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added this pointer:
added pointer to this review, with focus on the case of TIs protected by crystallographic group-symmetry:
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
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$]$
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$]$
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