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 predicted at very low electron densities. Here we explain both high- and low-density phase transitions, studying the behavior of an external electron added to the periodic potential of a Wigner lattice. The band structure of this electron is calculated within a model of a quasi-two-dimensional lattice. The T=0 melting criterion is derived, comparing the chemical potentials of an additional electron when it joins the lattice or stays delocalized. Good qualitative agreement is found between our results and those obtained from the quantum extension of the Kosterlitz-Thouless melting theory.