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A warm welcome for Weyl physics

A rendering of a semimetal band structure in which bands touch at single points. (Credit: S. Kelley/NIST)

This is part one of a two-part series on Weyl semimetals and Weyl fermions, newly discovered materials and particles that have drawn great interest from researchers at JQI and the Condensed Matter Theory Center at the University of Maryland. The first part focuses on the history and basic physics of these materials. Part two focuses on theoretical work at Maryland.

For decades, particle accelerators have grabbed headlines while smashing matter together at faster and faster speeds. But in recent years, alongside the progress in high-energy experiments, another realm of physics has been taking its own exciting strides forward.

That realm, which researchers call condensed matter physics, studies chunks of matter moving decidedly slower than the protons in the LHC. In fact, the materials under study—typically solids or liquids—are usually sitting still. That doesn't make them boring, though. Their calm appearance can often hide exotic physics that arises from their microscopic activity.

"In condensed matter physics, the energy scales are much lower," says Pallab Goswami, a postdoctoral researcher at JQI and the Condensed Matter Theory Center (CMTC) at the University of Maryland. "We want to go to lower energies and find new phenomena, which is exactly the opposite of what is done in particle physics."

Historically, that's been a fruitful approach. The field has explained the physics of semiconductors—like the silicon that makes computer chips—and many superconductors, which generate the large magnetic fields required for clinical MRI machines.

Over the past decade, that success has continued. In 2004, researchers at the University of Manchester in the UK discovered a way to make single-atom-thick sheets of carbon by sticking Scotch tape onto graphite and peeling it off. It was a shockingly low-tech way to make graphene, a material with stellar electrical properties and incredible strength, and it led quickly to a Nobel Prize in physics in 2010.

A few years later, researchers discovered topological insulators, materials that trap their internal electrons but let charges on the surface flow freely. It’s a behavior that requires sophisticated math to explain—math that earned three researchers a share of the 2016 Nobel Prize in physics for theoretical discoveries that ultimately explain the physics of these and other materials.

In 2012, experimentalists studying the junction between a superconductor and a thin wire spotted evidence for Majorana fermions, particles that behave like uncharged electrons. Originally studied in the context of high-energy physics, these exotic particles never showed up in accelerators, but scientists at JQI predicted that they might make an appearance at much lower energies.

Last year, separate research groups at Princeton University, MIT and the Chinese Academy of Sciences discovered yet another exotic material—a Weyl semimetal—and with it yet another particle: the Weyl fermion. It brought an end to a decades-long search that began in the 1930s and earned acclaim as a top-10 discovery of the year, according to Physics World.

Like graphene, Weyl semimetals have appealing electrical properties and may one day make their way into electronic devices. But, perhaps more intriguingly for theorists, they also share some of the rich physics of topological insulators and have provoked a flurry new research. Scientists working with JQI Fellow Sankar Das Sarma, the Director of CMTC, have published 18 papers on the subject since 2014.

Das Sarma says that the progress in understanding solid state materials over the past decade has been astonishing, especially the discovery of phenomena researchers once thought were confined to high-energy physics. “It shows how clever nature is, as concepts and laws developed in one area of physics show up in a completely disparate area in unanticipated ways,” he says.

An article next week will explore some of the work on Weyl materials at JQI and CMTC. This week's story will focus on the fundamental physics at play in these unusual materials.

Spotted at long last

Within two weeks last summer, three research groups reported evidence for Weyl semimetals. Teams from the US and China measured the energy of electrons on the surface of tantalum arsenide, a metallic crystal that some had predicted might be a semimetal. By shining light on the material and capturing electrons ejected from the sample, researchers were able to map out a characteristic sign of Weyl semimetals—a band of energies that electrons on the surface inhabit, known as a Fermi arc. It was a feature predicted only for Weyl semimetals.

Much of the stuff on Earth, from wood and glass to copper and water, is not a semimetal. It's either an insulator, which does a bad job of conducting electricity, or a conductor, which lets electrical current flow with ease.

Quantum physics ultimately explains the differences between conductors, insulators, semiconductors and semimetals. The early successes of quantum physics—like explaining the spectrum of light emitted by hydrogen atoms—revolved around the idea that quantum objects have discrete energy levels. For instance, in the case of hydrogen, the single electron orbiting the nucleus can only occupy certain energies. The pattern of light emanating from hot hydrogen gas matches up with the spacing between these levels.

In a solid, which has many, many atoms, electrons still occupy a discrete set of energies. But with so many electrons come many more levels, and those levels tend to bunch together. This leads to a series of energy bands, where electrons can live, and gaps, where they can't. The figure below illustrates this.

Electrons pile into these bands, filling up the allowed energies and skipping the gaps. Depending on where in the band structure the last few electrons sit, a material will have dramatically different electrical behavior. Insulators have an outer band that is completely filled up, with an energy gap to a higher empty band. Metals have their most energetic electrons sitting in a partially filled band, with lots of slightly higher energies to jump to if they are prodded by a voltage from a battery.

A Weyl semimetal is a different beast. There, electrons pile in and completely fill a band, but there is no gap to the higher, unfilled band. Instead, the two touch at isolated points, which are responsible for some interesting properties of Weyl materials.

Quasiparticles lead the charge

We often think of electrons as carrying the current in a wire, but that’s not the whole story. The charge carriers look like electrons, but due to their microscopic interactions they behave like they have a different mass. These effective charge carriers, which have different properties in different materials, are called quasiparticles.

By examining a material's bands and gaps, it's possible to glean some of the properties of these quasiparticles. For a Weyl semimetal, the charge carriers satisfy an equation first studied in 1929 by a German mathematician named Hermann Weyl, and they are now called Weyl fermions.

But the structure of the bands doesn't capture everything about the material, says Johannes Hofmann, a former postdoctoral researcher at JQI and CMTC who is now at the University of Cambridge. "In a sense, these Weyl materials are very similar to graphene," Hofmann says. "But they are not only described by the band structure. There is a topological structure as well, just as in topological insulators."

Hofmann says that although the single-point crossings in the bands play an important role, they don't tell the whole story. Weyl semimetals also have a topological character, which means that the overall shape of the bands and gaps, as well as the way electrons spread out in space, affect their properties. Topology can account for these other properties by capturing the global differences in these shapes, like the distinction between an untwisted ribbon and a Moebius strip.

The interplay between the topological structure and the properties of Weyl materials is an active area of research. Experiments, though, are still in the earliest stages of sorting out these questions.

A theorist’s dream

Researchers at JQI and elsewhere are studying many of the theoretical details, from the transport properties on the surfaces of Weyl materials to the emergence of new types of order. They are even finding Weyl physics useful in tackling condensed matter quandaries that have long proved intractable.

Jed Pixley, a postdoctoral researcher at CMTC, has studied how Weyl semimetals behave in the presence of disorder. Pixley says that such investigations are crucial if Weyl materials are to find practical applications. "If you are hoping semimetals have these really interesting aspects,” he says, “then things better not change when they get a little dirty."

Please return next week for a sampling of the research into Weyl materials underway at JQI and CMTC. Written by Chris Cesare with illustrations and figures by Sean Kelley.

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