nLab topological insulator




For the moment see at topological phase of matter.




The term “topological insulator” originates with:


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

Via coarse topology:


See also:

Review in the more general context of topological phases of matter

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 1xSb xBi_{1-x}Sb_x, Phys. Rev. B 78, 045426 (2008) doi

  • J. Kellendonk, On the C *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:

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 2Te 3Bi_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):

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):

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

Last revised on March 26, 2024 at 19:35:52. See the history of this page for a list of all contributions to it.