Topological Quantum Materials from the Viewpoint of Chemistry Nitesh Kumar,* Satya N. Guin, Kaustuv Manna, Chandra Shekhar, and Claudia Felser* Cite This: Chem. Rev. 2021, 121, 2780-2815 Read Online ACCESS Metrics & More Article Recommendations 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. CONTENTS 1. Introduction 2780 2. Topological and Trivial States of Matter 2781 2.1. Bands in Insulators, Metals, and Topological Insulators 2781 2.2. Transport Signatures of Insulators, Metals, and Topological Insulators 2783 2.3. Classification of Topological Semimetals 2784 3. Single Crystals Growth Techniques 2785 3.1. Metal Flux Method 2786 3.2. Chemical Vapor Transport (CVT) 2787 3.3. Bridgman Method 2788 3.4. Czochralski Method 2788 3.5. Optical Floating Zone (OFZ) 2789 4. Electrical Transport Properties of Topological Materials 2790 4.1. Electrical Resistivity 2790 4.2. Electron Hydrodynamics 2792 4.3. Hall Effect 2793 4.4. Quantization of the Hall Effect 2795 4.5. Anomalous Hall Effect 2795 5. Berry Phase and Curvature 2797 6. Thermal Transport in Topological Materials 2797 6.1. Thermoelectricity 2797 6.2. Seebeck Effect 2798 6.3. Nernst Effect 2799 6.4. Anomalous Nernst Effect 2800 7. Topology in Oxides 2800 8. New Fermions 2801 9. Nonlinear Optical Responses 2802 10. Topological Surface States 2803 11. Outlook and Future Directions 2803 Author Information 2804 Corresponding Authors 2804 Authors 2804 Notes 2804 Biographies 2804 Acknowledgments 2805 References 2805 1. INTRODUCTION We use a variety of synthetic and natural solid materials in our daily lives. Recently, solids have been reclassified through the lens of topology, which goes far beyond the simple sum of their symmetry elements. All known inorganic compounds have been categorized using a single electron approach to trivial and topological materials 1−4 and published on the Web. 5,6 All scientists can now search for new topological compounds on these Web pages. This new viewpoint has led to the discovery of many unexpected properties, that include large responses to Special Issue: Quantum Materials Received: July 13, 2020 Published: November 5, 2020 Review pubs.acs.org/CR © 2020 American Chemical Society 2780 https://dx.doi.org/10.1021/acs.chemrev.0c00732 Chem. Rev. 2021, 121, 2780−2815 This is an open access article published under a Creative Commons Attribution (CC-BY) License, which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited. Downloaded via 3.239.56.152 on August 31, 2021 at 20:37:26 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.