Structure of a two-dimensional Wigner crystal in a parabolic potential trap with 600 electrons. Triangles and squares mark positions of the topological defects.
A Wigner crystal is the solid (crystalline) phase of electrons first predicted by Eugene Wigner in 1934.[1][2] 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.[3] A crystalline state of the 2D electron gas can also be realized by applying a sufficiently strong magnetic field. [citation needed] 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.[clarification needed]
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.[citation needed]
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Wigner, E. (1934). "On the Interaction of Electrons in Metals". Physical Review. 46 (11): 1002–1011. Bibcode:1934PhRv...46.1002W. doi:10.1103/PhysRev.46.1002.
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Wigner, E. P. (1938). "Effects of the electron interaction on the energy levels of electrons in metals". Transactions of the Faraday Society. 34: 678. doi:10.1039/TF9383400678.
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Radzvilavicius, A.; Anisimovas, E. (2011). "Topological defect motifs in two-dimensional Coulomb clusters". Journal of Physics: Condensed Matter. 23 (38): 385301. arXiv:1204.6028. Bibcode:2011JPCM...23L5301R. doi:10.1088/0953-8984/23/38/385301. PMID 21891854. S2CID 22775297.
A Wignercrystal is the solid (crystalline) phase of electrons first predicted by Eugene Wigner in 1934. A gas of electrons moving in a uniform, inert...
plasma, Rydberg matter, Rydberg polaron, photonic matter, wignercrystal, and time crystal but whose properties are entirely within the realm of mainstream...
so-called Wignercrystal, in which the single-particle orbitals are of approximately Gaussian form centered on crystal lattice sites. Once a Wignercrystal has...
The Wigner effect (named for its discoverer, Eugene Wigner), also known as the discomposition effect or Wigner's disease, is the displacement of atoms...
temperature and pressure, present properties of both a solid and liquid. Wignercrystal: a crystalline phase of low-density electrons. Hexatic state, a state...
Seed crystal – a small piece of a single crystal used to initiate growth of a larger crystalWigner–Seitz cell – a primitive cell of a crystal lattice...
reduces electron tunneling across supercells. They can be used to form Wignercrystals. Electrodes can be attached to regulate an electric field. The electric...
more than one lattice point. Wigner–Seitz cell Bravais lattice Wallpaper group Space group In n dimensions the crystal translation vector would be T...
gamma-ray laser. C.J. Campbell; A.G. Radnaev; A. Kuzmich (2 June 2011). "Wignercrystals of 229Th for optical excitation of the nuclear isomer". Phys. Rev....
reciprocal space. In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice is broken up into...
also be realized in phase space. Under the Wigner map, the density matrix transforms into the equivalent Wigner function, W ( x , p ) = d e f 1 π ℏ ∫...
this process, one can infer the atomic arrangement of a crystal. The Brillouin zone is a Wigner–Seitz cell of the reciprocal lattice. Reciprocal space...
continuum. Bound states in the continuum were first predicted in 1929 by Eugene Wigner and John von Neumann. Two potentials were described, in which BICs appear...
in Physics in 1963, which she shared with J. Hans D. Jensen and Eugene Wigner. In 1960, she was appointed full professor of physics at the University...
crystal is less than the theoretical density of the material. Frenkel defect Wigner effect Crystallographic defects Kittel, Charles (2005). Introduction to...
Before the 1970s the term was usually used in reference to the von Neumann–Wigner interpretation, but was later more closely associated with the purportedly...
and are used to create new states of matter including ionic liquids, Wignercrystals and Bose–Einstein condensates. This ability to manipulate the quantum...
the "transition state theory" of chemical reactions, formulated by Eugene Wigner, Henry Eyring, Michael Polanyi and M. G. Evans in the 1930s. The Eyring...
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