The shear modulus and the phase diagram for two-dimensional Wigner electron crystals

Abstract

Defect energies in two- and three-dimensional classical crystals correlate with the shear modulus mu ; in turn this relates the melting temperature Tm intimately to mu . Thus, a model is first proposed for the shear modulus for two-dimensional Wigner crystals. The melting temperature is then determined from the Kosterlitz-Thouless melting criterion or from an anharmonic instability inherent in the model. The relative positrons of these transitions depend on the model parameters used. The calculation is generalized to include (a) zero-point motion which is dominant in the quantum limit and (b) the effect of a magnetic field. For the high field case, this modelling allows Tm to be plotted versus the Landau-level filling factor nu . The predictions of the model are thereby brought into contact with the experiments of Andrei et al. (1988), and Glattli et al. (1990) which have been interpreted as evidence for a magnetically induced Wigner solid (MIWS) in the electron assembly in a GaAs/AlGaAs heterojunction in strong magnetic fields. The model exhibits of the features observed experimentally.