topological insulators

Novel insulators with conducting edges

Posted on June 1, 2018August 17, 2018 by Catherine Zandonella

Article courtesy of the University of Zurich

An international team including scientists at Princeton University is researching a new class of materials: higher-order topological insulators. The edges of these crystalline solids conduct electric current without dissipation, while the rest of the crystal remains insulating. These materials could be useful for applications in semiconductor technology and for building quantum computers. The study was published in the journal Sciences Advances.

Topology examines the properties of objects and solids that are protected against perturbations and deformations. Topological materials known so far include topological insulators, which are crystals that insulate on the inside but conduct electrical current on their surface. The conducting surfaces are topologically protected, which means that they cannot easily be brought into an insulating state.

A new class of materials: Higher-order topological insulators

Theoretical physicists have now predicted a new class of topological insulators that have conducting properties on the edges of crystals rather than on the surface. The research team, made up of scientists from University of Zurich (UZH), Princeton University, the Donostia International Physics Center, and the Max Planck Institute of Microstructure Physics in Halle, dubbed the new material class “higher-order topological insulators.” The extraordinary robustness of the conducting edges makes them particularly interesting: The current of topological electrons cannot be stopped by disorder or impurities. If an imperfection gets in the way of the current, it simply flows around the impurity.

Like a highway for electrons

In addition, the crystal edges do not have to be specially prepared to conduct electrical current. If the crystal breaks, the new edges also conduct current. “The most exciting aspect is that electricity can at least in theory be conducted without any dissipation,” said Titus Neupert, professor in the Department of Physics at UZH. “You could think of the crystal edges as a kind of highway for electrons. They can’t simply make a U-turn.” Neupert and his team collaborated with B. Andrei Bernevig, professor of physics, and his team at Princeton University.

This property of dissipationless conductance, more commonly associated with superconductors at low temperatures, is not shared with the previously known topological insulator crystals that have conducting surfaces, but is specific to the higher-order topological crystals.

Further theoretical and experimental research needed

The physicists’ study still mostly relies on theoretical aspects. They have proposed tin telluride as the first compound to show these novel properties. “More material candidates have to be identified and probed in experiments,” says Neupert. The researchers hope that in the future, nanowires made of higher-order topological insulators may be used as conducting paths in electric circuits. These nanowires could be combined with magnetic and superconducting materials for use in building quantum computers.

Funding was provided by the U.S. Department of Energy (DE-SC0016239), a Simons Investigator Award, the David and Lucile Packard Foundation, and the Eric and Wendy Schmidt Transformative Technology Fund at Princeton University. The computational part of the Princeton work was performed with funding from the National Science Foundation’s Early-Concept Grants for Exploratory Research (DMR-1643312) and Materials Research Science and Engineering Centers (DMR-1420541), the Office of Naval Research (ONR-N00014-14-1-0330), and the Army Research Office (MURI W911NF-12-1-0461). Support was also provided by the Swiss National Science Foundation (grant number: 200021_169061), the European Union’s Horizon 2020 research and innovation program (ERC-StG-Neupert-757867-PARATOP), and the Spanish Ministry of Economy and Competitiveness (FIS2016-75862-P).

The study, “Higher-order topological insulators,” by Frank Schindler, Ashley M. Cook, Maia G. Vergniory, Zhijun Wang, Stuart S. P. Parkin, B. Andrei Bernevig, Titus Neupert was published online in Science Advances, on June 1st, 2018. DOI: 10.1126/sciadv.aat0346.

Spotting the spin of the Majorana fermion under the microscope

Posted on October 12, 2017October 12, 2017 by Catherine Zandonella

Majorana detection — The figure shows a schematic of the experiment. A magnetized scanning tunneling microscope tip was used to probe the spin property of the quantum wave function of the Majorana fermion at the end of a chain of iron atoms on the surface of a superconductor made of lead. Image courtesy of Yazdani Lab, Princeton University.

By Catherine Zandonella, Office of the Dean for Research

Researchers at Princeton University have detected a unique quantum property of an elusive particle notable for behaving simultaneously like matter and antimatter. The particle, known as the Majorana fermion, is prized by researchers for its potential to open the doors to new quantum computing possibilities.

In the study published this week in the journal Science, the research team described how they enhanced an existing imaging technique, called scanning tunneling microscopy, to capture signals from the Majorana particle at both ends of an atomically thin iron wire stretched on the surface of a crystal of lead. Their method involved detecting a distinctive quantum property known as spin, which has been proposed for transmitting quantum information in circuits that contain the Majorana particle.

“The spin property of Majoranas distinguishes them from other types of quasi-particles that emerge in materials,” said Ali Yazdani, Princeton’s Class of 1909 Professor of Physics. “The experimental detection of this property provides a unique signature of this exotic particle.”

The finding builds on the team’s 2014 discovery, also published in Science, of the Majorana fermion in a single atom-wide chain of iron atoms atop a lead substrate. In that study, the scanning tunneling microscope was used to visualize Majoranas for the first time, but provided no other measurements of their properties.

“Our aim has been to probe some of the specific quantum properties of Majoranas. Such experiments provide not only further confirmation of their existence in our chains, but open up possible ways of using them.” Yazdani said.

First theorized in the late 1930s by the Italian physicist Ettore Majorana, the particle is fascinating because it acts as its own antiparticle. In the last few years, scientists have realized that they can engineer one-dimensional wires, such as the chains of atoms on the superconducting surface in the current study, to make Majorana fermions emerge in solids. In these wires, Majoranas occur as pairs at either end of the chains, provided the chains are long enough for the Majoranas to stay far enough apart that they do not annihilate each other. In a quantum computing system, information could be simultaneously stored at both ends of the wire, providing a robustness against outside disruptions to the inherently fragile quantum states.

Previous experimental efforts to detect Majoranas have used the fact that it is both a particle and an antiparticle. The telltale signature is called a zero-bias peak in a quantum tunneling measurement. But studies have shown that such signals could also occur due to a pair of ordinary quasiparticles that can emerge in superconductors. Professor of Physics Andrei Bernevig and his team, who with Yazdani’s group proposed the atomic chain platform, developed the theory that showed that spin-polarized measurements made using a scanning tunneling microscope can distinguish between the presence of a pair of ordinary quasi-particles and a Majorana.

