Quantum-mechanical wigner electron crystallization with and without magnetic fields

Abstract

More than 50 years ago, Wigner argued that Coulombically interacting electrons moving in a uniform, nonresponsive, neutralizing background would exhibit a phase transition in the ground state, at sufficiently low density, to a localized electron crystal. For jellium, Ceperley and Alder demonstrated, in the ′80s, by quantum computer simulation, that the Wigner electron crystal formed when the mean interelectronic spacing rs was ˜80–100 Bohr radii. The electron crystal is (a) an insulator, (b) magnetic, probably with long-range Neel-type antiferromagnetism, (c) phononlike in its low-lying non-current-carrying excited states, and (d) defective at elevated temperatures, with hopping conduction likely to occur. Durkan, Elliott, and March pointed out, again some 30 years after Wigner, that, under suitable conditions, Wigner electron crystallization could be aided by appropriate application of magnetic fields. These workers considered n-type InSb in a magnetic field, and stressed the importance of observing Bragg reflections in X-ray or neutron experiments. While their considerations were immediately relevant to 3-dimensional Wigner electron crystals, advances in semiconductor technology have now led Andrei et al. to use a high-quality GaAs/GaAlAs heterojunction to study 2-dimensional Wigner crystallization, as induced by application of a magnetic field. Here, after a brief review of these experiments, some discussion is given of the melting curve of a 2-dimensional Wigner crystal in a magnetic field.