Temperature Dependence of the Shear Modulus and Melting of the Two-Dimensional Electron Solid

Abstract

The temperature dependence of the shear modulus $\mu$ in the two-dimensional electron solid has been determined in a computer simulation. It is found that at low temperatures $T$, $\mu$ decreases linearly with increasing $T$. A sharp drop of $\mu$ together with the onset of electron diffusion in the range $140>\mathrm{}\Gamma >120\mathrm{}$, where $\Gamma =\frac{e^2{\left(\pi n_s\right)}^{\frac{1}{2}}}{k_{\mathrm{B}}T}$, suggestes a melting point consistent with the experiment by Grimes and Adams. The results presented here are consistent with recent theories of dislocation-mediated melting in two dimensions.