Typically, scanning tunneling microscopy (STM) involves dragging a fine-tipped electrode over a structure, in this case the chain of iron atoms, and detecting its electronic properties, from which an image can be constructed. To perform spin-sensitive measurements, the researchers create electrodes that are magnetized in different orientations. These “spin-polarized” STM measurements revealed signatures that agree with the theoretical calculations by Bernevig and his team.

“It turns out that, unlike in the case of a conventional quasi-particle, the spin of the Majorana cannot be screened out by the background. In this sense it is a litmus test for the presence of the Majorana state,” Bernevig said.

The quantum spin property of Majorana may also make them more useful for applications in quantum information. For example, wires with Majoranas at either end can be used to transfer information between far away quantum bits that rely on the spin of electrons. Entanglement of the spins of electrons and Majoranas may be the next step in harnessing their properties for quantum information transfer.

The STM studies were conducted by three co-first authors in the Yazdani group: scientist Sangjun Jeon, graduate student Yonglong Xie, and former postdoctoral research associate Jian Li (now a professor at Westlake University in Hangzhou, China). The research also included contributions from postdoctoral research associate Zhijun Wang in Bernevig’s group.

This work has been supported by the Gordon and Betty Moore Foundation as part of the EPiQS initiative (grant GBMF4530), U.S. Office of Naval Research (grants ONR-N00014-14-1-0330, ONR-N00014-11-1-0635, and ONR- N00014-13-1-0661) , the National Science Foundation through the NSF-MRSEC program (grants DMR-142054 and DMR-1608848) and an EAGER Award (grant NOA -AWD1004957), the U.S. Army Research Office MURI program (grant W911NF-12-1-046), the U.S. Department of Energy Office of Basic Energy Sciences, the Simons Foundation, the David and Lucile Packard Foundation, and the Eric and Wendy Schmidt Transformative Technology Fund at Princeton.

The study, “Distinguishing a Majorana zero mode using spin resolved measurements,” was published in the journal Science on Thursday, October 12, 2017.

Artificial topological matter opens new research directions

Posted on April 5, 2017April 5, 2017 by Catherine Zandonella

By Catherine Zandonella, Office of the Dean for Research

An international team of researchers have created a new structure that allows the tuning of topological properties in such a way as to turn on or off these unique behaviors. The structure could open up possibilities for new explorations into the properties of topological states of matter.

“This is an exciting new direction in topological matter research,” said M. Zahid Hasan, professor of physics at Princeton University and an investigator at Lawrence Berkeley National Laboratory in California who led the study, which was published March 24th in the journal Science Advances. “We are engineering new topological states that do not occur naturally, opening up numerous exotic possibilities for controlling the behaviors of these materials.”

The new structure consists of alternating layers of topological and normal, or trivial, insulators, an architecture that allows the researchers to turn on or off the flow of current through the structure. The ability to control the current suggests possibilities for circuits based on topological behaviors, but perhaps more importantly presents a new artificial crystal lattice structure for studying quantum behaviors.

Theories behind the topological properties of matter were the subject of the 2016 Nobel Prize in physics awarded to Princeton University’s F. Duncan Haldane and two other scientists. One class of matter is topological insulators, which are insulators on the inside but allow current to flow without resistance on the surfaces.

In the new structure, interfaces between the layers create a one-dimensional lattice in which topological states can exist. The one-dimensional nature of the lattice can be thought of as if one were to cut into the material and remove a very thin slice, and then look at the thin edge of the slice. This one-dimensional lattice resembles a chain of artificial atoms. This behavior is emergent because it arises only when many layers are stacked together.

Artificial topological matter — The researchers made different samples where they could control how the electrons tunnel from interface to interface through alternating layers of trivial and topological insulators, forming an emergent, tunable one-dimensional quantum lattice. The top panel (A, B, C, and D) shows a structure where the trivial layer is relatively thin, enabling electron-like particles to tunnel through the layers (topological phase). The bottom panel (G, H, I, and J) shows a structure where the trivial insulator is relatively thick and blocks tunneling (trivial phase). (Image courtesy of Science/AAAS)

By changing the composition of the layers, the researchers can control the hopping of electron-like particles, called Dirac fermions, through the material. For example, by making the trivial-insulator layer relatively thick – still only about four nanometers – the Dirac fermions cannot travel through it, making the entire structure effectively a trivial insulator. However, if the trivial-insulator layer is thin – about one nanometer – the Dirac fermions can tunnel from one topological layer to the next.

To fashion the two materials, the Princeton team worked with researchers at Rutgers University led by Seongshik Oh, associate professor of physics, who in collaboration with Hasan and others showed in 2012 that adding indium to a topological insulator, bismuth selenide, caused it to become a trivial insulator. Prior to that, bismuth selenide (Bi2Se3) was theoretically and experimentally identified as a topological insulator by Hasan’s team, a finding which was published in the journal Nature in 2009.

“We had shown that, depending on how much indium you add, the resulting material had this nice tunable property from trivial to topological insulator,” Oh said, referring to the work published in Physical Review Letters in 2012.

Graduate students Ilya Belopolski of Princeton and Nikesh Koirala of Rutgers combined two state-of-the-art techniques with new instrumentation development and worked together on layering these two materials, bismuth selenide and indium bismuth selenide, to design the optimal structure. One of the challenges was getting the lattice structures of the two materials to match up so that the Dirac fermions can hop from one layer to the next. Belopolski and Suyang Xu worked with colleagues at Princeton University, Lawrence Berkeley National Laboratory and multiple institutions to use high resolution angle-resolved photoemission spectroscopy to optimize the behavior of the Dirac fermions based on a growth to measurement feedback loop.

Photo of research team — Princeton research team from L to R: Guang Bian, M. Zahid Hasan, Nasser Alidoust, Hao Zheng, Daniel Sanchez, Suyang Xu and Ilya Belopolski (Image credit: Princeton University)

Although no topologically similar states exist naturally, the researchers note that analogous behavior can be found in a chain of polyacetylene, which is a known model of one-dimensional topological behavior as described by the 1979 Su-Schrieffer-Heeger’s theoretical model of an organic polymer.

