  We investigate the stability, the dynamical properties and melting of a
two-dimensional (2D) Wigner crystal (WC) of classical Coulombic particles in a
bi-layer structure. Compared to the single-layer WC, this system shows a rich
phase diagram. Five different crystalline phases are stable; the energetically
favoured structure can be tuned by changing either the inter-layer 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 bi-layer 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/inter-layer distance
and we found no temperature-induced structural phase transition.
