Stability, dynamical properties, and melting of a classical bilayer 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 system shows a rich phase diagram. Five different crystalline phases are stable; the energetically favored structure can be tuned by changing either the interlayer distance or the particle density. Phase boundaries consist of both continuous and discontinuous transitions. We calculated the phonon excitations of the system within the harmonic approximation and we evaluated the melting temperature of the bilayer WC by use of a modified Lindemann criterion, appropriate to 2D systems. We minimized the harmonic free energy of the system with respect to the lattice geometry at different values of temperature/interlayer distance and we found no temperature-induced structural phase transition.