The research presents a foray into making artificial topological materials, Hasan said. “In nature, whatever a material is, topological insulator or not, you are stuck with that,” Hasan said. “Here we are tuning the system in a way that we can decide in which phase it should exist; we can design the topological behavior.”

The ability to control the travel of light-like Dirac fermions could eventually lead future researchers to harness the resistance-less flow of current seen in topological materials. “These types of topologically tunable heterostructures are a step toward applications, making devices where topological effects can be utilized,” Hasan said.

The Hasan group plans to further explore ways to tune the thickness and explore the topological states in connection to the quantum Hall effect, superconductivity, magnetism, and Majorana and Weyl fermion states of matter.

In addition to work done at Princeton and Rutgers, the research featured contributions from the following institutions: South University of Science and Technology of China; Swiss Light Source, Paul Scherrer Institute; National University of Singapore; University of Central Florida; Universität Würzburg; Diamond Light Source, Didcot, U.K.; and Synchrotron SOLEIL, Saint-Aubin, France.

Work at Princeton University and synchrotron-based ARPES measurements led by Princeton researchers were supported by the U.S. Department of Energy under Basic Energy AQ29 Sciences grant no. DE-FG-02-05ER46200 (to M.Z.H.). I.B. was supported by an NSF Graduate Research Fellowship. N.K., M.B., and S.O. were supported by the Emergent Phenomena in Quantum Systems Initiative of the Gordon and Betty Moore Foundation under grant no. GBMF4418 and by the NSF under grant no. NSF-EFMA-1542798. H.L. acknowledges support from the Singapore National Research Foundation under award no. NRF-NRFF2013-03. M.N. was supported by start-up funds from the University of Central Florida. The work acknowledges support of Diamond Light Source, Didcot, U.K., for time on beamline I05 under proposal SI11742-1. Some measurements were carried out at the ADRESS beamline (24) of the Swiss Light Source, Paul Scherrer Institute, Switzerland. This study was in part supported by grant AQ30 no. 11504159 of the National Natural Science Foundation of China (NSFC), grant no. 2016A030313650 of NSFC Guangdong, and project no. JCY20150630145302240 of the Shenzhen Science and Technology Innovations Committee.

The paper, “A novel artificial condensed matter lattice and a new platform for one-dimensional topological phases,” by Ilya Belopolski, Su-Yang Xu, Nikesh Koirala, Chang Liu, Guang Bian, Vladimir Strocov, Guoqing Chang, Madhab Neupane, Nasser Alidoust, Daniel Sanchez, Hao Zheng, Matthew Brahlek, Victor Rogalev, Timur Kim, Nicholas C. Plumb, Chaoyu Chen, François Bertran, Patrick Le Fèvre, Amina Taleb-Ibrahimi, Maria-Carmen Asensio, Ming Shi, Hsin Lin, Moritz Hoesch, Seongshik Oh and M. Zahid Hasan, was published in the journal Science Advances on March 24, 2017. (Belopolski et al., Sci. Adv. 2017;3: e1501692 24 March 2017)

Theorists propose new class of topological metals with exotic electronic properties (Physics Review X)

Posted on January 30, 2017January 30, 2017 by Catherine Zandonella

Band structure spectral function — A new theory explains the behavior of a class of metals with exotic electronic properties. Credit: Muechler et al., Physics Review X

By Tien Nguyen, Department of Chemistry

Researchers at Princeton, Yale, and the University of Zurich have proposed a theory-based approach to characterize a class of metals that possess exotic electronic properties that could help scientists find other, similarly-endowed materials.

Published in the journal Physical Review X, the study described a new class of metals based on their symmetry and a mathematical classification known as a topological number, which is predictive of special electronic properties. Topological materials have drawn intense research interest since the early 2000s culminating in last year’s Nobel Prize in Physics awarded to three physicists, including F. Duncan Haldane, Princeton’s Eugene Higgins Professor of Physics, for theoretical discoveries in this area.

“Topological classification is a very general way of looking at the properties of materials,” said Lukas Muechler, a Princeton graduate student in the laboratory of Roberto Car, Princeton’s Ralph W. *31 Dornte Professor in Chemistry and lead author on the article.

A popular way of explaining this abstract mathematical classification involves breakfast items. In topological classification, donuts and coffee cups are equivalent because they both have one hole and can be smoothly deformed into one another. Meanwhile donuts cannot deform into muffins which makes them inequivalent. The number of holes is an example of a topological invariant that is equal for the donut and coffee cup, but distinguishes between the donut and the muffin.

“The idea is that you don’t really care about the details. As long as two materials have the same topological invariants, we can say they are topologically equivalent,” he said.

Muechler and his colleagues’ interest in the topological classification of this new class of metals was sparked by a peculiar discovery in the neighboring laboratory of Robert Cava, Princeton’s Russell Wellman Moore Professor of Chemistry. While searching for superconductivity in a crystal called tungsten telluride (WTe₂₎, the Cava lab instead found that the material could continually increase its resistance in response to ever stronger magnetic fields – a property that might be used to build a sensor of magnetic fields.

The origin of this property was, however, mysterious. “This material has very interesting properties, but there had been no theory around it,” Muechler said.

The researchers first considered the arrangement of the atoms in the WTe₂crystal. Patterns in the arrangement of atoms are known as symmetries, and they fall into two fundamentally different classes – symmorphic and nonsymmorphic – which lead to profound differences in electronic properties, such as the transport of current in an electromagnetic field.

a) Symmorphic symmetry b) Nonsymmorphic symmetry Credit: Lukas Muechler

While WTe₂is composed of many layers of atoms stacked upon each other, Car’s team found that a single layer of atoms has a particular nonsymmorphic symmetry, where the atomic arrangement is unchanged overall if it is first rotated and then translated by a fraction of the lattice period (see figure).

