This is part two of a two-part series on Weyl semimetals and Weyl fermions, newly discovered materials and particles that have drawn great interest from physicists at JQI and the Condensed Matter Theory Center at the University of Maryland. The second part focuses on the theoretical questions about Weyl materials that Maryland researchers are exploring. Part one, which was published last week, introduced their history and basic physics. If you haven’t read part one, we encourage you to head there first before getting into the details of part two.

The 2015 discovery of a Weyl semimetal—and the Weyl fermions it harbored—provoked a flurry of activity from researchers around the globe. A quick glance at a recent physics journal or the online arXiv preprint server testifies to the topic’s popularity. The arXiv alone has had more than 200 papers on Weyl semimetals posted in 2016.

Researchers at JQI and the Condensed Matter Theory Center (CMTC) at the University of Maryland have been interested in Weyl physics since before last summer’s discovery, publishing 18 papers on the topic over the past two years. In all, more than a dozen scientists at Maryland have been working to understand the fundamental properties of these curious new materials.

In addition to studying specific topics, researchers are also realizing that the physics of Weyl fermions—particles first studied decades ago in different setting—might have wider reach. They may account for the low-energy behavior of certain superconductors and other materials, especially those that are strongly correlated—that is, materials in which interactions between electrons cannot be ignored.

"Weyl physics should be abundant in many, many correlated materials," says Pallab Goswami, a theorist and postdoctoral researcher at JQI and CMTC. "If we can understand the exotic thermodynamic, transport and electrodynamic properties of Weyl fermions, we can probably understand more about low temperature physics in general," Goswami says.

Taking a wider approach

Goswami is not only interested in discovering new Weyl semimetals. He also wants to find strongly interacting materials where Weyl semimetal physics can help explain unresolved puzzles. That behavior is often related to the unique magnetic properties of Weyl fermions.

Recently, he and several colleagues examined a family of compounds known as pyrochlore iridates, formed from iridium, oxygen and a rare earth element such as neodymium or praseodymium. While most of these are insulators at low temperatures, the compound with praseodymium is an exception. It remains a metal and, intriguingly, has an anomalous current that flows without any external influence. This current, due to a phenomenon called the Hall effect, appears in other materials, but it is usually driven by an applied magnetic field or the magnetic properties of the material itself. In the praseodymium iridate, though, it appears even without a magnetic field and despite the fact that the compound has no magnetic properties that have been seen by experiment.

Goswami and his colleagues have argued that Weyl fermions can account for this puzzling behavior. They can distort a material’s magnetic landscape, making it look to other particles as if a large magnetic field is there. This effect is hard to spot in the lab, though, due to the challenge of keeping samples at very cold temperatures. The team has suggested how future experiments might confirm the presence of Weyl fermions through precise measurements with a scanning tunneling microscope.

On the surface

Parallel to Goswami’s efforts to expand the applications of Weyl physics, Johannes Hofmann, a former JQI and CMTC theorist who is now at the University of Cambridge in the UK, is diving into the details of Weyl semimetals. Hofmann has studied Weyl semimetals divorced from any real material and predicted a generic behavior that electrons on the surface of a semimetal will have. It’s a feature that could ultimately find applications to electronics and photonics.

In particular, he studied undulating charge distributions on the surface of semimetals, created by regions with more electrons and regions with less. Such charge fluctuations are dynamic, moving back and forth in response to their mutual electrical attraction, and in Weyl semimetals they support waves that move in only one direction.

The charge fluctuations generate electric and magnetic fields just outside the surface. And on the surface, positive and negative regions are packed close together—so close, in fact, that their separation can be much smaller than the wavelength of visible light. Since these fluctuations occur on such a small scale, they can also be used to detect small features in other objects. For instance, bringing a sample of some other material near the surface will modify the distribution of charges in a way that could be measured. Getting the same resolution with light would require high-energy photons that could destroy the object being imaged. Indeed, researchers have already shown that this is a viable imaging technique, as demonstrated in experiments with ordinary metals.

On the surface of Weyl semimetals one-way waves can travel through these charge fluctuations. Ordinary metals, too, can carry waves but require huge magnetic fields to steer them in only one direction. Hofmann showed that in a Weyl semimetal, it’s possible to create these waves without a magnetic field, a fact that could enable applications of the materials to microscopy and lithography.

Too much disorder?

Although many studies imagine that Weyl materials are perfectly clean, such a situation rarely occurs in real experiments. Contaminants inevitably lodge themselves into the ideal crystal structure of any solid. Consequently, JQI scientists have looked at how disorder—the dirt that prevents samples from behaving like perfect theoretical models—affects the properties of Weyl materials. Their work has settled an argument theorists have been having for years.

One camp thought that weak disorder—dirt that doesn’t cause big changes—was essentially harmless to Weyl semimetals, since tiny wobbles in the material's electrical landscape could safely be ignored. The other camp argued that certain fluctuations, though weak, affect a wide enough area of the landscape that they cannot be ignored.

Settling the dispute took intense numerical study, requiring the use of supercomputing resources at Maryland. "It was very hard to do this," says Jed Pixley, a postdoctoral researcher at JQI and CMTC who finally helped solve the disorder conundrum. "It turns out that the effects of large local fluctuations of the disorder are weak, but they’re there."

Pixley’s calculations found that large regions of weak disorder create a new type of low-energy excitation, in addition to Weyl fermions. These new excitations live around the disordered regions and divert energy away from the Weyl fermion quasiparticles. The upshot is that the quasiparticles have a finite lifetime, instead of the infinite lifetime predicted by previous studies. The result has consequences for the stability of Weyl semimetals in a technical sense, although the lifetime of the quasiparticles is still quite long. In typical experiments, the effects of large areas of disorder would be tough to spot, although experiments on Weyl semimetals are still in their early days.

Research into Weyl materials shows little sign of slowing down. And the broader role that Weyl fermions play in condensed matter physics is still evolving and growing, with many more surprises likely in the future. As more and more experimental groups join the hunt for exotic physics, theoretical investigations, like those of the scientists at JQI and CMTC, will be crucial to identifying new behaviors and suggesting new experiments, steering the study of Weyl physics toward new horizons.