Metals usually become less conductive as they get thinner. Niobium phosphide, however, is different. According to researchers at Stanford University, US, a very thin film of this non-crystalline topological semimetal conducts electricity better than copper even in non-crystalline films. This surprising result could aid the development of ultrathin low-resistivity wires for nanoelectronics applications.

“As today’s electronic devices and chips become smaller and more complex, the ultrathin metallic wires that carry electrical signals within these chips can become a bottleneck when they are scaled down,” explains study leader Asir Intisar Khan, a visiting postdoctoral scholar and former PhD student in Eric Pop’s group at Stanford.

The solution, he says, is to create ultrathin conductors with a lower electrical resistivity to make the metal interconnects that enable dense logic and memory operations within neuromorphic and spintronic devices. “Low resistance will lead to lower voltage drops and lower signal delays, ultimately helping to reduce power dissipation at the system level,” Khan says.

The problem is that the resistivity of conventional metals increases when they are made into thin films. The thinner the film, the less good it is at conducting electricity.

Topological semimetals are different

Topological semimetals are different. Analogous to the better-known topological insulators, which conduct electricity along special edge states while remaining insulating in their bulk, these materials can carry large amounts of current along their surface even when their structure is somewhat disordered. Crucially, they maintain this surface-conducting property even as they are thinned down.

In the new work, Khan and colleagues found that the effective resistivity of non-crystalline films of niobium phosphide (NbP) decreases dramatically as the film thickness is reduced. Indeed, the thinnest films (< 5 nm) have resistivities lower than conventional metals like copper of similar thicknesses at room temperature.

Another advantage is that these films can be created and deposited on substrates at relatively low temperatures (around 400 °C). This makes them compatible with modern semiconductor and chip fabrication processes such as industrial back-end-of-line (BEOL). Such materials would therefore be relatively easy to integrate into state-of-the-art nanoelectronics. The fact that the films are non-crystalline is also an important practical advantage.

A “huge” collaboration

Khan says he began thinking about this project in 2022 after discussions with a colleague, Ching-Tzu Chen, from IBM’s TJ Watson Research Center. “At IBM, they were exploring the theory concept of using topological semimetals for this purpose,” he recalls. “Upon further discussion with Prof. Eric Pop, we wanted to explore the possibility of experimental realization of thin films of such semimetals at Stanford.”

This turned out to more difficult than expected, he says. While physicists have been experimenting with single crystals of bulk NbP and this class of topological semimetals since 2015, fabricating them at the ultrathin film limit of less than 5 nm at a temperature and using deposition methods compatible with industry and nanoelectronic fabrication was new. “We therefore had to optimize the deposition process from a variety of angles: substrate choice, strain engineering, temperature, pressure and stoichiometry, to name a few,” Khan tells Physics World.

The project turned out to be a “huge” collaboration in the end, with researchers from Stanford, Ajou University, Korea, and IBM Watson all getting involved, he adds.

The researchers says they will now be running further tests on their material. “We also think NbP is not the only material with this property, so there’s much more to discover,” Pop says.

The results are detailed in Science.

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Physicists at Penn State and Columbia University in the US say they have seen the “smoking gun” signature of an elusive quasiparticle predicted by theorists 16 years ago. Known as semi-Dirac fermions, the quasiparticles were spotted in a crystal of the topological semimetal ZrSiS and they have a peculiar property: they only behave like they have mass when they’re moving in a certain direction.

“When we shine infrared light on ZrSiS crystals and carefully measure the reflected light, we observed optical transitions that follow a unique power-law scaling, B^2/3, with B being the magnetic field,” explains Yinming Shao, a physicist at Penn State and lead author of a study in Physical Review X on the quasiparticle. “This special power-law turns out to be the exact prediction from 16 years ago of semi-Dirac fermions.”

The team performed the experiments using the 17.5 Tesla magnet at the US National High Magnetic Field Laboratory in Florida. This high field was crucial to the result, Shao explains, because applying a magnetic field to a material causes its electronic energy levels to become quantized into discrete (Landau) levels. The energy gap between these levels then depends on the electrons’ mass and the strength of the field.

Normally, the energy levels of the electrons should increase by set amounts as the magnetic field increases, but in this case they didn’t. Instead, they followed the B^2/3 pattern.

Realizing semi-Dirac fermions

Previous efforts to create semi-Dirac fermions relied on stretching graphene (a sheet of carbon just one atom thick) until the material’s two so-called Dirac points touch. These points occur in the region where the material’s valence and conduction bands meet. At these points, something special happens: the relationship between the energy and momentum of charge carriers (electrons and holes) in graphene is described by the Dirac equation, rather than the standard Schrödinger equation as is the case for most crystalline materials. The presence of these unusual band structures (known as Dirac cones) enables the charge carriers in graphene to behave like massless particles.

The problem is that making Dirac points touch in graphene turned out to require an unrealistically high level of strain. Shao and colleagues chose to work with ZrSiS instead because it also has Dirac points, but in this case, they exist continuously along a so-called nodal line. The researchers found evidence for semi-Dirac fermions at the crossing points of these nodal lines.