Having established the symmetry, the researchers mathematically characterized all possible electronic states having this symmetry, and classified those states that can be smoothly deformed into each other as topologically equivalent, just as a donut can be deformed into a cup. From this classification, they found WTe₂belongs to a new class of metals which they coined nonsymmorphic topological metals. These metals are characterized by a different electron number than the nonsymmorphic metals that have previously been studied.

In nonsymmorphic topological metals, the current-carrying electrons behave like relativistic particles, in other words, as particles traveling at nearly the speed of light. This property is not as susceptible to impurities and defects as ordinary metals, making them attractive candidates for electronic devices.

The abstract topological classification also led the researchers to suggest some explanations for some of the outstanding electronic properties of bulk WTe₂, most importantly its perfect compensation, meaning that it has an equal number of holes and electrons. Through theoretical simulations, the researchers found that this property could be achieved in the three-dimensional crystalline stacking of the WTe₂ monolayers, which was a surprising result, Muechler said.

“Usually in theory research there isn’t much that’s unexpected, but this just popped out,” he said. “This abstract classification directly led us to explaining this property. In this sense, it’s a very elegant way of looking at this compound and now you can actually understand or design new compounds with similar properties.”

Recent photoemission experiments have also shown that the electrons in WTe₂ absorb right-handed photons differently than they would left-handed photons. The theory formulated by the researchers showed that these photoemission experiments on WTe₂ can be understood based on the topological properties of this new class of metals.

In future studies, the theorists want to test whether these topological properties are also present in atomically-thin layers of these metals, which could be exfoliated from a larger crystal to make electronic devices. “The study of this phenomena has big implications for the electronics industry, but it’s still in its infant years,” Muechler said.

This work was supported by the U.S. Department of Energy (DE-FG02-05ER46201), the Yale Postdoctoral Prize Fellowship, the National Science Foundation (NSF CAREER DMR-095242 and NSF-MRSEC DMR-0819860), the Office of Naval Research (ONR-N00014-11-1- 0635), the U.S. Department of Defense (MURI-130-6082), the David and Lucile Packard Foundation, the W. M. Keck Foundation, and the Eric and Wendy Schmidt Transformative Technology Fund.

Unconventional quasiparticles predicted in conventional crystals (Science)

Posted on July 22, 2016 by Catherine Zandonella

Fermi arcs on the surface of uncoventional materials — Two electronic states known as Fermi arcs, localized on the surface of a material, stem out of the projection of a 3-fold degenerate bulk new fermion. This new fermion is a cousin of the Weyl fermion discovered last year in another class of topological semimetals. The new fermion has a spin-1, a reflection of the 3- fold degeneracy, unlike the spin-½ that the recently discovered Weyl fermions have.

By Staff

An international team of researchers has predicted the existence of several previously unknown types of quantum particles in materials. The particles — which belong to the class of particles known as fermions — can be distinguished by several intrinsic properties, such as their responses to applied magnetic and electric fields. In several cases, fermions in the interior of the material show their presence on the surface via the appearance of electron states called Fermi arcs, which link the different types of fermion states in the material’s bulk.

The research, published online this week in the journal Science, was conducted by a team at Princeton University in collaboration with researchers at the Donostia International Physics Center (DIPC) in Spain and the Max Planck Institute for Chemical Physics of Solids in Germany. The investigators propose that many of the materials hosting the new types of fermions are “protected metals,” which are metals that do not allow, in most circumstances, an insulating state to develop. This research represents the newest avenue in the physics of “topological materials,” an area of science that has already fundamentally changed the way researchers see and interpret states of matter.

The team at Princeton included Barry Bradlyn and Jennifer Cano, both associate research scholars at the Princeton Center for Theoretical Science; Zhijun Wang, a postdoctoral research associate in the Department of Physics, Robert Cava, the Russell Wellman Moore Professor of Chemistry; and B. Andrei Bernevig, associate professor of physics. The research team also included Maia Vergniory, a postdoctoral research fellow at DIPC, and Claudia Felser, a professor of physics and chemistry and director of the Max Planck Institute for Chemical Physics of Solids.

For the past century, gapless fermions, which are quantum particles with no energy gap between their highest filled and lowest unfilled states, were thought to come in three varieties: Dirac, Majorana and Weyl. Condensed matter physics, which pioneers the study of quantum phases of matter, has become fertile ground for the discovery of these fermions in different materials through experiments conducted in crystals. These experiments enable researchers to explore exotic particles using relatively inexpensive laboratory equipment rather than large particle accelerators.

In the past four years, all three varieties of gapless fermions have been theoretically predicted and experimentally observed in different types of crystalline materials grown in laboratories around the world. The Weyl fermion was thought to be last of the group of predicted quasiparticles in nature. Research published earlier this year in the journal Nature (Wang et al., doi:10.1038/nature17410) has shown, however, that this is not the case, with the discovery of a bulk insulator which hosts an exotic surface fermion.

In the current paper, the team predicted and classified the possible exotic fermions that can appear in the bulk of materials. The energy of these fermions can be characterized as a function of their momentum into so-called energy bands, or branches. Unlike the Weyl and Dirac fermions, which, roughly speaking, exhibit an energy spectrum with 2- and 4-fold branches of allowed energy states, the new fermions can exhibit 3-, 6- and 8-fold branches. The 3-, 6-, or 8-fold branches meet up at points – called degeneracy points – in the Brillouin zone, which is the parameter space where the fermion momentum takes its values.

“Symmetries are essential to keep the fermions well-defined, as well as to uncover their physical properties,” Bradlyn said. “Locally, by inspecting the physics close to the degeneracy points, one can think of them as new particles, but this is only part of the story,” he said.

Cano added, “The new fermions know about the global topology of the material. Crucially, they connect to other points in the Brillouin zone in nontrivial ways.”

During the search for materials exhibiting the new fermions, the team uncovered a fundamentally new and systematic way of finding metals in nature. Until now, searching for metals involved performing detailed calculations of the electronic states of matter.

“The presence of the new fermions allows for a much easier way to determine whether a given system is a protected metal or not, in some cases without the need to do a detailed calculation,” Wang said.

