Many everyday objects have a property called chirality, or “handedness”, meaning that they look different when reflected in a mirror. For example, your right hand reflects into a left hand, and vice versa. Even microscopic particles can have this property; photons, particles of light, can be imparted with chirality to make them “left-handed” or “right-handed”, which can be useful for detecting toxic chemicals (see our previous blog post on chiral light).
Chirality also plays an important role in fundamental physics. According to theoretical predictions, if a matter particle (or fermion) has zero mass, it must possess a deeply-ingrained form of chirality that cannot be altered.
The catch is that no fundamental fermions are known to be truly massless. Electrons, for example, have a mass of around 10-30 kg. The elusive fermions known as neutrinos were once thought to be massless and hence intrinsically chiral, but experiments now show that they have an exceedingly small but nonzero mass.
Nanyang Assistant Professor Guoqing Chang (left) and Dr Mohammad Yahyavi (right) used computational studies to predict how chiral electrons influence the properties of materials like RhSi and CoSi. Photo credit: M. Fadly
Remarkably, however, chiral fermions can manifest in materials physics, allowing them to be studied in the laboratory. Nanyang Assistant Professor Guoqing Chang, a theoretical physicist at the School of Physical and Mathematical Sciences at Nanyang Technological University (NTU Singapore), has been exploring a new class of materials called higher-fold chiral semimetals. The electrons in these materials interact in a complicated way with the surrounding atoms, causing them to behave like massless chiral fermions.
Asst. Prof. Chang’s theoretical group has teamed up with the group of Professor M. Zahid Hasan, an experimentalist at Princeton University, to create higher-fold chiral semimetals. Their latest results, uncovering two novel properties of these materials, have been reported in Physical Review Letters and Nature Physics. Such materials may, in the future, be used in novel “opto-electronic” devices to emit and absorb light more efficiently.
A Material with a New Kind of Chiral Fermion
The higher-fold chiral semimetals developed by Asst. Prof. Chang and his collaborators are part of a broader class of materials known as topological semimetals. (The word “topological” refers to a mathematical concept used to classify materials; see some of our previous blog posts about topological materials here and here.)
When electrons flow through a material, their quantum states are grouped into different bands. An electrically insulating material has a band gap: a range of energies in which there are no bands, preventing electrons from moving. A topological semimetal, on the other hand, features a set of bands that barely touch (i.e., a band gap that barely closes). Near the band-touching energy, the electrons are described by formulas analogous to those of massless chiral fermions. (These electrons do not move at the actual speed of light, but at a reduced speed acting as an “effective speed of light”.)
The first topological semimetals, discovered in 2012, featured chiral electrons that behave like Weyl fermions—a hypothetical fundamental particle proposed in 1929, but never found by particle physicists. In 2016, however, a group of theorists suggested that there could also be topological semimetals based on chiral electrons with no counterpart in fundamental particle physics. A crucial feature of these chiral electrons is their “higher-fold degeneracy,” meaning that they occur where three or more bands touch. By contrast, the earlier Weyl-type topological semimetals have two touching bands.
In 2017–2018, Asst. Prof. Chang predicted in a series of papers that materials like rhodium silicide (RhSi) would be ideal candidates for observing chiral electrons with higher-fold degeneracy. Subsequently, several experimental groups attempted to create such materials, but none were able to find direct evidence for three-band chiral electrons.
The chemical structure of RhSi and CoSi (left). Calculations of the energy bands (right) were used to guide the experiments showing that these materials are indeed higher-fold topological semimetals. Figure credit: G. Chang et al.
In 2021, Asst. Prof. Chang realized that supplying RhSi with additional electrons could provide the missing “smoking gun” evidence for the theory. Using computational studies, his research group found that “doping” RhSi with nitrogen atoms progressively shifts the electron energies across the three chiral bands. Most importantly, unlike previously-studied materials, the doping would not distort the bands enough to spoil its identity as a topological semimetal.
To test these ideas, Asst. Prof. Chang contacted his longtime collaborator, Prof. Hasan of Princeton University, along with Prof. Shuang Jia of Peking University, and Prof. Claudia Felser of the Max Planck Institute in Germany, to synthesize and study RhSi. Using an experimental method known as angle-resolved photoemission spectroscopy (ARPES), Prof. Hasan’s group managed to study RhSi samples with doping levels of up to 5 percent (considered extraordinarily high in materials physics). The ARPES results gave the first unambiguous evidence for the existence of three chiral electron bands.
“Our experimental method allows us to directly visualize the new higher-fold chiral fermions,” said Tyler A. Cochran, a graduate student at Princeton University who was the lead author on the study. The findings were published in the journal Physical Review Letters in February 2023.
Strange Surfaces
In higher-fold topological semimetals, the Fermi arcs are unusually prominent and can easily intersect with each other. During their studies of RhSi, the team began to suspect that Fermi arc intersections could produce unusual material properties, never before been seen in other topological semimetals.
In computer simulations, when electrons on the surface of a higher-fold topological semimetal are plotted by their momentum, the “Fermi arcs” are visible as long strands (left). The touching of these Fermi arcs was observed in experiments (right). Left figure credit: G. Chang et al. Right figure excerpted from Sanchez et al., Nature Physics
At each intersection, two groups of electrons with exotic properties can interact easily with each other. Such electrons have a tendency to turn into quantum entities called strongly-correlated electron phases, which behave completely differently from the “weakly correlated” electrons in most materials (including most topological materials).
According to Asst. Prof. Chang’s calculations, the Fermi arc intersections in RhSi take place at much higher doping levels than what the team had previously studied. Armed with this insight, however, Prof. Hasan’s group managed to develop these higher-doped RhSi samples. They also identified and synthesized a new higher-fold topological semimetal, cobalt silicide (CoSi), in which Fermi arc intersections are more easily observable.
Using ARPES measurements, the team obtained evidence for the touching of Fermi arcs in the new experimental samples. These experimental features, known as “van Hove singularities of Fermi arcs” in the parlance of spectroscopy, have never before been observed. This work has been accepted for publication in an upcoming issue of Nature Physics, and has been available online since February 2023.
The Road Ahead for Chiral Fermion Materials
The team is now working to show that the van Hove singularities in topological chiral semimetals can give rise to strongly-correlated electron phases. Indeed, Asst. Prof. Chang notes that other experimentalists working on related materials have previously obtained results consistent with strongly-correlated electron phases. However, the role of Fermi arcs in these experimental findings has yet not been conclusively demonstrated.
The optical properties of higher-fold topological semimetals may also have technological potential. Due to peculiarities in the way chiral electrons interact with light, RhSi and CoSi may be able to absorb light beams, and convert them into different frequencies, more efficiently than other materials.
“Our calculations show optical resonances across multiple topological gaps can be enhanced by at least one order”, said Mohammad Yahyavi, a postdoctoral research fellow in Asst. Prof. Chang’s group at NTU Singapore. The collaboration is currently performing theoretical and experimental studies to investigate this possibility.
References
Tyler A. Cochran et al., Visualizing Higher-Fold Topology in Chiral Crystals, Physical Review Letters 130, 066402 (2023)
D. S. Sanchez et al., Tunable topologically driven Fermi arc van Hove singularities, Nature Physics (2023)