A Princeton-led study has revealed an emergent electronic behavior on the surface of bismuth crystals that could lead to insights on the growing area of technology known as “valleytronics.”

The term refers to energy valleys that form in crystals and that can trap single electrons. These valleys potentially could be used to store information, greatly enhancing what is capable with modern electronic devices.

In the new study, researchers observed that electrons in bismuth prefer to crowd into one valley rather than distributing equally into the six available valleys. This behavior creates a type of electricity called ferroelectricity, which involves the separation of positive and negative charges onto opposite sides of a material. This study was made available online in May 2018 and published this month in Nature Physics.

The finding confirms a recent prediction that ferroelectricity arises naturally on the surface of bismuth when electrons collect in a single valley. These valleys are not literal pits in the crystal but rather are like pockets of low energy where electrons prefer to rest.

The researchers detected the electrons congregating in the valley using a technique called scanning tunneling microscopy, which involves moving an extremely fine needle back and forth across the surface of the crystal. They did this at temperatures hovering close to absolute zero and under a very strong magnetic field, up to 300,000 times greater than Earth’s magnetic field.

The behavior of these electrons is one that could be exploited in future technologies. Crystals consist of highly ordered, repeating units of atoms, and with this order comes precise electronic behaviors. Silicon’s electronic behaviors have driven modern advances in technology, but to extend our capabilities, researchers are exploring new materials. Valleytronics attempts to manipulate electrons to occupy certain energy pockets over others.

The existence of six valleys in bismuth raises the possibility of distributing information in six different states, where the presence or absence of an electron can be used to represent information. The finding that electrons prefer to cluster in a single valley is an example of “emergent behavior” in that the electrons act together to allow new behaviors to emerge that wouldn’t otherwise occur, according to Mallika Randeria, the first author on the study and a graduate student at Princeton working in the laboratory of Ali Yazdani, the Class of 1909 Professor of Physics.

“The idea that you can have behavior that emerges because of interactions between electrons is something that is very fundamental in physics,” Randeria said. Other examples of interaction-driven emergent behavior include superconductivity and magnetism.

The general public might think of the 21st century as an era of revolutionary technological platforms, such as smartphones or social media. But for many scientists, this century is the era of another type of platform: two-dimensional materials, and their unexpected secrets.

When two monolayers of WTe2 are stacked into a bilayer, a spontaneous electrical polarization appears, one layer becoming positively charged and the other negatively charged. This polarization can be flipped by applying an electric field. Credit: Joshua Kahn

These 2-D materials can be prepared in crystalline sheets as thin as a single monolayer, only one or a few atoms thick. Within a monolayer, electrons are restricted in how they can move: Like pieces on a board game, they can move front to back, side to side or diagonally — but not up or down. This constraint makes monolayers functionally two-dimensional.

The 2-D realm exposes properties predicted by quantum mechanics — the probability-wave-based rules that underlie the behavior of all matter. Since graphene — the first monolayer — debuted in 2004, scientists have isolated many other 2-D materials and shown that they harbor unique physical and chemical properties that could revolutionize computing and telecommunications, among other fields.

For a team led by scientists at the University of Washington, the 2-D form of one metallic compound — tungsten ditelluride, or WTe2 — is a bevy of quantum revelations. In a paper published online July 23 in the journal Nature, researchers report their latest discovery about WTe2: Its 2-D form can undergo “ferroelectric switching.” They found that when two monolayers are combined, the resulting “bilayer” develops a spontaneous electrical polarization. This polarization can be flipped between two opposite states by an applied electric field.

“Finding ferroelectric switching in this 2-D material was a complete surprise,” said senior author David Cobden, a UW professor of physics. “We weren’t looking for it, but we saw odd behavior, and after making a hypothesis about its nature we designed some experiments that confirmed it nicely.”

Materials with ferroelectric properties can have applications in memory storage, capacitors, RFID card technologies and even medical sensors.