Verginory added, “One can just count the number of electrons of a crystal, and figure out, based on symmetry, if a new fermion exists within observable range.”

The researchers suggest that this is because the new fermions require multiple electronic states to meet in energy: The 8-branch fermion requires the presence of 8 electronic states. As such, a system with only 4 electrons can only occupy half of those states and cannot be insulating, thereby creating a protected metal.

“The interplay between symmetry, topology and material science hinted by the presence of the new fermions is likely to play a more fundamental role in our future understanding of topological materials – both semimetals and insulators,” Cava said.

Felser added, “We all envision a future for quantum physical chemistry where one can write down the formula of a material, look at both the symmetries of the crystal lattice and at the valence orbitals of each element, and, without a calculation, be able to tell whether the material is a topological insulator or a protected metal.”

Read the abstract.

Funding for this study was provided by the US Army Research Office Multidisciplinary University Research Initiative, the US Office of Naval Research, the National Science Foundation, the David and Lucile Packard Foundation, the W. M. Keck Foundation, and the Spanish Ministry of Economy and Competitiveness.

Electrons slide through the hourglass on surface of bizarre material (Nature)

Posted on April 13, 2016April 18, 2016 by Catherine Zandonella

An illustration of the hourglass fermion predicted to lie on the surface of crystals of potassium mercury antimony. (Bernevig et al., Princeton University) — An illustration of the hourglass fermion predicted to lie on the surface of crystals of potassium mercury antimony. (Image credit: Laura R. Park and Aris Alexandradinata)

By Staff

A team of researchers at Princeton University has predicted the existence of a new state of matter in which current flows only through a set of surface channels that resemble an hourglass. These channels are created through the action of a newly theorized particle, dubbed the “hourglass fermion,” which arises due to a special property of the material. The tuning of this property can sequentially create and destroy the hourglass fermions, suggesting a range of potential applications such as efficient transistor switching.

In an article published in the journal Nature this week, the researchers theorize the existence of these hourglass fermions in crystals made of potassium and mercury combined with either antimony, arsenic or bismuth. The crystals are insulators in their interiors and on their top and bottom surfaces, but perfect conductors on two of their sides where the fermions create hourglass-shaped channels that enable electrons to flow.

The research was performed by Princeton University postdoctoral researcher Zhi Jun Wang and former graduate student Aris Alexandradinata, now a postdoctoral researcher at Yale University, working with Robert Cava, Princeton’s Russell Wellman Moore Professor of Chemistry, and Associate Professor of Physics B. Andrei Bernevig.

The new hourglass fermion exists – theoretically for now, until detected experimentally – in a family of materials broadly called topological insulators, which were first observed experimentally in the mid-2000s and have since become one of the most active and interesting branches of quantum physics research. The bulk, or interior, acts as an insulator, which means it prohibits the travel of electrons, but the surface of the material is conducting, allowing electrons to travel through a set of channels created by particles known as Dirac fermions.

Fermions are a family of subatomic particles that include electrons, protons and neutrons, but they also appear in nature in many lesser known forms such as the massless Dirac, Majorana and Weyl fermions. After years of searching for these particles in high-energy accelerators and other large-scale experiments, researchers found that they can detect these elusive fermions in table-top laboratory experiments on crystals. Over the past few years, researchers have used these “condensed matter” systems to first predict and then confirm the existence of Majorana and Weyl fermions in a wide array of materials.

The next frontier in condensed matter physics is the discovery of particles that can exist in the so-called “material universe” inside crystals but not in the universe at large. Such particles come about due to the properties of the materials but cannot exist outside the crystal the way other subatomic particles do. Classifying and discovering all the possible particles that can exist in the material universe is just beginning. The work reported by the Princeton team lays the foundations of one of the most interesting of these systems, according to the researchers.

In the current study, the researchers theorize that the laws of physics prohibit current from flowing in the crystal’s bulk and top and bottom surfaces, but permit electron flow in completely different ways on the side surfaces through the hourglass-shaped channels. This type of channel, known more precisely as a dispersion, was completely unknown before.

The researchers then asked whether this dispersion is a generic feature found in certain materials or just a fluke arising from a specific crystal model.

It turned out to be no fluke.

A long-standing collaboration with Cava, a material science expert, enabled Bernevig, Wang, and Alexandradinata to uncover more materials exhibiting this remarkable behavior.

“Our hourglass fermion is curiously movable but unremovable,” said Bernevig. “It is impossible to remove the hourglass channel from the surface of the crystal.”

Bernevig explained that this robust property arises from the intertwining of spatial symmetries, which are characteristics of the crystal structure, with the modern band theory of crystals. Spatial symmetries in crystals are distinguished by whether a crystal can be rotated or otherwise moved without altering its basic character.

In a paper published in Physical Review X this week to coincide with the Nature paper, the team detailed the theory behind how the crystal structure leads to the existence of the hourglass fermion.

An illustration of the complicated dispersion of the surface fermion arising from a background of mercury and bismuth atoms (blue and red). (Image credit: Mingyee Tsang and Aris Alexandradinata)

“Our work demonstrates how this basic geometric property gives rise to a new topology in band insulators,” Alexandradinata said. The hourglass is a robust consequence of spatial symmetries that translate the origin by a fraction of the lattice period, he explained. “Surface bands connect one hourglass to the next in an unbreakable zigzag pattern,” he said.

The team found esoteric connections between their system and high-level mathematics. Origin-translating symmetries, also called non-symmorphic symmetries, are described by a field of mathematics called cohomology, which classifies all the possible crystal symmetries in nature. For example, cohomology gives the answer to how many crystal types exist in three spatial dimensions: 230.

In the cohomological perspective, there are 230 ways to combine origin-preserving symmetries with real-space translations, known as the “space groups.” The theoretical framework to understand the crystals in the current study requires a cohomological description with momentum-space translations.

“The hourglass theory is the first of its kind that describes time-reversal-symmetric crystals, and moreover, the crystals in our study are the first topological material class which relies on origin-translating symmetries,” added Wang.

Out of the 230 space groups in which materials can exist in nature, 157 are non-symmorphic, meaning they can potentially host interesting electronic behavior such as the hourglass fermion.

