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Importance of Topology in Materials Science

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The Role of Topology in Materials

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 189))

Abstract

We underscore the substantial need for understanding a wide range of multifunctional materials through the notions of topology-geometry interrelationships such as genus, Euler characteristic and network connectivity. After introducing the basic concepts of topology we first illustrate these notions on nanocarbon allotropes as a case study. Next, we consider the growing class of emergent topological materials that encompass both real-space and k-space topological materials including Dirac materials, topological insulators, Weyl semimetals as well as soft and polymeric matter, supramacromolecular assemblies and biophotonic materials. Finally, we emphasize and evaluate metrics to quantify topology in order to study and classify materials properties relevant for wide ranging modern and future technologies.

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Acknowledgements

The authors acknowledge stimulating and helpful discussions with several colleagues around the world over the past decade. This work was supported in parts by the U.S. Department of Energy and Western Kentucky University Research Foundation Inc.

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Authors and Affiliations

  1. Department of Physics and Astronomy, Western Kentucky University, Bowling Green, KY, 42101, USA

    Sanju Gupta

  2. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Avadh Saxena

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  1. Sanju Gupta
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Correspondence to Sanju Gupta or Avadh Saxena .

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Editors and Affiliations

  1. Department of Physics and Astronomy, Western Kentucky University, Bowling Green, Kentucky, USA

    Sanju Gupta

  2. Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, USA

    Avadh Saxena

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Gupta, S., Saxena, A. (2018). Importance of Topology in Materials Science. In: Gupta, S., Saxena, A. (eds) The Role of Topology in Materials. Springer Series in Solid-State Sciences, vol 189. Springer, Cham. https://doi.org/10.1007/978-3-319-76596-9_1

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