# 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

For the moment see at topological phase of matter.

## References

### General

The term “topological insulator” originates with:

Reviews:

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

Textbook account:

Review in the more general context of topological phases of matter

• 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)

### 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

Last revised on September 10, 2022 at 11:53:55. See the history of this page for a list of all contributions to it.