“The exploration of the behavior of these interesting fermions, their mathematical description, and the materials where they can be observed, is poised to create an onslaught of activity in quantum, solid state and material physics,” Cava said. “We are just at the beginning.”

The study was funded by the National Science Foundation, the Office of Naval Research, the David and Lucile Packard Foundation, the W. M. Keck Foundation, and the Eric and Wendy Schmidt Transformative Technology Fund at Princeton University.

The paper, “Hourglass fermions” by Zhijun Wang, A. Alexandradinata, R. J. Cava and B. Andrei Bernevig, was published in the April 14, 2016 issue of Nature, 532,189–194, doi:10.1038/nature17410. Read the preprint.

The paper, “Topological insulators from group cohomology” by A. Alexandradinata, Zhijun Wang, and B. Andrei Bernevig, was published in the April 15, 2016 issue of Phys. Rev. X 6, 021008.

Down the rabbit hole: how electrons travel through exotic new material (Science)

Posted on March 10, 2016March 10, 2016 by Catherine Zandonella

Electrons on the surface of a Weyl semi-metal — Three-dimensional image using scanning tunneling electron microscopy of electrons on the surface of a Weyl semi-metal, a kind of crystal with unusual conducting and insulating properties. Image credit: Yazdani et al, Princeton University.

By Catherine Zandonella, Office of the Dean for Research

Researchers at Princeton University have observed a bizarre behavior in a strange new crystal that could hold the key for future electronic technologies. Unlike most materials in which electrons travel on the surface, in these new materials the electrons sink into the depths of the crystal through special conductive channels.

“It is like these electrons go down a rabbit hole and show up on the opposite surface,” said Ali Yazdani, the Class of 1909 Professor of Physics. “You don’t find anything else like this in other materials.”

The research was published in the journal Science.

Tantalum arsenide — Crystal structure of tantalum arsenide (TaAs), with Ta in blue and As in green. Image credit: Yazdani et al., Princeton University.

Yazdani and his colleagues discovered the odd behavior while studying electrons in a crystal made of layers of tantalum and arsenic. The material, called a Weyl semi-metal, behaves both like a metal, which conducts electrons, and an insulator, which blocks them. A better understanding of these and other “topological” materials someday could lead to new, faster electronic devices.

The team’s experimental results suggest that the surface electrons plunge into the crystal only when traveling at a certain speed and direction of travel called the Weyl momentum, said Yazdani. “It is as if you have an electron on one surface, and it is cruising along, and when it hits some special value of momentum, it sinks into the crystal and appears on the opposite surface,” he said.

These special values of momentum, also called Weyl points, can be thought of as portals where the electrons can depart from the surface and be conducted to the opposing surface. The theory predicts that the points come in pairs, so that a departing electron will make the return trip through the partner point.

Schematic of the connections between the top and bottom surface of a crystal — New research from Princeton University demonstrates the bizarre movement of electrons through a novel material called a Weyl semi-metal. The image shows a schematic of the connections at special values of electron momentum, which come in pairs and are called Weyl points (red and blue dots). An electron that leaves the surface on a red point can return through its partner blue point, and vice versa. This bizarre behavior is due to the “topological” connections through the bulk of the material. Image credit: Yazdani et al., Princeton University.

The team decided to explore the behavior of these electrons following research, published in Science last year by another Princeton team and separately by two independent groups, revealing that electrons in Weyl semi-metals are quite unusual. For example, their experiments implied that while most surface electrons create a wave pattern that resembles the spreading rings that ripple out when a stone is thrown into a pond, the surface electrons in the new materials should make only a half circle, earning them the name “Fermi arcs.”

To get a more direct look at the patterns of electron flow in Weyl semi-metals, postdoctoral researcher Hiroyuki Inoue and graduate student András Gyenis in Yazdani’s lab, with help from graduate student Seong Woo Oh, used a highly sensitive instrument called a scanning tunneling microscope, one of the few tools that can observe electron waves on a crystal surface.

They obtained the tantalum arsenide crystals from graduate student Shan Jiang and assistant professor Ni Ni at the University of California-Los Angeles.

The results were puzzling. “Some of the interference patterns that we expected to see were missing,” Yazdani said.

Comparison of experiment (left) to theory (right): The image on the left shows a pattern of waves imaged with scanning tunneling microscopy, revealing all the possible ways in which electrons can interfere with each other on the surface. This pattern is dictated by the connection of the surface electrons with the interior of the crystal, which is determined by the Weyl momentum of electrons, the special momentum when the electrons sink easily through the sample. The observed pattern closely matches the pattern predicted by theoretical calculations (right). Image credit: Yazdani et al., Princeton University.

To help explain the phenomenon, Yazdani consulted B. Andrei Bernevig, associate professor of physics at Princeton, who has expertise in the theory of topological materials and whose group was involved in the first predictions of Weyl semi-metals in a 2015 paper published in Physical Review X.

Bernevig, with help from postdoctoral researchers Jian Li and Zhijun Wang, realized that the observed pattern made sense if the electrons in these unusual materials were sinking into the bulk of the crystal. “Nobody had predicted that there would be signals of this type of transport from a scanning tunneling microscope, so it came as a bit of a surprise,” said Bernevig.

The next step, said Bernevig, is to look for the behavior in other crystals.

The research at Princeton was supported by the Army Research Office Multidisciplinary University Research Initiative program (W911NF-12-1-0461), the Gordon and Betty Moore Foundation as part of EPiQS initiative (GBMF4530), the National Science Foundation Materials Research Science and Engineering Centers programs through the Princeton Center for Complex Materials (DMR-1420541, NSF-DMR-1104612, NSF CAREER DMR-0952428), the David and Lucile Packard Foundation, and the W. M. Keck Foundation. This project was also made possible through use of the facilities at Princeton Nanoscale Microscopy Laboratory (ARO-W911NF-1-0262, ONR-N00014-14-1-0330, ONR-N00014-13-10661), the U.S. Department of Energy Basic Energy Sciences (DOE-BES) Defense Advanced Research Projects Agency, the U.S. Space and Naval Warfare Systems Command Meso program (N6601-11-1-4110, LPS and ARO-W911NF-1-0606), and the Eric and Wendy Schmidt Transformative Technology Fund at Princeton. Work at University of California–Los Angeles was supported by the DOE-BES (DE-SC0011978).

