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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeAug 8th 2018
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexNeatened things up a little. <a href="https://ncatlab.org/nlab/revision/diff/topological+insulator/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/topological+insulator/10">v10</a>, <a href="https://ncatlab.org/nlab/show/topological+insulator">current</a>

   Neatened things up a little.

   diff, v10, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 19th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded this pointer: * [[Tudor D. Stanescu]], Section II.5 of: *Introduction to Topological Quantum Matter & Quantum Computation*, CRC Press 2020 ([ISBN:9780367574116](https://www.routledge.com/Introduction-to-Topological-Quantum-Matter--Quantum-Computation/Stanescu/p/book/9780367574116)) <a href="https://ncatlab.org/nlab/revision/diff/topological+insulator/15">diff</a>, <a href="https://ncatlab.org/nlab/revision/topological+insulator/15">v15</a>, <a href="https://ncatlab.org/nlab/show/topological+insulator">current</a>

   added this pointer:

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

   diff, v15, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 8th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to this review, with focus on the case of TIs [[symmetry protected topological phase|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](https://arxiv.org/abs/1501.00531), [doi:10.1146/annurev-conmatphys-031214-014501](https://doi.org/10.1146/annurev-conmatphys-031214-014501)$]$ <a href="https://ncatlab.org/nlab/revision/diff/topological+insulator/19">diff</a>, <a href="https://ncatlab.org/nlab/revision/topological+insulator/19">v19</a>, <a href="https://ncatlab.org/nlab/show/topological+insulator">current</a>

   added pointer to this review, with focus on the case of TIs 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

   diff, v19, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeMay 10th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexfor the moment I have deleted the few old lines (from 2013) that constituted the "Idea"-section here, since they were not only grammatically incorrect. Until somebody has the energy to write a dedicated Idea-section here, we might copy over part of what I just have now written at *[[topological phase of matter]]* <a href="https://ncatlab.org/nlab/revision/diff/topological+insulator/20">diff</a>, <a href="https://ncatlab.org/nlab/revision/topological+insulator/20">v20</a>, <a href="https://ncatlab.org/nlab/show/topological+insulator">current</a>

   for the moment I have deleted the few old lines (from 2013) that constituted the “Idea”-section here, since they were not only grammatically incorrect. Until somebody has the energy to write a dedicated Idea-section here, we might copy over part of what I just have now written at topological phase of matter

   diff, v20, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMay 13th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded also pointer to the earlier reviews: * [[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](https://doi.org/10.1103/PhysRevB.75.121306)$]$ * [[Liang Fu]], [[Charles Kane]], [[Eugene Mele]], *Topological Insulators in Three Dimensions*, Phys. Rev. Lett. **98** (2007) 106803 $[$[doi:10.1103/PhysRevLett.98.106803](https://doi.org/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](https://doi.org/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](https://doi.org/10.1103/RevModPhys.82.3045)$]$ <a href="https://ncatlab.org/nlab/revision/diff/topological+insulator/24">diff</a>, <a href="https://ncatlab.org/nlab/revision/topological+insulator/24">v24</a>, <a href="https://ncatlab.org/nlab/show/topological+insulator">current</a>

   added also pointer to the earlier reviews:

   • 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

   • 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

   diff, v24, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJun 17th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded these references on interacting TIs: * 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](https://doi.org/10.1103/PhysRevB.93.155122)$]$ * Benjamin Moy, Hart Goldman, Ramanjit Sohal, Eduardo Fradkin, *Theory of oblique topological insulators* $[$[arXiv:2206.07725](https://arxiv.org/abs/2206.07725)$]$ <a href="https://ncatlab.org/nlab/revision/diff/topological+insulator/31">diff</a>, <a href="https://ncatlab.org/nlab/revision/topological+insulator/31">v31</a>, <a href="https://ncatlab.org/nlab/show/topological+insulator">current</a>

   added these references on interacting TIs:

   • 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

   diff, v31, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeOct 2nd 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[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 &lbrack;[arXiv:1708.03636](https://arxiv.org/abs/1708.03636), [doi:10.1126/sciadv.aat0346](https://doi.org/10.1126/sciadv.aat0346)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/topological+insulator/37">diff</a>, <a href="https://ncatlab.org/nlab/revision/topological+insulator/37">v37</a>, <a href="https://ncatlab.org/nlab/show/topological+insulator">current</a>

   added pointer to:

   • 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]

   diff, v37, current