HEXAGONAL CRYSTALLIZATION IN A 2-DIMENSIONAL ELECTRON-GAS WITH DISORDER

We develop a theory for the solidification of the two-dimensional electron-gas in the presence of disorder. Our mean field theory includes the electron-electron interaction in the Hartree-Fock approximation and the potential of random impurities in the self-consistent Born approximation. It is shown that the electron solid is stable in a wide range of disorder strengths and that the impurity interaction leads to a considerable lowering of the ground-state energy. At low disorder we obtain a Wigner crystal with a gap in the density of states, and at stronger disorder a phase with a nonvanishing density of states is formed. In the presence of disorder there is still a sharp melting transition of the electron solid. Depending on the disorder strength it occurs at a significantly lower temperature. This can explain differences in recent experiments.