Read the abstract.

The article, “Quasiparticle interference of the Fermi arcs and surface-bulk connectivity of a Weyl semimetal,” by Hiroyuki Inoue, András Gyenis, Zhijun Wang, Jian Li, Seong Woo Oh, Shan Jiang, Ni Ni, B. Andrei Bernevig,and Ali Yazdani, was published in the March 11, 2016 issue of the journal Science.

‘Material universe’ yields surprising new particle (Nature)

Posted on November 25, 2015 by Catherine Zandonella

By Staff

An international team of researchers has predicted the existence of a new type of particle called the type-II Weyl fermion in metallic materials. When subjected to a magnetic field, the materials containing the particle act as insulators for current applied in some directions and as conductors for current applied in other directions. This behavior suggests a range of potential applications, from low-energy devices to efficient transistors.

The researchers theorize that the particle exists in a material known as tungsten ditelluride (WTe2), which the researchers liken to a “material universe” because it contains several particles, some of which exist under normal conditions in our universe and others that may exist only in these specialized types of crystals. The research appeared in the journal Nature this week.

The new particle is a cousin of the Weyl fermion, one of the particles in standard quantum field theory. However, the type-II particle exhibits very different responses to electromagnetic fields, being a near perfect conductor in some directions of the field and an insulator in others.

The research was led by Princeton University Associate Professor of Physics B. Andrei Bernevig, as well as Matthias Troyer and Alexey Soluyanov of ETH Zurich, and Xi Dai of the Chinese Academy of Sciences Institute of Physics. The team included Postdoctoral Research Associates Zhijun Wang at Princeton and QuanSheng Wu at ETH Zurich, and graduate student Dominik Gresch at ETH Zurich.

The particle’s existence was missed by physicist Hermann Weyl during the initial development of quantum theory 85 years ago, say the researchers, because it violated a fundamental rule, called Lorentz symmetry, that does not apply in the materials where the new type of fermion arises.

Particles in our universe are described by relativistic quantum field theory, which combines quantum mechanics with Einstein’s theory of relativity. Under this theory, solids are formed of atoms that consist of a nuclei surrounded by electrons. Because of the sheer number of electrons interacting with each other, it is not possible to solve exactly the problem of many-electron motion in solids using quantum mechanical theory.

Instead, our current knowledge of materials is derived from a simplified perspective where electrons in solids are described in terms of special non-interacting particles, called quasiparticles, that move in the effective field created by charged entities called ions and electrons. These quasiparticles, dubbed Bloch electrons, are also fermions.

Just as electrons are elementary particles in our universe, Bloch electrons can be considered the elementary particles of a solid. In other words, the crystal itself becomes a “universe,” with its own elementary particles.

In recent years, researchers have discovered that such a “material universe” can host all other particles of relativistic quantum field theory. Three of these quasiparticles, the Dirac, Majorana, and Weyl fermions, were discovered in such materials, despite the fact that the latter two had long been elusive in experiments, opening the path to simulate certain predictions of quantum field theory in relatively inexpensive and small-scale experiments carried out in these “condensed matter” crystals.

These crystals can be grown in the laboratory, so experiments can be done to look for the newly predicted fermion in WTe2 and another candidate material, molybdenum ditelluride (MoTe2).

“One’s imagination can go further and wonder whether particles that are unknown to relativistic quantum field theory can arise in condensed matter,” said Bernevig. There is reason to believe they can, according to the researchers.

The universe described by quantum field theory is subject to the stringent constraint of a certain rule-set, or symmetry, known as Lorentz symmetry, which is characteristic of high-energy particles. However, Lorentz symmetry does not apply in condensed matter because typical electron velocities in solids are very small compared to the speed of light, making condensed matter physics an inherently low-energy theory.

“One may wonder,” Soluyanov said, “if it is possible that some material universes host non-relativistic ‘elementary’ particles that are not Lorentz-symmetric?”

This question was answered positively by the work of the international collaboration. The work started when Soluyanov and Dai were visiting Bernevig in Princeton in November 2014 and the discussion turned to strange unexpected behavior of certain metals in magnetic fields (Nature 514, 205-208, 2014, doi:10.1038/nature13763). This behavior had already been observed by experimentalists in some materials, but more work is needed to confirm it is linked to the new particle.

The researchers found that while relativistic theory only allows a single species of Weyl fermions to exist, in condensed matter solids two physically distinct Weyl fermions are possible. The standard type-I Weyl fermion has only two possible states in which it can reside at zero energy, similar to the states of an electron which can be either spin-up or spin-down. As such, the density of states at zero energy is zero, and the fermion is immune to many interesting thermodynamic effects. This Weyl fermion exists in relativistic field theory, and is the only one allowed if Lorentz invariance is preserved.

The newly predicted type-2 Weyl fermion has a thermodynamic number of states in which it can reside at zero energy – it has what is called a Fermi surface. Its Fermi surface is exotic, in that it appears along with touching points between electron and hole pockets. This endows the new fermion with a scale, a finite density of states, which breaks Lorentz symmetry.

Left: Allowed states for the standard type-I Weyl fermion. When energy is tuned from below, at zero energy, a pinch in the number of allowed states guarantees the absence of many-body phenomena such as superconductivity or ordering. Right: The newly discovered type-II Weyl fermion. At zero energy, a large number of allowed states are still available. This allows for the presence of superconductivity, magnetism, and pair-density wave phenomena. Credit B. Andrei Bernevig et al. — Left: Allowed states for the standard type-I Weyl fermion. When energy is tuned from below, at zero energy, a pinch in the number of allowed states guarantees the absence of many-body phenomena such as superconductivity or ordering.
Right: The newly discovered type-II Weyl fermion. At zero energy, a large number of allowed states are still available. This allows for the presence of superconductivity, magnetism, and pair-density wave phenomena.
Credit
B. Andrei Bernevig et al.

