Abstract
Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space, namely atoms, valence electrons, bonds, and orbitals, and reciprocal space, namely bands and Fermi surfaces, via symmetry and topology, classifying topological materials within a single-particle picture is possible. Currently, most materials are classified as trivial insulators, semimetals, and metals or as topological insulators, Dirac and Weyl nodal-line semimetals, and topological metals. The key ingredients for topology are certain symmetries, the inert pair effect of the outer electrons leading to inversion of the conduction and valence bands, and spin–orbit coupling. This review presents the topological concepts related to solids from the viewpoint of a solid-state chemist, summarizes techniques for growing single crystals, and describes basic physical property measurement techniques to characterize topological materials beyond their structure and provide examples of such materials. Finally, a brief outlook on the impact of topology in other areas of chemistry is provided at the end of the article.
Highlights
Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science
A number of solid-state chemists, those who have been influenced by the works of Roald Hoffman,[13,14] have joined the topological community.[15−18] Now is the time for topology to consider new avenues beyond those of condensed matter physics for example, for catalysis, and solar cells and beyond
Relativity contributes in two ways to topological materials, via the inert pair effect and via spin−orbit coupling (SOC)
Summary
All solid materials can be broadly divided in two categories: metals, which conduct electricity and insulators, which do not. An even number of band crossings is often observed in more layered structures with no dispersion in one direction of the band structure These systems are known as weak topological insulators.[53] The term “weak” was adopted because it was initially believed that the surface states were not robust against crystal disorder, and an energy gap can be created in the Dirac cones by the inclusion of defects. KHgSb is an example of the layered version of HgTe (a two-dimensional topological insulator), predicted as a weak topological insulator in 2012,76 which was later identified to be an hourglass fermion.[77] The first experimental weak topological insulator phase was discovered in the hexagonal compound Bi14Rh3I9 wherein the layers with conducting edges can be assumed to stack along the [001].17 This means that the topological surface states will be absent on the surface normal to [001], while all other facets will contain an even number of surface Dirac cones. The competition between such two-channel electron transport mechanisms explains the typical temperature dependentbehavior of resistivity in topological insulators.[88−91]
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