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Metallic surface of a Mott insulator - Mott insulating surface of a metal

The dynamical mean-field theory (DMFT) is employed to study the Mott transition in the semi-infinite Hubbard model at half-filling and zero temperature. We consider the low-index surfaces of the three-dimensional simple-cubic lattice and systematically vary the model parameters at the very surface. Within the DMFT the problem is self-consistently mapped onto a set of coupled effective impurity models corresponding to the inequivalent layers parallel to the surface. Assuming that the influence of the Hubbard bands on the low-energy quasi-particle resonance can be neglected at the critical point, a simplified ``linearized DMFT'' becomes possible which is formally equivalent to the Weiss molecular-field theory for the semi-infinite Ising model. This implies that qualitatively the rich phenomenology of the Landau description of second-order phase transitions at surfaces has a direct analogue for the surface Mott transition. Motivated by this formal analogy, we work out the predictions of the linearized DMFT in detail. It is found that under certain circumstances the surface of a Mott insulator can be metallic while a Mott-insulating surface of a normal metal is not possible. The corresponding phase diagrams, the (mean-field) critical exponents and the critical profiles of the quasi-particle weight are derived. The results are confirmed by a fully numerical evaluation of the DMFT equations using the exact-diagonalization (ED) method.