Thread by @anderssandberg

#FridayPhysicsFun – Normal crystals consist of atoms or molecules arranged in a regular lattice. Recently there has been experimental demonstrations of 2D Wigner crystals – crystals made of just electrons.
quantamagazine.org/physicists-cre…

The idea is pretty old: Eugene Wigner proposed in 1934 that electrons would repel each other and if the density was low enough form a lattice. The repulsion dominates over the kinetic energy and makes it “solid”.
en.wikipedia.org/wiki/Wigner_cr…

Too high density and they “quantum melt” as the kinetic energy dominates and the lattice dissolves. Too high temperature and they melt normally because of thermal vibration. 3D Wigner crystals need a lower density than 2D crystals to solidify.

Previous work involved 1D crystals, quantum dots, on liquid helium or using magnetic fields (uncertain). The recent results involve electrons trapped in thin conducting layers, forming a neat triangular lattice. arxiv.org/abs/2010.03037 arxiv.org/abs/2010.03078

In quantum dots one can keep a handful of electrons, forming a “Wigner molecule” where they arrange themselves neatly. arxiv.org/abs/0711.0637

The same is true for the crystals on liquid helium: electrons can float on the helium, forming “nanoislands”. There has been interest in turning them into qubits for quantum computing.
physics.aps.org/articles/v2/4
en.wikipedia.org/wiki/Electron-…

Ions trapped in ion traps also form similar patterns.

arxiv.org/abs/1411.4945

These patterns are related to “The Thomson problem”, how to distribute N charges on or in a sphere or other shape with minimal energy. J.J. Thomson tried to construct an atomic model based on this in 1905.
ub.edu/hcub/hfq/sites…
en.wikipedia.org/wiki/Thomson_p…

This is also related to the stability of things packed on spheres (like virus proteins or lipid bilayers), where it is important to know what kind of grain boundaries and defects emerge.
cnls.lanl.gov/external/Kac%2…
journals.aps.org/prl/abstract/1…
arxiv.org/pdf/0812.3064.…

The problem of distributing points evenly is found in lot of applications, such as half-toning in graphics. You want even distances yet avoid too regular pattern. Random distribution doesn’t cut it but melted Wigner crystal does. en.wikipedia.org/wiki/Dither page.math.tu-berlin.de/~steidl/PDFs/G…

While Wigner crystals are fragile on Earth, the counterpart where ionized nuclei form a crystal surrounded by a sea of electrons, Coulomb crystals, are believed to form much of white dwarfs and the crust of neutron stars. They are potentially very strong.

I have been interested in Wigner crystals held in the potential of neutrino stars as a very hypothetical computational medium for very far future computing. They would be stable against proton decay, and maybe able to perform collision-based computation. hal.archives-ouvertes.fr/hal-00461197/d…