A fundamental physical constant known as the elementary charge, e, indicates the electric charge of a single electron. 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 interactions1. In the past few years, researchers have predicted that the equilibrium state of peculiar materials known as topological crystalline insulators2 could contain fractionally charged objects that stick to imperfections in the material structure3,4. In two papers in Nature, Peterson et al.5 and Liu et al.6 bring this concept to reality by reporting experimental observations of fractional charges at structural defects called disclinations.
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 × 1023), 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. And disclinations, in particular, 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 Volterra7: take, for instance, a square lattice, remove an entire quadrant from it, and then bend the structure to attach the lone edges (Fig. 1a).
Disclinations naturally occur in materials during their growth or as a response to mechanical deformation. These imperfections usually form in closely spaced pairs because it would require too much elastic energy (the energy stored when the structure is distorted) to form a single disclination. In each pair, one disclination has a negative value and the other a positive value for the Frank angle — a quantity that measures the wedge of material removed from or added to the ideal crystal to produce the defect. However, this feature represents a major roadblock to the direct observation of solitary trapped charges because the disclinations in each pair electrically neutralize each other.
The two research teams got around this problem by using synthetic structures called metamaterials. Peterson et al. constructed a metamaterial in which electric-circuit elements act as artificial atoms, and Liu et al. made one in which the artificial atoms are structures known as optical waveguides. Because metamaterials can be built one artificial atom at a time, producing a single disclination does not need elastic energy. Moreover, metamaterials can be engineered to mimic the properties of almost all materials, including the topological crystalline insulators in question.
But perhaps more central to the findings of both teams is that the distance between the artificial atoms can even be on the scale of a few centimetres — 100 million times larger than the distance between atoms in a material. Consequently, the teams could probe the local distribution of the synthetic electric charge with unprecedented precision, and show that a fractional charge accumulates at the disclination cores. This charge is precisely quantized (it has discrete values) and is a bulk quantity (it is independent of the specific details of how the disclination was engineered). Peterson et al. found that the charge is quantized in units of e/4 for a square lattice (Fig. 1b). By contrast, Liu et al. showed that it is quantized in units of e/6 for a hexagonal lattice (Fig. 1c).
The techniques developed by both teams to detect such a bulk quantity are not limited to metamaterials of topological crystalline insulators. For example, one might probe quantized charges in quantum materials called fragile topological insulators, which have been discovered in the past few years8. Unlike the topological insulators found in the mid-2000s9,10, these materials lack any spectral signature, and their properties remain uncertain.
Fractional charges could also be explored at dislocations — defects in which it is the discrete translational symmetry of the crystalline structure that is locally broken. Unlike disclinations, these defects are (at least somewhat) mobile because they can move freely in certain directions. This property endows the fractional charges trapped by dislocations with a dynamic capability resembling those of fractionally charged quasiparticles.
Because the formation of dislocations requires less elastic energy than does that of disclinations, fractional charges trapped at these defects might even be observable in a conventional material, rather than in just metamaterials. But many challenges remain before this vision can become a reality. For instance, the number of materials hosting fractional charges is limited by an intrinsic property of electrons called spin that is absent in metamaterials. This property doubles the values of the trapped charges and can mask their quantized fractional nature, so material candidates should be carefully selected. Detecting fractional charges would also require local probe techniques, such as scanning tunnelling spectroscopy, to be pushed to their resolution limits. The efforts will be huge, but the successes of the current studies make the observation of fractional charges at material defects more likely in the foreseeable future.
Nature 589, 356-357 (2021)