 (two-dimensional) up to d = 8. Using the dynamical mean-field theory, the lattice (film) proble m is self-consistently mapped onto a set of d single-impurity Anderson mode ls which are indirectly coupled via the respective baths of conduction elec trons. The impurity models are solved at zero temperature using the exact-d iagonalization algorithm. We investigate the layer and thickness dependence of the electronic structure in the low-energy regime. Effects due to the f inite film thickness are found to be the more pronounced the lower is the f ilm-surface coordination number. For the comparatively open sc(lll) geometr y we find a strong layer dependence of the quasi-particle weight while it i s much less pronounced for the sc(110) and the sc(100) film geometries. For a given geometry and thickness d there is a unique critical interaction st rength U-c2(d) at which all effective masses diverge and there is a unique strength U-c1(d) where the insulating solution disappears. U-c2(d) and U-c1 (d) gradually increase with increasing thickness eventually approaching the ir bulk values. A simple analytical argument explains the complete geometry and thickness dependence of U-c2. U-c1 is found to scale linearly with U-c 2.