“Think of ferroelectrics as nature’s switch,” said Cobden. “The polarized state of the ferroelectric material means that you have an uneven distribution of charges within the material — and when the ferroelectric switching occurs, the charges move collectively, rather as they would in an artificial electronic switch based on transistors.”

The UW team created WTe2 monolayers from its the 3-D crystalline form, which was grown by co-authors Jiaqiang Yan at Oak Ridge National Laboratory and Zhiying Zhao at the University of Tennessee, Knoxville. Then the UW team, working in an oxygen-free isolation box to prevent WTe2 from degrading, used Scotch Tape to exfoliate thin sheets of WTe2 from the crystal — a technique widely used to isolate graphene and other 2-D materials. With these sheets isolated, they could measure their physical and chemical properties, which led to the discovery of the ferroelectric characteristics.

WTe2 is the first exfoliated 2-D material known to undergo ferroelectric switching. Before this discovery, scientists had only seen ferroelectric switching in electrical insulators. But WTe2 isn’t an electrical insulator; it is actually a metal, albeit not a very good one. WTe2 also maintains the ferroelectric switching at room temperature, and its switching is reliable and doesn’t degrade over time, unlike many conventional 3-D ferroelectric materials, according to Cobden. These characteristics may make WTe2 a promising material for smaller, more robust technological applications than other ferroelectric compounds.

“The unique combination of physical characteristics we saw in WTe2 is a reminder that all sorts of new phenomena can be observed in 2-D materials,” said Cobden.

Ferroelectric switching is the second major discovery Cobden and his team have made about monolayer WTe2. In a 2017 paper in Nature Physics, the team reported that this material is also a “topological insulator,” the first 2-D material with this exotic property.

In a topological insulator, the electrons’ wave functions — mathematical summaries of their quantum mechanical states — have a kind of built-in twist. Thanks to the difficulty of removing this twist, topological insulators could have applications in quantum computing — a field that seeks to exploit the quantum-mechanical properties of electrons, atoms or crystals to generate computing power that is exponentially faster than today’s technology. The UW team’s discovery also stemmed from theories developed by David J. Thouless, a UW professor emeritus of physics who shared the 2016 Nobel Prize in Physics in part for his work on topology in the 2-D realm.

Cobden and his colleagues plan to keep exploring monolayer WTe2 to see what else they can learn.

“Everything we have measured so far about WTe2 has some surprise in it,” said Cobden. “It’s exciting to think what we might find next.”

Scientists are experimenting with narrow strips of graphene, called nanoribbons, in hopes of making cool new electronic devices, but University of California, Berkeley scientists have discovered another possible role for them: as nanoscale electron traps with potential applications in quantum computers.

This is a scanning tunneling microscope image of a topological nanoribbon superlattice. Electrons are trapped at the interfaces between wide ribbon segments (which are topologically non-trivial) and narrow ribbon segments (which are topologically trivial). The wide segments are 9 carbon atoms across (1.65 nanometers) while the narrow segments are only 7 carbon atoms across (1.40 nanometers). Credit: Michael Crommie, Felix Fischer, UC Berkeley

Graphene, a sheet of carbon atoms arranged in a rigid, honeycomb lattice resembling chicken wire, has interesting electronic properties of its own. But when scientists cut off a strip less than about 5 nanometers in width – less than one ten-thousandth the width of a human hair – the graphene nanoribbon takes on new quantum properties, making it a potential alternative to silicon semiconductors.

UC Berkeley theoretician Steven Louie, a professor of physics, predicted last year that joining two different types of nanoribbons could yield a unique material, one that immobilizes single electrons at the junction between ribbon segments.

In order to accomplish this, however, the electron “topology” of the two nanoribbon pieces must be different. Topology here refers to the shape that propagating electron states adopt as they move quantum mechanically through a nanoribbon, a subtle property that had been ignored in graphene nanoribbons until Louie’s prediction.

Two of Louie’s colleagues, chemist Felix Fischer and physicist Michael Crommie, became excited by his idea and the potential applications of trapping electrons in nanoribbons and teamed up to test the prediction. Together they were able to experimentally demonstrate that junctions of nanoribbons having the proper topology are occupied by individual localized electrons.

