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

The temperature dependence of the shear modulus μ in the two-dimensional electron solid has been determined in a computer simulation. It is found that at low temperatures T, μ decreases linearly with increasing T. A sharp drop of μ together with the onset of electron diffusion in the range 140>Γ>120, where Γ=e²(πnₛ)1/2kBT, 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.