nLab topological insulator

Idea

For the moment see at topological phase of matter.

Examples

• quantum Hall effect

• Chern insulator

• Haldane model

Related concepts

• topological crystalline insulator

• photonic topological insulator

• gapped Hamiltonian

• topological phase of matter

• Chern insulator

• topological photonics

• quantum material

• Majorana zero mode

References

General

The term “topological insulator” originates with:

• Joel E. Moore, Leon Balents, Topological invariants of time-reversal-invariant band structures, Phys. Rev. B 75 (2007) 121306(R) $[$doi:10.1103/PhysRevB.75.121306$]$

Reviews:

• Liang Fu, Charles Kane, Eugene Mele, Topological Insulators in Three Dimensions, Phys. Rev. Lett. 98 (2007) 106803 $[$doi:10.1103/PhysRevLett.98.106803$]$

• Rahul Roy, Topological phases and the quantum spin Hall effect in three dimensions, Phys. Rev. B 79 (2009) 195322 $[$doi:10.1103/PhysRevB.79.195322$]$

• M. Zahid Hasan, Charles Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82 (2010) 3045 $[$doi:10.1103/RevModPhys.82.3045$]$

• Joel E. Moore, The birth of topological insulators, Nature volume 464, pages 194–198 (2010) (doi:10.1038/nature08916)

• Xiao-Liang Qi, Shou-Cheng Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83 (2011) 1057-1110 $[$arXiv:1008.2026, doi:10.1103/RevModPhys.83.1057$]$

• M. Zahid Hasan, Joel E. Moore, Three-Dimensional Topological Insulators, Ann. Review.Condensed Matter Physics 2 (2011) 55-78 $[$arXiv:1011.5462, doi:10.1146/annurev-conmatphys-062910-140432$]$

• Marcel Franz, Laurens Molenkamp (eds.), Topological Insulators, Contemporary Concepts of Condensed Matter Science 6 (2013) $[$ISBN:978-0-444-63314-9$]$

• Michel Fruchart, David Carpentier, An introduction to topological insulators, Comptes Rendus Physique 14 9–10, (2013) 779-815 (doi:10.1016/j.crhy.2013.09.013)

• Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen:

  Sec. 5 of: Quantum Information Meets Quantum Matter – From Quantum Entanglement to Topological Phases of Many-Body Systems, Quantum Science and Technology (QST), Springer (2019) $[$arXiv:1508.02595, doi:10.1007/978-1-4939-9084-9$]$

• Ben Webster et al. 2024 roadmap on 2D topological insulators, Journal of Physics: Materials 7 2 (2024) 022501 [doi:10.1088/2515-7639/ad2083]

With focus on the case protected by crystallographic group-symmetry:

• Yoichi Ando, Liang Fu, Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials, Annual Review of Condensed Matter Physics 6 (2015) 361-381 $[$arXiv:1501.00531, doi:10.1146/annurev-conmatphys-031214-014501$]$

• Tanmoy Das, A pedagogic review on designing model topological insulators, Journal of the Indian Institute of Science 96 77-106 (2016) $[$arXiv:1604.07546, ISSN:0970-4140]

Via coarse topology:

• Matthias Ludewig, Coarse geometry and its applications in solid state physics, in Encyclopedia of Mathematical Physics 2nd ed, Elsevier (2024) [arXiv:2308.06384]

Monographs:

• Shun-Qing Shen, Topological Insulators, Springer 2012 (doi:10.1007/978-3-642-32858-9)

• Panagiotis Kotetes, Topological Insulators, IOP Science 2019 (ISBN:978-1-68174-517-6)

See also:

• Wikipedia, Topological insulator

Review in the more general context of topological phases of matter

• Shou-cheng Zhang, Viewpoint: Topological states of quantum matter, APS Physics 1, 6 (2008) doi:10.1103/Physics.1.6

• Vishal Bhardwaj, Ratnamala Chatterjee, Topological Materials – New Quantum Phases of Matter, Resonance 25 (2020) 431–441 (doi:10.1007/s12045-020-0955-5, pdf)

• Tudor D. Stanescu, Section II.5 of: Introduction to Topological Quantum Matter & Quantum Computation, CRC Press 2020 (ISBN:9780367574116)

See also:

• Liang Fu, Charles L. Kane, Topological insulators with inversion symmetry, Physical Review B 76 (4): 045302. arXiv:cond-mat/0611341 doi;

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator, Phys. Rev. Lett. 100: 096407, arXiv:0707.1692 doi

• Jeffrey C. Y. Teo, Liang Fu, Charles L. Kane, Surface states and topological invariants in three-dimensional topological insulators: Application to $Bi_{1-x}Sb_x$, Phys. Rev. B 78, 045426 (2008) doi

• J. Kellendonk, On the $C^\ast$-algebraic approach to topological phases for insulators, arxiv/1509.06271

• A. Kitaev, Periodic table for topological insulators and superconductors. (Advances in Theoretical Physics: Landau Memorial Conference) AIP Conference Proceedings 1134, 22-30 (2009).

