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We investigate the stability, the dynamical properties and melting of atwo-dimensional (2D) Wigner crystal (WC) of classical Coulombic particles in abi-layer structure. Compared to the single-layer WC, this system shows a richphase diagram. Five different crystalline phases are stable; the energeticallyfavoured structure can be tuned by changing either the inter-layer distance orthe particle density. Phase boundaries consist of both continuous anddiscontinuous transitions. We calculated the phonon excitations of the systemwithin the harmonic approximation and we evaluated the melting temperature ofthe bi-layer WC by use of a modified Lindemann criterion, appropriate to 2Dsystems. We minimized the harmonic free-energy of the system with respect tothe lattice geometry at different values of temperature/inter-layer distanceand we found no temperature-induced structural phase transition.

Stability, dynamical properties, and melting of a classical bilayer Wigner crystal