A nanoribbon made according to Louie’s recipe with alternating ribbon strips of different widths, forming a nanoribbon superlattice, produces a conga line of electrons that interact quantum mechanically. Depending on the strips’ distance apart, the new hybrid nanoribbon is either a metal, a semiconductor or a chain of qubits, the basic elements of a quantum computer.

“This gives us a new way to control the electronic and magnetic properties of graphene nanoribbons,” said Crommie, a UC Berkeley professor of physics. “We spent years changing the properties of nanoribbons using more conventional methods, but playing with their topology gives us a powerful new way to modify the fundamental properties of nanoribbons that we never suspected existed until now.”

Louie’s theory implies that nanoribbons are topological insulators: unusual materials that are insulators, that is, non-conducting in the interior, but metallic conductors along their surface. The 2016 Nobel Prize in Physics was awarded to three scientists who first used the mathematical principles of topology to explain strange, quantum states of matter, now classified as topological materials.

Three-dimensional topological insulators conduct electricity along their sides, sheets of 2D topological insulators conduct electricity along their edges, and these new 1D nanoribbon topological insulators have the equivalent of zero-dimensional (0D) metals at their edges, with the caveat that a single 0D electron at a ribbon junction is confined in all directions and can’t move anywhere. If another electron is similarly trapped nearby, however, the two can tunnel along the nanoribbon and meet up via the rules of quantum mechanics. And the spins of adjacent electrons, if spaced just right, should become entangled so that tweaking one affects the others, a feature that is essential for a quantum computer.

The synthesis of the hybrid nanoribbons was a difficult feat, said Fischer, a UC Berkeley professor of chemistry. While theoreticians can predict the structure of many topological insulators, that doesn’t mean that they can be synthesized in the real world.

“Here you have a very simple recipe for how to create topological states in a material that is very accessible,” Fischer said. “It is just organic chemistry. The synthesis is not trivial, granted, but we can do it. This is a breakthrough in that we can now start thinking about how to use this to achieve new, unprecedented electronic structures.”

The researchers will report their synthesis, theory and analysis in the Aug. 9 issue of the journal Nature. Louie, Fischer and Crommie are also faculty scientists at Lawrence Berkeley National Laboratory.

Knitting nanoribbons together

Louie, who specializes in the quantum theory of unusual forms of matter, from superconductors to nanostructures, authored a 2017 paper that described how to make graphene nanoribbon junctions that take advantage of the theoretical discovery that nanoribbons are 1D topological insulators. His recipe required taking so-called topologically trivial nanoribbons and pairing them with topologically non-trivial nanoribbons, where Louie explained how to tell the difference between the two by looking at the shape of the quantum mechanical states that are adopted by electrons in the ribbons.

Fischer, who specializes in synthesizing and characterizing unusual nanomolecules, discovered a new way to make atomically precise nanoribbon structures that would exhibit these properties from complex carbon compounds based on anthracene.

Working side by side, Fischer’s and Crommie’s research teams then built the nanoribbons on top of a gold catalyst heated inside a vacuum chamber, and Crommie’s team used a scanning tunneling microscope to confirm the electronic structure of the nanoribbon. It perfectly matched Louie’s theory and calculations. The hybrid nanoribbons they made had between 50 and 100 junctions, each occupied by an individual electron able to quantum mechanically interact with its neighbors.

“When you heat the building blocks, you get a patchwork quilt of molecules knitted together into this beautiful nanoribbon,” Crommie said. “But because the different molecules can have different structures, the nanoribbon can be designed to have interesting new properties.”

Fischer said that the length of each segment of nanoribbon can be varied to change the distance between trapped electrons, thus changing how they interact quantum mechanically. When close together the electrons interact strongly and split into two quantum states (bonding and anti-bonding) whose properties can be controlled, allowing the fabrication of new 1D metals and insulators. When the trapped electrons are slightly more separated, however, they act like small, quantum magnets (spins) that can be entangled and are ideal for quantum computing.

