Polarization vectors in a 2D Wigner crystal

We analyse the polarization vectors of two acoustic phonon modes propagatin g in a two-dimensional (2D) electron crystal formed above a dielectric laye r (liquid He) on a metallic substrate. The electrons are described with a f inite extent in the perpendicular direction, thus forming a quasi-2D Wigner lattice. We have found that the acoustic modes are strictly polarized in t he longitudinal (L) and transverse (T) direction only close to the centre o f the first Brillouin zone, whereas towards the zone edge the polarization can be shifted from the L and T directions (depending on the propagating wa ve direction) up to 30 degrees. We have also shown that the shape of the el ectron wave function has no significant influence on the polarization vecto rs, i.e. similar results are derived for a delocalized as well as a strictl y localized (confined to a plane) 2D Wigner crystal. (C) 2001 Elsevier Scie nce Ltd. All rights reserved.