  We report magneto-transport studies of a two-dimensional electron system
formed in an inversion layer at the interface between a hydrogen-passivated
Si(111) surface and vacuum. Measurements in the integer quantum Hall regime
demonstrate the expected sixfold valley degeneracy for these surfaces is
broken, resulting in an unequal occupation of the six valleys and anisotropy in
the resistance. We hypothesize the misorientation of Si surface breaks the
valley states into three unequally spaced pairs, but the observation of odd
filling factors, is difficult to reconcile with non-interacting electron
theory.
