MELTING OF THE WIGNER LATTICE AT T=0

A two-dimensional electron system is expected to form a Wigner lattice at zero temperature, but at very high electron densities even at T = 0 one expects a phase transition from a crystal to a gas phase. For a Wigner lattice on a dielectric layer, a T = 0 melting was also predict ed at very low electron densities. Here we explain both high- and low- density phase transitions studying the behavior of an external electro n added to the periodic potential of a Wigner lattice. The band struct ure of this electron is calculated within a model of a quasi-two-dimen sional lattice. The T = 0 melting criterion is derived, comparing the chemical potentials of an additional electron when it joins the lattic e or stays delocalized. Good qualitative agreement is found between ou r results and those obtained from the quantum extension of the Kosterl itz-Thouless melting theory.