Wigner crystal
[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.
The uniform, neutralizing background then gives rise to a smeared positive charge of density
[11] It is believed that ions, such as those of iron, form a Wigner crystal in the interiors of white dwarf stars.
In practice, it is difficult to experimentally realize a Wigner crystal because quantum mechanical fluctuations overpower the Coulomb repulsion and quickly cause disorder.
One notable example occurs in quantum dots with low electron densities or high magnetic fields where electrons will spontaneously localize in some situations, forming a so-called rotating "Wigner molecule",[12] a crystalline-like state adapted to the finite size of the quantum dot.
Wigner crystallization in a two-dimensional electron gas under high magnetic fields was predicted (and was observed experimentally)[13] to occur for small filling factors[14] (less than
,[15] and led to a new understanding[16] (based on the pinning of a rotating Wigner molecule) for the interplay between quantum-liquid and pinned-solid phases in the lowest Landau level.
The device design allowed the electron density in the 1D channel to vary relatively independently of the strength of transverse confining potential, thus allowing experiments to be performed in the regime in which Coulomb interactions between electrons dominate the kinetic energy.
In a strictly 1D system, electrons occupy equidistant points along a line, i.e. a 1D Wigner crystal.
[19][20] The evidence of a double row observed by Hew et al. may point towards the beginnings of a Wigner crystal in a 1D system.
It provides direct evidence and a better understanding of the nature of zigzag Wigner crystallization by unveiling both the structural and the spin phase diagrams.
[22] In 2024, physicists managed to directly image a Wigner crystal with a scanning tunneling microscope.
[23][24] Some layered Van der Waals materials, such as transition metal dichalcogenides have intrinsically large rs values which exceed the 2D theoretical Wigner crystal limit rs=31~38.
The origin of the large rs is partly due to the suppressed kinetic energy arising from a strong electron phonon interaction which leads to polaronic band narrowing, and partly due to the low carrier density n at low temperatures.
[25] Thus, Wigner crystal superlattices in so-called CDW systems may be considered to be the first direct observation of ordered electron states localised by mutual Coulomb interaction.
An important criterion for is the depth of charge modulation, which depends on the material, and only systems where rs exceeds the theoretical limit can be regarded as Wigner crystals.
In 2020, a direct image of a Wigner crystal observed by microscopy was obtained in molybdenum diselenide/molybdenum disulfide (MoSe2/MoS2) moiré heterostructures.
[26][27] A 2021 experiment created a Wigner crystal near 0K by confining electrons using a monolayer sheet of molybdenum diselenide.
The resulting electron spacing was around 20 nanometers, as measured by the stationary appearance of light-agitated excitons.
