Free Energies of Isolated 5- and 7-fold Disclinations in Hexatic Membranes

TL;DR

This paper investigates the shapes and energies of 5- and 7-fold disclinations in hexatic membranes, revealing how thermal fluctuations influence defect proliferation and shape characteristics.

Contribution

It provides a detailed numerical and analytical study of disclination buckling, shape power laws, and the impact of thermal fluctuations on defect proliferation in hexatic membranes.

Findings

Disclinations buckle at different rigidity ratios, indicating two defect proliferation temperatures.

Thermal fluctuations drive the system into an unbuckled regime at long wavelengths.

Power law shapes with variable exponents characterize defects in the unbuckled regime.

Abstract

We examine the shapes and energies of 5- and 7-fold disclinations in low-temperature hexatic membranes. These defects buckle at different values of the ratio of the bending rigidity, $\kappa$, to the hexatic stiffness constant, $K_A$, suggesting {\em two} distinct Kosterlitz-Thouless defect proliferation temperatures. Seven-fold disclinations are studied in detail numerically for arbitrary $\kappa/K_A$. We argue that thermal fluctuations always drive $\kappa/K_A$ into an ``unbuckled'' regime at long wavelengths, so that disclinations should, in fact, proliferate at the {\em same} critical temperature. We show analytically that both types of defects have power law shapes with continuously variable exponents in the ``unbuckled'' regime. Thermal fluctuations then lock in specific power laws at long wavelengths, which we calculate for 5- and 7-fold defects at low temperatures.