The discovery opens many new directions. Most normal metals exhibit an increase in resistivity when subject to magnetic fields, a known effect used in many current technologies. The recent prediction and experimental realization of standard type-I Weyl fermions in semimetals by two groups in Princeton and one group in IOP Beijing showed that the resistivity can actually decrease if the electric field is applied in the same direction as the magnetic field, an effect called negative longitudinal magnetoresistance. The new work shows that materials hosting a type-II Weyl fermion have mixed behavior: While for some directions of magnetic fields the resistivity increases just like in normal metals, for other directions of the fields, the resistivity can decrease like in the Weyl semimetals, offering possible technological applications.

“Even more intriguing is the perspective of finding more ‘elementary’ particles in other condensed matter systems,” the researchers say. “What kind of other particles can be hidden in the infinite variety of material universes? The large variety of emergent fermions in these materials has only begun to be unraveled.”

Researchers at Princeton University were supported by the U.S. Department of Defense, the U.S. Office of Naval Research, the U.S. National Science Foundation, the David and Lucile Packard Foundation and the W.M. Keck Foundation. Researchers at ETH Zurich were supported by Microsoft Research, the Swiss National Science Foundation and the European Research Council. Xi Dai was supported by the National Natural Science Foundation of China, the 973 program of China and the Chinese Academy of Sciences.

The article, “Type II Weyl Semimetals,” by Alexey A. Soluyanov, Dominik Gresch, Zhijun Wang, QuanSheng Wu, Matthias Troyer, Xi Dai, and B. Andrei Bernevig was published in the journal Nature on November 26, 2015.

Read the abstract.

Long-sought chiral anomaly detected in crystalline material (Science)

Posted on September 3, 2015September 3, 2015 by Catherine Zandonella

By Catherine Zandonella, Office of the Dean for Research

A study by Princeton researchers presents evidence for a long-sought phenomenon — first theorized in the 1960s and predicted to be found in crystals in 1983 — called the “chiral anomaly” in a metallic compound of sodium and bismuth. The additional finding of an increase in conductivity in the material may suggest ways to improve electrical conductance and minimize energy consumption in future electronic devices.

“Our research fulfills a famous prediction in physics for which confirmation seemed unattainable,” said N. Phuan Ong, Princeton’s Eugene Higgins Professor of Physics, who co-led the research with Robert Cava, Princeton’s Russell Wellman Moore Professor of Chemistry. “The increase in conductivity in the crystal and its dramatic appearance under the right conditions left little doubt that we had observed the long-sought chiral anomaly.”

The study was published online today in the journal Science.

Handedness — This sketch illustrates the concept of handedness, or chirality, which is found throughout nature. Most chemical structures and many elementary particles come in right- and left-handed forms. Source: Princeton University

The chiral anomaly – which describes how elementary particles can switch their orientation in the presence of electric and magnetic fields – stems from the observation that right- and left-handedness (or “chirality” after the Greek word for hand) is ubiquitous in nature. For example, most chemical structures and many elementary particles come in right- and left-handed forms that are mirror images of each other.

Early research leading up to the discovery of the anomaly goes back to the 1940s, when Hermann Weyl at the Institute for Advanced Study in Princeton, New Jersey, and others, discovered that all elementary particles that have zero mass (including neutrinos, despite their having an extremely small mass) strictly segregate into left- and right-handed populations that never intermix.

A few decades later, theorists discovered that the presence of electric and magnetic fields ruins the segregation of these particles, causing the two populations to transform into each other with observable consequences.

This field-induced mixing, which became known as the chiral anomaly, was first encountered in 1969 in work by Stephen Adler of the Institute for Advanced Study, John Bell of the European Organization for Nuclear Research (CERN) and Roman Jackiw of the Massachusetts Institute of Technology, who successfully explained why certain elementary particles, called neutral pions, decay much faster — by a factor of 300 million — than their charged cousins. Over the decades the anomaly has played an important if perplexing role in the grand quest to unify the four fundamental forces of nature.

The prediction that the chiral anomaly could also be observed in crystals came in 1983 from physicists Holger Bech Nielsen of the University of Copenhagen and Masao Ninomiya of the Okayama Institute for Quantum Physics. They suggested that it may be possible to detect the anomaly in a laboratory setting, which would enable researchers to apply intense magnetic fields to test predictions under conditions that would be impossible in high-energy particle colliders.

Recent progress in the development of certain kinds of crystals known as “topological” materials has paved the way toward realizing this prediction, Ong said. In the crystal of Na₃Bi, which is a topological material known as a Dirac semi-metal, electrons occupy quantum states which mimic massless particles that segregate into left- and right-handed populations.

To see if they could observe the anomaly in Na₃Bi, Jun Xiong, a graduate student in physics advised by Ong, cooled a crystal of Na₃Bi grown by Satya Kushwaha, a postdoctoral research associate in chemistry who works with Cava, to cryogenic temperatures in the presence of a strong magnetic field that can be rotated relative to the direction of the applied electrical current in the crystal. When the magnetic field was aligned parallel to the current, the two chiral populations intermixed to produce a novel increase in conductivity, which the researchers call the “axial current plume.” The experiment confirmed the existence of the chiral anomaly in a crystal.

“One of the key findings in the experiment is that the intermixing leads to a charge current, or axial current, that resists depletion caused by scattering from impurities,” Ong said. “Understanding how to minimize the scattering of current-carrying electrons by impurities — which causes electronic devices to lose energy as heat — is important for realizing future electronic devices that are more energy-efficient. While these are early days, experiments on the long-lived axial current may help us to develop low-dissipation devices.”

The research was supported by the National Science Foundation, the Army Research Office and the Gordon and Betty Moore Foundation.

Read the abstract or paper.

The paper, “Evidence for the chiral anomaly in the Dirac semimetal Na₃Bi,” was published online in the journal Science by Jun Xiong; Satya K. Kushwaha; Tian Liang; Jason W. Krizan; Max Hirschberger; Wudi Wang; Robert J. Cava; and N. Phuan Ong.

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