Recently, an International Research Team has developed an innovative technique to ascertain whether a crystal is a topological insulator, and also to estimate the chemical compositions and crystal structures needed for the synthesis of new crystals. The outcomes of the study have been reported in the journal Nature on 20th July 2017 and demonstrate that topological insulators occur abundantly in nature than assumed at present.
The fascinating electronic characteristics of topological materials enable them to be propitiously used for a broad array of technological applications, due to which they have evoked a fair amount of experimental as well as theoretical interest in the last 10 years. This interest has resulted in the Nobel Prize for Physics in the year 2016. The electronic characteristics of the material include the potential of current flow without resistance and to respond in untraditional ways to magnetic and electric fields.
However, to date, innovative topological materials have been found principally by means of trial-and-error methods. The new technique reported in Nature enables identification of a wide range of new, propitious topological insulators. The research appears to be a basic progress in the physical aspects of topological materials and transforms the manner in which topological characteristics are perceived.
The Princeton University team included Barry Bradlyn and Jennifer Cano, both of whom are Associate Research Scholars at the Princeton Center for Theoretical Science; Zhijun Wang, a Postdoctoral Research Associate; and B. Andrei Bernevig, Professor of Physics. The team also included Professors Luis Elcoro and Mois Aroyo from the University of the Basque Country in Bilbao; Assistant Professor Maia Garcia Vergniory from the University of the Basque Country and Donostia International Physics Center (DIPC) in Spain and Claudia Felser, Professor at the Max Planck Institute for Chemical Physics of Solids in Germany.
Our approach allows for a much easier way to find topological materials, avoiding the need for detailed calculations.
Claudia Felser, Professor, the Max Planck Institute for Chemical Physics of Solids, Germany
“For some special lattices, we can say that, regardless of whether a material is an insulator or a metal, something topological will be going on,” further added Bradlyn.
The research team states that to date, only a few hundred of the approximately 200,000 materials listed in materials databases have been recognized to exhibit topological properties.
This raised the question for the team: Are topological materials really that scarce, or does this merely reflect an incomplete understanding of solids?
Jennifer Cano, Associate Research Scholar, the Princeton Center for Theoretical Science
In order to answer this question, the research teams used the century-old band theory of solids, which is believed to be an early monumental accomplishment in the field of quantum mechanics. The theory was first developed by Felix Bloch, a Swiss-born Physicist, and others, and proposes that electrons in crystals occupy particular energy levels, called bands. When the electrons occupy all the states in a group of bands, they are unable to move, hence the material becomes an insulator. On the contrary, if certain states remain unfilled, the electrons are free to move from one atom to another, hence the material can conduct electricity.
However, the symmetry characteristics of crystals result in the distinctive characteristics of quantum states of electrons in solids. Such states can be taken to be a set of interconnected bands identified by their shape, energy and momentum. The connections between the bands look like intertwined spaghetti strands on a graph, and result in topological behaviors, for example, ability of electrons to traverse along edges or surfaces without resistance.
In order to discover various unexplored classes of prospective topological materials, the Researchers employed a systematic search. The technique involved integrating various tools from different areas such as Physics, Chemistry, Materials Science and Mathematics.
Initially, the Researchers identified all probable electronic band structures emerging out of electronic orbitals at all the prospective atomic positions for all probable crystal patterns, or symmetry groups, occurring in nature, except for magnetic crystals. In order to look for topological bands, the Researchers initially developed a technique to outline all permitted non-topological bands, with the perception that the bands omitted from the list have to be topological. The Researchers applied tools from group theory and classified all the prospective non-topological band structures that might occur in nature into different families.
Subsequently, the Researchers used graph theory, a branch of mathematics used by search engines to ascertain links between websites, and zeroed in on the permitted connectivity patterns for the entire band structures. The bands can be separated or connected as a whole. The entire probable band structures in nature, topological as well as non-topological, can be ascertained by using mathematical tools. However, as the Researchers had already outlined the non-topological ones, they were in a position to ascertain the topological band structures.
The Researchers analyzed the connectivity and symmetry characteristics of various crystals and identified a number of crystal structures which, on account of their band connectivity, might include topological bands. The Researchers have published the entire data related to non-topological bands as well as band connectivity in the Bilbao Crystallographic Server. “Using these tools, along with our results, researchers from around the world can quickly determine if a material of interest can potentially be topological,” stated Elcoro.
According to Bernevig, the study demonstrates that chemistry symmetry, physics, and topology all have a fundamental role in gaining an in-depth knowledge of materials. “The new theory embeds two previously missing ingredients, band topology and orbital hybridization, into Bloch's theory and provides a prescriptive path for the discovery and characterization of metals and insulators with topological properties.”
Most of us thought it would be many years before the topological possibilities could be cataloged exhaustively in this enormous space of crystal classes. This is why the work of Bradlyn and co-workers comes as such a surprise. They have developed a remarkable set of principles and algorithms that allow them to construct this catalog at a single stroke. Moreover, they have combined their theoretical approach with materials database search methods to make concrete predictions of a wealth of new topological insulator materials.
David Vanderbilt, a Professor of Physics and Astronomy, Rutgers University
The theoretical basis for such materials, which are termed “topological” due to their properties that remain unaltered upon deforming, stretching or twisting an object culminated in the granting of the 2016 Nobel Prize for Physics to F. Duncan M. Haldane, Princeton University’s Sherman Fairchild University Professor of Physics, J. Michael Kosterlitz from Brown University, and David J. Thouless from the University of Washington.
Physics and Chemistry describe crystalline materials with different perspective, where atoms in such materials exist in regularly ordered symmetries or patterns. While the focus of Chemists is likely on atoms and their surrounding electron clouds, or orbitals, Physicists focus specifically on the electrons, which have the ability to carry electric current while moving from one atom to another and are described by means of their momentum.
This simple fact—that the physics of electrons is usually described in terms of momentum, while the chemistry of electrons is usually described in terms of electronic orbitals—has left material discovery in this field at the mercy of chance.
Zhijun Wang, a Postdoctoral Research Associate
“We initially set out to better understand the chemistry of topological materials—to understand why some materials have to be topological,” stated Vergniory.
Aroyo further stated that, “What came out was, however, much more interesting: a way to marry chemistry, physics and mathematics that adds the last missing ingredient in a century-old theory of electronics, and in the present-day search for topological materials.”