Novel insulators with conducting edges

Posted on by Catherine Zandonella
Current flowing on the edges

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 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.

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

Posted on 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 WTe2 crystal. 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
a) Symmorphic symmetry b) Nonsymmorphic symmetry Credit: Lukas Muechler

While WTe2 is 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 WTe2 belongs 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.