  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.
