Abstract
We give an introduction to topological crystalline insulators, that is, gapped ground states of quantum matter that are not adiabatically connected to an atomic limit without breaking symmetries that include spatial transformations, like mirror or rotational symmetries. To deduce the topological properties, we use non-Abelian Wilson loops. We also discuss in detail higher-order topological insulators with hinge and corner states, and in particular, present interacting bosonic models for the latter class of systems.
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X.L. Qi, T.L. Hughes, S.C. Zhang, Phys. Rev. B 78, 195424 (2008). https://doi.org/10.1103/PhysRevB.78.195424
M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010). https://doi.org/10.1103/RevModPhys.82.3045
B.A. Bernevig, Topological Insulators and Topological Superconductors (Princeton University Press, New Jercy, 2013)
J.K. Asbóth, L. Oroszlány, A. Pályi, A short course on topological insulators. Lect. Notes Phys. 919. https://link.springer.com/book/10.1007%2F978-3-319-25607-8
A. Bernevig, T. Neupert, ArXiv e-prints (2015). https://arxiv.org/abs/1506.05805
N. Marzari, A.A. Mostofi, J.R. Yates, I. Souza, D. Vanderbilt, Rev. Mod. Phys. 84, 1419 (2012). https://doi.org/10.1103/RevModPhys.84.1419
N.A. Spaldin, J. Solid State Chem. Fr. 195, 2 (2012). https://doi.org/10.1016/j.jssc.2012.05.010
H. Nielsen, M. Ninomiya, Phys. Lett. B 130(6), 389 (1983). https://doi.org/10.1016/0370-2693(83)91529-0
L. Fidkowski, T.S. Jackson, I. Klich, Phys. Rev. Lett. 107, 036601 (2011). https://doi.org/10.1103/PhysRevLett.107.036601
L. Fu, Phys. Rev. Lett. 106, 106802 (2011). https://doi.org/10.1103/PhysRevLett.106.106802
T.H. Hsieh, H. Lin, J. Liu, W. Duan, A. Bansil, L. Fu, Nat. Commun. 3, 982 (2012). https://doi.org/10.1038/ncomms1969
C. Fang, L. Fu, Phys. Rev. B 91, 161105 (2015). https://doi.org/10.1103/PhysRevB.91.161105
F. Schindler, A.M. Cook, M.G. Vergniory, Z. Wang, S.S Parkin, B.A. Bernevig, T. Neupert, Higher-order topological insulators. Sci. Adv. 4(6), eaat0346 (2018). http://advances.sciencemag.org/content/4/6/eaat0346
W.A. Benalcazar, B.A. Bernevig, T.L. Hughes, Science 357(6346), 61 (2017). https://doi.org/10.1126/science.aah6442, http://science.sciencemag.org/content/357/6346/61
R. Jackiw, C. Rebbi, Phys. Rev. D 13, 3398 (1976). https://doi.org/10.1103/PhysRevD.13.3398
Ann. Rev. Condens. Matter Phys. 6(1), 299 (2015). https://doi.org/10.1146/annurev-conmatphys-031214-014740
X. Chen, Z.C. Gu, Z.X. Liu, X.G. Wen, Phys. Rev. B 87, 155114 (2013). https://doi.org/10.1103/PhysRevB.87.155114
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Neupert, T., Schindler, F. (2018). Topological Crystalline Insulators. In: Bercioux, D., Cayssol, J., Vergniory, M., Reyes Calvo, M. (eds) Topological Matter. Springer Series in Solid-State Sciences, vol 190. Springer, Cham. https://doi.org/10.1007/978-3-319-76388-0_2
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DOI: https://doi.org/10.1007/978-3-319-76388-0_2
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