“This provides us with a completely new system that alleviates some of the problems expected for future quantum computers, such as how to easily mass-produce highly precise quantum dots with engineered entanglement that can be incorporated into electronic devices in a straightforward way,” Fischer said.

Co-lead authors of the paper are Daniel Rizzo and Ting Cao from the Department of Physics and Gregory Veber from the Department of Chemistry, along with their colleagues Christopher Bronner, Ting Chen, Fangzhou Zhao and Henry Rodriguez. Fischer and Crommie are both members of the Kavli Energy NanoSciences Institute at UC Berkeley and Berkeley Lab.

The research was supported by the Office of Naval Research, Department of Energy, Center for Energy Efficient Electronics Science and National Science Foundation.

Rice University researchers have found that fracture-resistant “rebar graphene” is more than twice as tough as pristine graphene.

Rice University graduate student Emily Hacopian holds the platform she used to study the strength of rebar graphene under a microscope. Hacopian and colleagues discovered that reinforcing graphene with carbon nanotubes makes the material twice as tough. Credit: Jeff Fitlow/Rice University

Graphene is a one-atom-thick sheet of carbon. On the two-dimensional scale, the material is stronger than steel, but because graphene is so thin, it is still subject to ripping and tearing.

Rebar graphene is the nanoscale analog of rebar (reinforcement bars) in concrete, in which embedded steel bars enhance the material’s strength and durability. Rebar graphene, developed by the Rice lab of chemist James Tour in 2014, uses carbon nanotubes for reinforcement.

In a new study in the American Chemical Society journal ACS Nano, Rice materials scientist Jun Lou, graduate student and lead author Emily Hacopian and collaborators, including Tour, stress-tested rebar graphene and found that nanotube rebar diverted and bridged cracks that would otherwise propagate in unreinforced graphene.

The experiments showed that nanotubes help graphene stay stretchy and also reduce the effects of cracks. That could be useful not only for flexible electronics but also electrically active wearables or other devices where stress tolerance, flexibility, transparency and mechanical stability are desired, Lou said.

Both the lab’s mechanical tests and molecular dynamics simulations by collaborators at Brown University revealed the material’s toughness.

Graphene’s excellent conductivity makes it a strong candidate for devices, but its brittle nature is a downside, Lou said. His lab reported two years ago that graphene is only as strong as its weakest link. Those tests showed the strength of pristine graphene to be “substantially lower” than its reported intrinsic strength. In a later study, the lab found molybdenum diselenide, another two-dimensional material of interest to researchers, is also brittle.

Tour approached Lou and his group to carry out similar tests on rebar graphene, made by spin-coating single-walled nanotubes onto a copper substrate and growing graphene atop them via chemical vapor deposition.

To stress-test rebar graphene, Hacopian, Yang and colleagues had to pull it to pieces and measure the force that was applied. Through trial and error, the lab developed a way to cut microscopic pieces of the material and mount it on a testbed for use with scanning electron and transmission electron microscopes.

“We couldn’t use glue, so we had to understand the intermolecular forces between the material and our testing devices,” Hacopian said. “With materials this fragile, it’s really difficult.”

Rebar didn’t keep graphene from ultimate failure, but the nanotubes slowed the process by forcing cracks to zig and zag as they propagated. When the force was too weak to completely break the graphene, nanotubes effectively bridged cracks and in some cases preserved the material’s conductivity.

In earlier tests, Lou’s lab showed graphene has a native fracture toughness of 4 megapascals. In contrast, rebar graphene has an average toughness of 10.7 megapascals, he said.

Simulations by study co-author Huajian Gao and his team at Brown confirmed results from the physical experiments. Gao’s team found the same effects in simulations with orderly rows of rebar in graphene as those measured in the physical samples with rebar pointing every which way.

“The simulations are important because they let us see the process on a time scale that isn’t available to us with microscopy techniques, which only give us snapshots,” Lou said. “The Brown team really helped us understand what’s happening behind the numbers.”

