  We investigated the electronic structure of the Si(111)--7$\times$7 surface
below 20 K by scanning tunneling and photoemission spectroscopies and by
density functional theory calculations. Previous experimental studies have
questioned the ground state of this surface, which is expected to be metallic
in a band picture because of the odd number of electrons per unit cell. Our
differential conductance spectra instead show the opening of an energy gap at
the Fermi level and a significant temperature dependence of the electronic
properties, especially for the adatoms at the center of the unfaulted half of
the unit cell. Complementary photoemission spectra with improved correction of
the surface photovoltage shift corroborate the differential conductance data
and demonstrate the absence of surface bands crossing the Fermi level at 17 K.
These consistent experimental observations point to an insulating ground state
and contradict the prediction of a metallic surface obtained by density
functional theory in the generalized gradient approximation. The calculations
indicate that this surface has or is near a magnetic instability, but remains
metallic in the magnetic phases even including correlation effects at
mean-field level. We discuss possible origins of the observed discrepancies
between experiments and calculations.
