The quest for more improved materials for various electronic devices, including computers, has concentrated on a class of materials called “topological insulators.”
These insulators have a unique property—that is, they can conduct electricity on the boundary of their surfaces, similar to traffic lanes on a highway. This would not only boost energy efficiency but would also decrease heat output.
In 2009, bismuth-antimony was first experimentally demonstrated as a topological insulator, but it was only recently that scientists discovered pure bismuth as the latest type of topological insulator. A research team in the U.S. and Europe provided theoretical analysis as well as experimental evidence in a report published in Nature Physics in 2018.
Now, MIT researchers together with coworkers in Taiwan, Singapore, and Boston have performed a theoretical analysis to expose a number of more formerly unknown topological characteristics of bismuth.
The researchers were headed by senior authors Professor Nuh Gedik and Associate Professor Liang Fu from MIT; Distinguished Professor Arun Bansil from Northeastern University; and Research Fellow Hsin Lin at Academica Sinica in Taiwan.
“It’s kind of a hidden topology where people did not know that it can be that way,” stated MIT postdoc Su-Yang Xu, a coauthor of the paper reported recently in PNAS.
Topology can be described as a mathematical tool that is used by physicists to inspect electronic characteristics and they do this by examining the quantum wave functions of electrons.
The “topological” characteristics lead to excellent stability in the material and make its electronic structure extremely strong against minor defects present in the crystal, for example, impurities, or slight distortions of its shape, like squeezing or stretching.
Let’s say I have a crystal that has imperfections. Those imperfections, as long as they are not so dramatic, then my electrical property will not change. If there is such topology and if the electronic properties are uniquely tied to the topology rather than the shape, then it will be very robust.
Su-Yang Xu, Study Coauthor and Postdoc, MIT
“In this particular compound, unless you somehow apply pressure or something to distort the crystal structure, otherwise this conduction will always be protected,” Xu added.
However, in these topological materials, the electrons carrying a specific spin can move only in one direction. That means, they cannot scatter or bounce backward—a behavior that makes electronic devices based on copper and silicon to heat up.
On the one hand, materials scientists search for materials that have low-heat output and fast electrical conduction for next-generation computers. On the other hand, physicists prefer to categorize the types of topological and other characteristics underlying these better-performing materials.
In the latest paper titled, “Topology on a new facet of bismuth,” the researchers estimated that bismuth should exhibit a state called a “Dirac surface state,” which is believed to be a hallmark of these topological insulators. The team discovered that the crystal is not altered by a half-circle rotation, that is, 180 °. This is referred to as a twofold rotational symmetry, which safeguards the Dirac surface states. Disruption of the twofold rotation symmetry of the crystal will cause the surface states to lose their topological protection.
In addition, bismuth has a topological state along some crystal edges, where two horizontal and vertical faces meet. This is known as a “hinge” state. In order to completely realize the preferred topological effects in this material, the various surface states, including the hinge state, should be joined to another electronic phenomenon called “band inversion”. According to the theorists’ calculations, this “band inversion” is also present in bismuth.
The researchers predicted that such topological surface states can be confirmed by applying an experimental method called photoemission spectroscopy.
If electrons passing through copper can be compared to a school of fish swimming across a lake in summer, then electrons passing through a topological surface can be compared to ice skaters crossing the frozen surface of the lake in winter.
However, for bismuth existing in the hinge state, the movement of the electrons would be more similar to skating on an ice cube’s corner edge.
The scientists also discovered that in the hinge state, the momentum of the electrons and another trait, known as spin, is “locked” as they move forward. Spin defines the electrons’ clockwise or counterclockwise rotation.
“Their direction of spinning is locked with respect to their direction of motion,” explained Xu.
These extra topological states could help demonstrate why bismuth allows electrons to flow through it considerably farther than a majority of other materials, and how it is able to conduct electricity efficiently with relatively less number of electrons than materials like copper.
If we really want to make these things useful and significantly improve the performance of our transistors, we need to find good topological materials—good in terms of they are easy to make, they are not toxic, and also they are relatively abundant on earth.
Su-Yang Xu, Study Coauthor and Postdoc, MIT
Bismuth is safe for human consumption and thus meets all these needs. This element is used in the form of remedies for treating heartburn, for instance.
“This work is a culmination of a decade and a half’s worth of advancement in our understanding of symmetry-protected topological materials,” stated David Hsieh, professor of physics at Caltech, who was not part of the study.
“I think that these theoretical results are robust, and it is simply a matter of experimentally imaging them using techniques like angle-resolved photoemission spectroscopy, which Professor Gedik is an expert in,” Hsieh added.
Bismuth-based compounds have long played a starring role in topological materials, though bismuth itself was originally believed to be topologically trivial.
Gregory Fiete, Professor, Northeastern University
“Now, this team has discovered that pure bismuth is multiply topological, with a pair of surface Dirac cones untethered to any particular momentum value,” added Fiete, who also was not involved in the study. “The possibility to move the Dirac cones through external parameter control may open the way to applications that exploit this feature.”
Hsieh from Caltech observed that the latest findings add to the number of strategies through which topologically protected metallic states can be stabilized in materials.
“If bismuth can be turned from semimetal into insulator, then isolation of these surface states in electrical transport can be realized, which may be useful for low-power electronics applications,” he explained.
The bismuth topology paper was also contributed by MIT postdoc Qiong Ma; Tay-Rong Chang of the Department of Physics, National Cheng Kung University, Taiwan, and the Center for Quantum Frontiers of Research and Technology, Taiwan; Xiaoting Zhou, Department of Physics, National Cheng Kung University, Taiwan; and Chuang-Han Hsu, Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore.
The study was partly supported by the Center for Integrated Quantum Materials and the U.S. Department of Energy, Materials Sciences and Engineering division.