Theory of nematic surface ordering via a Berezinskii-Kosterlitz-Thouless phase transition

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Abstract
For a surface interaction quadratic in the magnitude of the order parameter and favoring an in-plane molecular orientation, it is shown that a nematic surface state with quasi-two-dimensional order can exist in a narrow temperature range above the bulk transition point. This phase is characterized by fully biaxial order and the transition between it and the fully disordered one is via the Berezinskii-Kosterlitz-Thouless (BKT) mechanism. The BKT transition temperature is calculated as are the elastic and inelastic light-scattering intensities. The latter is a possible technique for observing the transition and confirming its BKT character. Numerical estimates indicate that systems having the surface interactions required to exhibit this type of nematic phase transition can be prepared.