Polaron in the Wigner lattice

We analyze the polaron in a Wigner lattice, i.e., the interaction of an ext ernal electron with electrons in a quasi-two-dimensional Wigner crystal, co nfigured on a dielectric layer with a metallic substrate. Particular attent ion is paid to the dynamics of the system and to the electron-phonon intera ction. The polaron wave function and ground-state energy of the system are calculated in the extended small-polaron theory. The theory is based on the complete set of Wannier functions, which enables us to treat also the pola ron dispersion and the first correction to the standard polaron self-energy . We also discuss the T=0 Wigner phase transition, i.e., melting of the ele ctron lattice due to increased electron density. The general agreement with the result's obtained previously within the Schrodinger-Rayleigh perturbat ion theory is good, but also we found some significant differences. The new calculations show that (i) the polaron dispersion is significant at all el ectron densities and in most cases it resembles the dispersion of lattice e lectrons; (ii) the critical density parameter r(c) for a Wigner phase trans ition in a high density region is close to the value r(c)approximate to 40 predicted for a strictly two-dimensional Wigner lattice, regardless of the dielectric layer thickness. [S0163-1829(99)02110-4].