Image: M. BONITZ, University of Rostock

To the list of intriguing structures that physicists hope to soon make in the lab, add Wigner crystalsstrange bull's-eye patterns formed only from electrons. Theorists have predicted that squeezing a handful of electrons in a liquid state might force them to crystallize in this way, the lowest energy configuration possible, since the 1930s. But only indirect evidence over the years supported the idea. Now scientists from Germany have developed a new model of Wigner crystals, which suggests not only how they might be created but how they might behave as well.

Michael Bonitz of the University of Rostock and his colleagues describe their work in today's issue of the Physical Review Letters (PRL 86, 3851). Part of the difficulty their new model had to overcome was accounting for both the Coulomb repulsion between electrons and quantum forces that rule over Wigner crystals. Once in place, the group used the model to analyze random electron arrangements, narrowing the results down to those with the lowest possible energy. To determine the exact conditions under which Wigner crystals form, they repeated the analysis at various temperatures and pressures.

They discovered that Wigner crystals form when the electrons are tightly compressed in a plane (see top image). Squeeze them too tightly, however, and the crystal will dissolve into a so-called quantum liquid as the electron wave functions begin to overlap (see bottom image). Another bit of advice they offer to would-be Wigner crystal makers: the stability of the crystals depends heavily on the number of electrons they contain.