J. Phys. I France
Volume 6, Numéro 4, April 1996
Page(s) 493 - 502
DOI: 10.1051/jp1:1996226
J. Phys. I France 6 (1996) 493-502

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

Jeong-Man Park and T.C. Lubensky

Laboratory for Research on the Structure of Matter, University of Pennsylvania, Philadelphia, PA 19104, USA

(Received 6 November 1995, received in final form 14 December 1995, accepted 21 December 1995)

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 bluckling transition from a flat to a buckled state as the ratio $k/K_{\rm A}$ of the bending rigidity k to the hexatic rigidity $K_{\rm A}$ 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 $k/K_{\rm A}$ 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.

© Les Editions de Physique 1996