  We study the Landau model of the class of incommensurate systems with a
scalar order parameter where the modulated phase is driven by a
gradient-squared term with negative coefficient. For example, theoretical
studies of cholesteric liquid crystals in a field (electric or magnetic)
suggest that such an modulated phase should exist at high chirality. The bulk
phase diagram in the presence of a bulk external field which couples linearly
to the order parameter exhibits a modulated phase inside a loop in the
temperature-field plane, and a homogeneous phase outside. On analyzing the same
model for a semi-infinite system, we find a surprising result; the system
exhibits surface states in a region where the bulk phase is homogeneous (but
close to the modulated region). These states are very different from the
well-known surface states induced either by a surface field or by enhanced
interactions at the surface, for they exist and are energetically favored even
when the sole effect of the surface is to terminate the bulk, as expressed by
free boundary conditions taken at the surface. Near the surface, the
surface-state order parameter is very different from the bulk value (in fact,
it has the opposite sign). When the temperature or the bulk field are varied to
move away from the modulated state, we find a surface phase transition at which
the surface states become energetically unfavorable, though they continue to
exist as metastable states. We then study how a surface field changes the
surface phase diagram.
