A Wigner crystal is the solid (crystalline) phase of electrons first predicted by Eugene Wigner in 1934. A gas of electrons moving in a uniform, inert, neutralizing background (i.e. Jellium Model) will crystallize and form a lattice if the electron density is less than a critical value. This is because the potential energy dominates the kinetic energy at low densities, so the detailed spatial arrangement of the electrons becomes important. To minimize the potential energy, the electrons form a bcc (body-centered cubic) lattice in 3D, a triangular lattice in 2D and an evenly spaced lattice in 1D. Most experimentally observed Wigner clusters exist due to the presence of the external confinement, i.e. external potential trap. As a consequence, deviations from the b.c.c or triangular lattice are observed. A crystalline state of the 2D electron gas can also be realized by applying a sufficiently strong magnetic field. However, it is still not clear whether it is the Wigner crystallization that has led to observation of insulating behaviour in magnetotransport measurements on 2D electron systems, since other candidates are present, such as Anderson localization. More generally, a Wigner crystal phase can also refer to a crystal phase occurring in non-electronic systems at low density. In contrast, most crystals melt as the density is lowered. Examples seen in the laboratory are charged colloids or charged plastic spheres. Description A uniform electron gas at zero temperature is characterised by a single dimensionless parameter, the so-called Wigner–Seitz radius rs = a / ab, where a is the average inter-particle spacing and ab is the Bohr radius. The kinetic energy of an electron gas scales as 1/rs2, this can be seen for instance by considering a simple Fermi gas. The potential energy, on the other hand, is proportional to 1/rs. When rs becomes larger at low density, the latter becomes dominant and forces the electrons as far apart as possible. As a consequence, they condense into a close-packed lattice. The resulting electron crystal is called the Wigner crystal. Based on the Lindemann criterion one can find an estimate for the critical rs. The criterion states that the crystal melts when the root-mean-square displacement of the electrons is about a quarter of the lattice spacing a. On the assumption that vibrations of the electrons are approximately harmonic, one can use that for a quantum harmonic oscillator the root mean square displacement in the ground state (in 3D)