Disclination Asymmetry in Deformable Hexatic Membranes and the Kosterlitz-Thouless Transitions
نویسنده
چکیده
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/KA of the bending rigidity κ to the hexatic rigidity KA 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/KA 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. PACS numbers: 05.70.Jk, 68.10.-m, 87.22.Bt Typeset using REVTEX 1
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