Interesting optical responses

The idea for the study stemmed from an earlier project in which researchers investigating a similar compound, ZrSiSe, spotted some interesting optical responses when they applied a magnetic field to the material out-of-plane. “I found that similar band-structure features that make ZrSiSe interesting would require applying a magnetic field in-plane for ZrSiS, so we carried out this measurement and indeed observed many unexpected features,” Shao says.

The greatest challenges, he recalls, was to figure out how to interpret the observations, since real materials like ZrSiS have a much more complicated Fermi surface than the ones that feature in early theoretical models. “We collaborated with many different theorists and eventually singled out the signatures originating from semi-Dirac fermions in this material,” he says.

The team still has much to understand about the material’s behaviour, he tells Physics World. “There are some unexplained fine electronic energy level-splitting in the data that we do not fully understand yet and which may originate from electronic interaction effects.”

As for applications, Shao notes that ZrSiS is a layered material, much like graphite – a form of carbon that is, in effect, made up of many layers of graphene. “This means that once we can figure out how to obtain a single layer cut of this compound, we can harness the power of semi-Dirac fermions and control its properties with the same precision as graphene,” he says.

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Physicists in the US have found an explanation for why electrons in a material called pentalayer moiré graphene carry fractional charges even in the absence of a magnetic field. This phenomenon is known as the fractional quantum anomalous Hall effect, and teams at the Massachusetts Institute of Technology (MIT), Johns Hopkins University and Harvard University/University of California, Berkeley have independently suggested that an interaction-induced topological “flat” band in the material’s electronic structure may be responsible.

Scientists already knew that electrons in graphene could, in effect, split into fractions of themselves in the presence of a very strong magnetic field. This is an example of the fractional quantum Hall effect, which occurs when a material’s Hall conductance is quantized at fractional multiples of e²/h.

In 2023, several teams of researchers introduced a new twist by observing this fractional quantization even without a magnetic field. The fractional quantum anomalous Hall effect, as it was dubbed, was initially observed in material called twisted molybdenum ditelluride (MoTe₂).

Then, in February this year, an MIT team led by physicist Long Ju spotted the same effect in pentalayer moiré graphene. This material consists of a layer of a two-dimensional hexagonal boron nitride (hBN) with five layers of graphene (carbon sheets just one atom thick) stacked on top of it. The graphene and hBN layers are twisted at a small angle with respect to each other, resulting in a moiré pattern that can induce conflicting properties such as superconductivity and insulating behaviour within the structure.

Answering questions

Although Ju and colleagues were the first to observe the fractional quantum anomalous Hall effect in graphene, their paper did not explain why it occurred. In the latest group of studies, other scientists have put forward a possible solution to the mystery.

According to MIT’s Senthil Todadri, the effect could stem from the fact that electrons in two-dimensional materials like graphene are confined in such small spaces that they start interacting strongly. This means that they can no longer be considered as independent charges that naturally repel each other. The Johns Hopkins team led by Ya-Hui Zhang and the Harvard/Berkeley team led by Ashvin Vishwanath and Daniel E Parker came to similar conclusions, and published their work in Physical Review Letters alongside that of the MIT team.

Crystal-like periodic patterns form an electronic “flat” band

Todadri and colleagues started their analyses with a reasonably realistic model of the pentalayer graphene. This model treats the inter-electron Coulomb repulsion in an approximate way, replacing the “push” of all the other electrons on any given electron with a single potential, Todadri explains. “Such a strategy is routinely employed in quantum mechanical calculations of, say, the structure of atoms, molecules or solids,” he notes.

The MIT physicists found that the moiré arrangement of pentalayer graphene induces a weak electron potential that forces electrons passing through it to arrange themselves in crystal-like periodic patterns that form a “flat” electronic band. This band is absent in calculations that do not account for electron–electron interactions, they say.

Such flat bands are especially interesting because electrons in them become “dispersionless” – that is, their kinetic energy is suppressed. As the electrons slow almost to a halt, their effective mass approaches infinity, leading to exotic topological phenomena as well as strongly correlated states of matter associated with high-temperature superconductivity and magnetism. Other quantum properties of solids such as fractional splitting of electrons can also occur.

“Mountain and valley” landscapes

So what causes the topological flat band in pentalayer graphene to form? The answer lies in the “mountain and valley” landscapes that naturally appear in the electronic crystal. Electrons in this material experience these landscapes as pseudo-magnetic fields, which affect their motion and, in effect, do away with the need to apply a real magnetic field to induce the fractional Hall quantization.

“This interaction-induced topological (‘valley-polarized Chern-1’) band is also predicted by our theory to occur in the four- and six-layer versions of multilayer graphene,” Todadri says. “These structures may then be expected to host phases where electron fractions appear.”

In this study, the MIT team presented only a crude treatment of the fractional states. Future work, Todadri says, may focus on understanding the precise role of the moiré potential produced by aligning the graphene with a substrate. One possibility, he suggests, is that it simply pins the topological electron crystal in place. However, it could also stabilize the crystal by tipping its energy to be lower than a competing liquid state. Another open question is whether these fractional electron phenomena at zero magnetic field require a periodic potential in the first place. “The important next question is to develop a better theoretical understanding of these states,” Todadri tells Physics World.

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