An electron is an elementary particle with a negative elementary charge. That supposed integral negativity is positively compensated by protons, thereby providing the balancing incentive for atomic matter. This fundamental physical charge constant is now known to be violated in everyday matter. Fractional charges have been found.

The quantization of natural phenomenon is the bedrock of modern physics. In 1900, German physicist Max Planck theorized that existence is naturally chunky, not continuous. All physical constructs, and even time, emanate from quantized coherencies.

Charge is theoretically quantized, coming in integer multiples of individual small units called the elementary charge – *e* – about 1.602×10^{-19} coulombs, which is the smallest charge which can exist ‘freely’. Or so it has been assumed. The idea of independence (‘freely’) is an ill-supported supposition, for all of existence is entangled.

Quarks combine in 3somes to comprise atomic nuclei: protons and neutrons. Each quark carries a 1/3 charge – whence the complete charge of protons, and, oddly, chargeless neutrons. Tetraquark particles with fractional charges exist, albeit only (supposedly) in high-energy environments.

Italian physicist Carmine Ortix elaborates: “The constituents of matter have a charge that is an integer multiple of *e*. Nevertheless, solitary physical entities that carry a fractional charge can be formed in many-particle systems as end products of processes called emergent phenomena. Such entities typically arise as excitations (quasiparticles) in certain solid-state structures that have strong electron interactions.”

Quasiparticles are emulations of integral subatomic particles by forces which are only coherent fakirs of quantum actors. Excitations are bosonic pretenders. Bosons are the hypothetical outfitters for fermions, which pose as quantum constructors of the physical world.

Ortix continues: “Crystalline solids consist of a spatially periodic array of atoms. Because the number of atoms in a solid is of the order of Avogadro’s number (6 × 10^{23}), such an array can be considered infinite. Consequently, the structure looks the same from whichever position in the atomic lattice the solid is viewed – a property known as discrete translational symmetry. Crystals are further characterized by geometric transformations, such as rotations and reflections, that leave the structure unchanged. For example, a square lattice looks the same after consecutive rotations of 90°.

“Crystal defects are regions in which this ideal symmetrical structure is distorted. Disclinations are defects that disrupt the rotational symmetry in a certain area of the solid. A simple way to picture a disclination is to consider a process devised by the Italian mathematician Vito Volterra: take, for instance, a square lattice, remove an entire quadrant from it, and then bend the structure to attach the lone edges.”

The figure below illustrates this process.

A disclination is characterized by specific deformation. In the example shown, a) a quadrant is removed from a square atomic lattice, and the structure is bent to attach the lone edges. b) A disclination can trap a fractional electric charge that comes in units of *e*/4, where *e* is the charge of a single electron. c) In the instance of a hexagonal lattice, a disclination may hold an *e*/6 charge.

Disclinations naturally occur in materials during their growth or from deformation. Owing to energetic economy, disclinations usually form in closely spaced pairs. Forming a single disclination would be a waste of elastic energy: the energy stored when the structure is distorted. In each pair, for each Frank angle, one disclination has a negative value and the other a positive value. A Frank angle represents the relative wedge of material removed from or added to the ideal crystal to produce the defect.

Fractional charges result from breaking the symmetry which defines crystals. Physics models suppose that existence itself results from the breaking of symmetry.

Fractional charges exemplify the byzantine intricacy by which the show we call Nature is constructed. In an exposition of endless complexity, what appears to be integral is instead divisible ad infinitum. Though the principle of localized quantization is apt, Planck’s “quantum of action” is an expression of approximation.

References:

Figure courtesy of *Nature* magazine (their copyright 2021, used via the “fair use” exemption for non-profit educational material).

Carmine Ortix, “Electrons broken into pieces at crystal defects,” *Nature* (20 January 2021).

Christopher W. Peterson *et al*, “Trapped fractional charges at bulk defects in topological insulators,” *Nature* (20 January 2021).

Yang Liu *et al*, “Bulk–disclination correspondence in topological crystalline insulators,” *Nature* (20 January 2021).

Ishi Nobu, “Quasiparticles,” (29 December 2019).

Figure courtesy of *Nature* magazine (their copyright 2021, used via the “fair use” exemption for non-profit educational material.)