Stability, dynamical properties, and melting of a bi-layer Wigner crystal

We investigate the stability, dynamical properties, and melting of a two-dimensional ~2D! Wigner crystal~WC! of classical Coulombic particles in a bilayer structure. Compared to the single-layer WC, this systemshows a rich phase diagram. Five different crystalline phases are stable; the energetically favored structure canbe tuned by changing either the interlayer distance or the particle density. Phase boundaries consist of bothcontinuous and discontinuous transitions. We calculated the phonon excitations of the system within theharmonic approximation and we evaluated the melting temperature of the bilayer WC by use of a modifiedLindemann criterion, appropriate to 2D systems. We minimized the harmonic free energy of the system withrespect to the lattice geometry at different values of temperature/interlayer distance and we found notemperature-induced structural phase transition.