# nLab topological insulator

Contents

### Context

#### Topological physics

Topological Physics – Phenomena in physics controlled by the topology (often: the homotopy theory) of the physical system.

General theory:

# Contents

## Idea

A topological insulator is a topological state of matter which behaves as insulator in the bulk but has conducting edge states on the surface. More specifically, it is U(1) and time reversal symmetry protected state of matter with trivial topological order, which behaves as an insulator in the bulk but has conducting edge states on the surface if the time reversal symmetry is not broken on the surface.

## References

Review:

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

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

Textbook account:

Review in the more general context of topological phases of matter

• Liang Fu, C. 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, C. 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).

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

(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)
category: physics

Last revised on May 25, 2021 at 03:19:33. See the history of this page for a list of all contributions to it.