He said the rebar graphene results are a first step toward the characterization of many new materials. “We hope this opens a direction people can pursue to engineer 2D material features for applications,” Lou said.

Scientists at the Florida State University-headquartered National High Magnetic Field Laboratory have discovered a behavior in materials called cuprates that suggests they carry current in a way entirely different from conventional metals such as copper.

The research, published today in the journal Science, adds new meaning to the materials’ moniker, “strange metals.”

Cuprates are high-temperature superconductors (HTS), meaning they can carry current without any loss of energy at somewhat warmer temperatures than conventional, low-temperature superconductors (LTS). Although scientists understand the physics of LTS, they haven’t yet cracked the nut of HTS materials. Exactly how the electrons travel through these materials remains the biggest mystery in the field.

For their research on one specific cuprate, lanthanum strontium copper oxide (LSCO), a team led by MagLab physicist Arkady Shekhter focused on its normal, metallic state — the state from which superconductivity eventually emerges when the temperature dips low enough. This normal state of cuprates is known as a “strange” or “bad” metal, in part because the electrons don’t conduct electricity particularly well.

Scientists have studied conventional metals for more than a century and generally agree on how electricity travels through them. They call the units that carry charge through those metals “quasiparticles,” which are essentially electrons after factoring in their environment. These quasiparticles act nearly independently of each other as they carry electric charge through a conductor.

But does quasiparticle flow also explain how electric current travels in the cuprates? At the National MagLab’s Pulsed Field Facility in Los Alamos, New Mexico, Shekhter and his team investigated the question. They put LSCO in a very high magnetic field, applied a current to it, then measured the resistance.

The resulting data revealed that the current cannot, in fact, travel via conventional quasiparticles, as it does in copper or doped silicon. The normal metallic state of the cuprate, it appeared, was anything but normal.

“This is a new way metals can conduct electricity that is not a bunch of quasiparticles flying around, which is the only well-understood and agreed-upon language so far,” Shekhter said. “Most metals work like that.”

If not by quasiparticles, exactly how is charge being carried in the strange metal phase of LSCO? The data suggests it may be some kind of team effort by the electrons.

Scientists have known for some time about an intriguing behavior of LSCO: In its normal conducting state, resistivity changes linearly with temperature. In other words, as the temperature goes up, LSCO’s resistance to electrical current goes up proportionately, which is not the case in conventional metals.

Shekhter and his colleagues decided to test LSCO’s resistivity, but using magnetic field as a parameter instead of temperature. They put the material in a very powerful magnet and measured resistivity in fields up to 80 teslas. (A hospital MRI magnet, by comparison, generates a field of about 3 teslas). They discovered another case of linear resistivity: As the strength of the magnetic field increased, LSCO’s resistivity went up proportionately.

The fact that the linear-in-field resistivity mirrored so elegantly the previously known linear-in-temperature resistivity of LSCO is highly significant, Shekhter said.

“Usually when you see such things, that means that it’s a very simple principle behind it,” he said.

The finding suggests the electrons seem to cooperate as they move through the material. Physicists have believed for some time that HTS materials exhibit such a “correlated electron behavior” in the superconducting phase, although the precise mechanism is not yet understood.

This new evidence suggests that LSCO in its normal conducting state may also carry current using something other than independent quasiparticles — although it’s not superconductivity, either. What that “something” is, scientists aren’t yet certain. Finding the answer may require a whole new way of looking at the problem.

“Here we have a situation where no existing language can help,” Shekhter said. “We need to find a new language to think about these materials.”

The new research raises plenty of questions and some tantalizing ideas, including ideas about the fundamentally different way in which resistivity could be tuned in cuprates. In conventional metals, explained Shekhter, resistivity can be tuned in multiple ways — imagine a set of dials, any of which could adjust that property.

But in cuprates, Shekhter said, “There is only one dial to adjust resistivity. And both temperature and magnetic field, in their own way, access that one dial.”

Odd, indeed. But from strange metals, one would expect nothing less.