  The ground state of Sn/Si(111) and Sn/Ge(111) surface $\alpha$-phases is
reexamined theoretically, based on $ab-initio$ calculations where correlations
are approximately included through the orbital dependence of the Coulomb
interaction (in the local density + Hubbard U approximation). The effect of
correlations is to destabilize the vertical buckling in Sn/Ge(111) and to make
the surface magnetic, with a metal-insulator transition for both systems. This
signals the onset of a stable narrow gap Mott-Hubbard insulating state, in
agreement with very recent experiments. Antiferromagnetic exchange is proposed
to be responsible for the observed $\Gamma$-point photoemission intensity, as
well asfor the partial metallization observed above above 60 K in Sn/Si(111).
  Extrinsic metallization of Sn/Si(111) by, $e.g.$ alkali doping, could lead to
a novel 2D triangular superconducting state of this and similar surfaces.