Interacting topological insulators:

• Stephan Rachel, Interacting topological insulators: a review, Rep. Prog. Phys. 81 116501 (2018) $[$arXiv:1804.10656, doi:10.1088/1361-6633/aad6a6$]$

The topological insulator in 2D exhibiting a quantum spin Hall effect has been first proposed in

• B. Andrei Bernevig, Taylor L. Hughes, Shou-Cheng Zhang, Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science 314, n. 5806, pp. 1757-1761, Dec 2006 doi

• Y. L. Chen et al. Experimental Realization of a Three-Dimensional Topological Insulator, $Bi_2 Te_3$, Science 325, no. 5937 pp. 178-181, July 2009, doi

Comment by X.-G. Wen: In fact, none of the above materials have quantum spin Hall effect since the spin is not conserved due to the spin-orbital interaction that makes those materials non trivial.

• Ricardo Kennedy, Charles Guggenheim, Homotopy theory of strong and weak topological insulators, arxiv/1409.2529

• L. Wu et al. Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator, Science (2016). doi

Discussion via AdS/CFT in solid state physics:

• Georgios Linardopoulos, Modelling Topological Materials with D-branes, INPP Annual Meeting 2017 (pdf, pdf)

Higher order topological insulators (with protected corner-modes beyond the edge-modes):

• Frank Schindler, Ashley M. Cook, Maia G. Vergniory, Zhijun Wang, Stuart S. P. Parkin, B. Andrei Bernevig, Titus Neupert, Higher-Order Topological Insulators, Science Advances 01 4 6 (2018) eaat0346 [arXiv:1708.03636, doi:10.1126/sciadv.aat0346]

Experimental realization

• Bo Song, Long Zhang, Chengdong He, Ting Fung Jeffrey Poon, Elnur Hajiyev, Shanchao Zhang, Xiong-Jun Liu, Gyu-Boong Jo, Observation of symmetry-protected topological band with ultracold fermions, Science Advances 4 eaao4748 (2018) $[$doi:10.1126/sciadv.aao4748$]$

External manipulation of topological phases via strain (see also the references here at graphene):

• Marwa Mannaï, Sonia Haddad, Strain tuned topology in the Haldane and the modified Haldane models., J of Physics: Condens. Matter 32 225501 (2020) $[$arXiv:1907.11213, doi:10.1088/1361-648X/ab73a1$]$

• Marwa Mannaï, Sonia Haddad, Twistronics versus straintronics in twisted bilayers of graphene and transition metal dichalcogenides, Phys. Rev. B 103 201112 (2021) $[$arXiv:2011.08818, doi:10.1103/PhysRevB.103.L121112$]$

• Jiesen Li, Wanxing Lin, D. X. Yao, Strain-induced topological phase transition in two-dimensional platinum ditelluride $[$arXiv:2106.16212$]$

• T. Kondo et al., Visualization of the strain-induced topological phase transition in a quasi-one-dimensional superconductor $TaSe_3$, Nature Materials 20 1093–1099 (2021) $[$doi:10.1038/s41563-021-01004-4$]$

• Phil D. C. King, Controlling topology with strain, Nat. Mater. 20 (2021) 1046–1047 $[$doi:10.1038/s41563-021-01043-x$]$

Interacting TIs

Discussion of topological insulators with non-negligible interactions:

• AtMa P. O. Chan, Thomas Kvorning, Shinsei Ryu, and Eduardo Fradkin, Effective hydrodynamic field theory and condensation picture of topological insulators, Phys. Rev. B 93 155122 (2016) $[$doi:10.1103/PhysRevB.93.155122$]$

• Benjamin Moy, Hart Goldman, Ramanjit Sohal, Eduardo Fradkin, Theory of oblique topological insulators $[$arXiv:2206.07725$]$

category: physics