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

Abstract

The temperature dependence of the shear modulus $\ensuremath{\mu}$ in the two-dimensional electron solid has been determined in a computer simulation. It is found that at low temperatures $T$, $\ensuremath{\mu}$ decreases linearly with increasing $T$. A sharp drop of $\ensuremath{\mu}$ together with the onset of electron diffusion in the range $140>\ensuremath{\Gamma}>120$, where $\ensuremath{\Gamma}=\frac{{e}^{2}{(\ensuremath{\pi}{n}_{s})}^{\frac{1}{2}}}{{k}_{\mathrm{B}}T}$, 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.