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-held plane, and a homogeneous phase outside. On analyzing the same model for a semi-infinite system, we fmd a surprising resu 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. [References: 12]
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