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Disclination Asymmetry in Deformable Hexatic Membranes and the Kosterlitz-Thouless Transitions

Jeong-Man Park·T. C. Lubensky
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Abstract

A disclination in a hexatic membrane favors the development of Gaussian curvature localized near its core. The resulting global structure of the membrane has mean curvature, which is disfavored by curvature energy. Thus a membrane with an isolated disclination undergoes a buckling transition from a flat to a buckled state as the ratio $κ/K_{A}$ of the bending rigidity $κ$ to the hexatic rigidity $K_{A}$ is decreased. In this paper we calculate the buckling transition and the energy of both a positive and a negative disclination. A negative disclination has a larger energy and a smaller critical value of $κ/K_{A}$ at buckling than does a positive disclination. We use our results to obtain a crude estimate of the Kosterlitz-Thouless transition temperature in a membrane. This estimate is higher than the transition temperature recently obtained by the authors in a renormalization calculation.

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Jeong-Man Park, T. C. Lubensky. 1995-12-14. Disclination Asymmetry in Deformable Hexatic Membranes and the Kosterlitz-Thouless Transitions. https://doi.org/10.1051/jp1%3A1996226

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