Topological Insulators and Topological Superconductors
Abstract
This graduate-level textbook is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for graduate students and researchers preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with simple concepts such as Berry phases, Dirac fermions, Hall conductance and its link to topology, and the Hofstadter problem of lattice electrons in a magnetic field. It moves on to explain topological phases of matter such as Chern insulators, two- and three-dimensional topological insulators, and Majorana p-wave wires. Additionally, the book covers zero modes on vortices in topological superconductors, time-reversal topological superconductors, and topological responses/field theory and topological indices. The book also analyzes recent topics in condensed matter theory and concludes by surveying active subfields of research such as insulators with point-group symmetries and the stability of topological semimetals. Problems at the end of each chapter offer opportunities to test knowledge and engage with frontier research issues. Topological Insulators and Topological Superconductors will provide graduate students and researchers with the physical understanding…
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The Dirac points are protected by the combined TR and inversion symmetries.
“The Dirac points are known to be protected by the combined TR and inversion (IS) symmetries [25].”
From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [25]
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Ozawa, T., Price, H. M., Amo, A., Goldman, N., Hafezi, M., Lu, L., Rechtsman, M. C., Schuster, D., Simon, J., Zilberberg, O., et al. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.015006 · Cited by 3,722 · see citing works
Bradlyn, B., Elcoro, L., Cano, J., Vergniory, M. G., Wang, Z., Felser, C., Aroyo, M. I., & Bernevig, B. A. (2017) · Nature · doi:10.1038/nature23268 · Cited by 1,624 · see citing works
Self-citationTopological bands for ultracold atoms
Cooper, N. R., Dalibard, J., & Spielman, I. B. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.015005 · Cited by 940 · see citing works
Light-induced anomalous Hall effect in graphene
McIver, J. W., Schulte, B., Stein, F.-U., Matsuyama, T., Jotzu, G., Meier, G., & Cavalleri, A. (2020) · Nature Physics · doi:10.1038/s41567-019-0698-y · Cited by 888 · see citing works
Observation of a Topological Transition in the Bulk of a Non-Hermitian System
Zeuner, J. M., Rechtsman, M. C., Plotnik, Y., Lumer, Y., Nolte, S., Rudner, M. S., Segev, M., & Szameit, A. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.040402 · Cited by 730 · see citing works
Quantum anomalous Hall effect and related topological electronic states
Weng, H., Yu, R., Hu, X., Dai, X., & Fang, Z. (2015) · Advances in Physics · doi:10.1080/00018732.2015.1068524 · Cited by 506 · see citing works
Topological Properties of Linear Circuit Lattices
Albert, V. V., Glazman, L. I., & Jiang, L. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.173902 · Cited by 352 · see citing works
Criteria for Directly Detecting Topological Fermi Arcs in Weyl Semimetals
Belopolski, I., Xu, S.-Y., Sanchez, D. S., Chang, G., Guo, C., Neupane, M., Zheng, H., Lee, C.-C., Huang, S.-M., Bian, G., et al. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.066802 · Cited by 177 · see citing works
Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene
Milićević, M., Montambaux, G., Ozawa, T., Jamadi, O., Real, B., Sagnes, I., Lemaître, A., Le Gratiet, L., Harouri, A., Bloch, J., et al. (2019) · Physical Review X · doi:10.1103/physrevx.9.031010 · Cited by 171 · see citing works
Topoelectrical circuit octupole insulator with topologically protected corner states
Bao, J., Zou, D., Zhang, W., He, W., Sun, H., & Zhang, X. (2019) · Physical Review B · doi:10.1103/physrevb.100.201406 · Cited by 149 · see citing works
“They have been constructed in various systems ranging from traditional electronic setups [2-5] to mechanical [6], electromagnetic [7-11] and acoustic [12-14] structures governed by classical wave equations.”
BackgroundInfluentialAnomalous and Quantum Hall Effects in Lossy Photonic Lattices
Ozawa, T., & Carusotto, I. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.133902 · Cited by 116 · see citing works
4D spinless topological insulator in a periodic electric circuit
Yu, R., Zhao, Y. X., & Schnyder, A. P. (2020) · National Science Review · doi:10.1093/nsr/nwaa065 · Cited by 106 · see citing works
Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions
Cheng, D., Wang, K., Roques-Carmes, C., Lustig, E., Long, O. Y., Wang, H., & Fan, S. (2025) · Nature · doi:10.1038/s41586-024-08259-2 · Cited by 58 · see citing works
“This topological charge manifests itself in the eigenstate trajectory on the Bloch sphere as the wavevector k varies along a closed loop in the two-dimensional Brillouin zone [44, 45].”
Unusual interlayer quantum transport behavior caused by the zeroth Landau level in YbMnBi2
Liu, J. Y., Hu, J., Graf, D., Zou, T., Zhu, M., Shi, Y., Che, S., Radmanesh, S. M. A., Lau, C. N., Spinu, L., et al. (2017) · Nature Communications · doi:10.1038/s41467-017-00673-7 · Cited by 48 · see citing works
Double Weyl points and Fermi arcs of topological semimetals in non-Abelian gauge potentials
Lepori, L., Fulga, I. C., Trombettoni, A., & Burrello, M. (2016) · Physical Review A · doi:10.1103/physreva.94.053633 · Cited by 43 · see citing works
Dirac Dynamics in Waveguide Arrays: From Zitterbewegung to Photonic Topological Insulators
Dreisow, F., Rechtsman, M. C., Zeuner, J. M., Plotnik, Y., Keil, R., Nolte, S., Segev, M., & Szameit, A. (2017) · Quantum Science and Technology · doi:10.1007/978-3-319-52025-4_8 · Cited by 4 · see citing works
- Authors
- Bernevig, B. A.
- Affiliations
- Princeton University (US)
- Corresponding author
- Bernevig, B. Andrei
- ORCID
- Bernevig, B. Andrei
- Venue
- Princeton University Press eBooks
- Publisher
- Princeton University Press
- Published
- 2013-12-31
- OpenAlex
- W326669990
- Cited by
- 1,947
- References
- 0
- Citations by year
- 2026: 77 · 2025: 137 · 2024: 176 · 2023: 154 · 2022: 163 · 2021: 198 · 2020: 269 · 2019: 179 · 2018: 176 · 2017: 153 · 2016: 125 · 2015: 83 · 2014: 43 · 2013: 13
- FWCI
- 41.23
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Princeton University Press eBooks (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
- Keywords
- topological insulators, topological superconductors, Berry phase, Dirac fermions, Hall conductance, Chern insulator, three-dimensional topological insulators, topological response, topological indices, topological semimetals, topological phases
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