Dynamical properties and Wigner transitions of two-dimensional electron lattices on dielectric substrates

The dynamical properties (phonon spectrum, sound velocities, vibrational energy) and phase transitions of a two-dimensional Wigner lattice are discussed in a model that takes into account the perpendicular delocalization of electron wave functions. The lattice floats above the dielectric substrate (He,Ar), with the dielectric constant determining the image force on the lattice. Those two effects, the perpendicular electron delocalization and the dielectric image force, which are obviously correlated, were usually neglected in the previous discussions of the Wigner-lattice dynamics. Here we show their influence on the electron-electron interaction and consequently on the dynamical properties of the Wigner lattice. We also suggest an experimental situation where those effects in the phase diagram could be eventually studied and detected.