nLab topological crystalline insulator

Idea

In solid state physics, a topological crystalline insulator is a crystalline quantum material in a topological phase of matter like a topological insulator, which as such is “protected” by (possibly time-reversal symmetry and) a crystallographic point group-symmetry of the underlying crystal.

This means that a topological crystalline insulator phase observed in the bulk of some crystal whose dynamics (or rather that of its electrons) respects a given point group may disappear for instance at boundary regions where the dynamics breaks this symmetry.

References

Original articles

• Liang Fu, Topological Crystalline Insulators, Phys. Rev. Lett. 106 (2011) 106802 (doi:10.1103/PhysRevLett.106.106802)

• Robert-Jan Slager, Andrej Mesaros, Vladimir Juricic, Jan Zaanen, The space group classification of topological band insulators, Nature Physics 9 98 (2013) $[$doi:10.1038/nphys2513, arXiv:1209.2610$]$

• Jie Shen, Judy J. Cha, Topological Crystalline Insulator Nanostructures, Nanoscale 6 23 (2014) 14133-14140 $[$doi:10.1039/c4nr05124f$]$

• Jorrit Kruthoff, Jan de Boer, Jasper van Wezel, Charles L. Kane, Robert-Jan Slager, Topological Classification of Crystalline Insulators through Band Structure Combinatorics, Phys. Rev. X 7 (2017) 041069 $[$doi:10.1103/PhysRevX.7.041069$]$

  (explicit relation to equivariant K-theory in appendix B)

See also:

• Jian-Hao Zhang, Shang-Qiang Ning, Yang Qi, Zheng-Cheng Gu, Construction and classification of crystalline topological superconductor and insulators in three-dimensional interacting fermion systems [arXiv:2204.13558]

Review

• Yoichi Ando and Liang Fu, Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials, Annual Review of Condensed Matter Physics 6 (2015) 361-381 [doi:10.1146/annurev-conmatphys-031214-014501]

• Titus Neupert, Frank Schindler, Lecture Notes on Topological Crystalline Insulators, in: Topological Matter Springer Series in Solid-State Sciences 190, Springer (2018) [arXiv:1810.03484, doi:10.1007/978-3-319-76388-0_2]

  (emphasis on Wilson loops of the Berry connection)

• Chieh-Wen Liu, Zhenhua Wang, Richard L J Qiu, Xuan P A Gao, Development of topological insulator and topological crystalline insulator nanostructures, Nanotechnology 31 (2020) 192001 [doi:10.1088/1361-6528/ab6dfc]

• M. Zahid Hasan, Topological Crystalline Insulators (research group page)

Experimental realization

• Y. Tanaka, Zhi Ren, T. Sato, K. Nakayama, S. Souma, T. Takahashi, Kouji Segawa, Yoichi Ando, Experimental realization of a topological crystalline insulator in SnTe, Nature Physics 8 (2012) 800–803 $[$doi:10.1038/nphys2442$]$

• M. Zahid Hasan et al., Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe, Nature Communications 3 1192 (2012) $[$doi:10.1038/ncomms2191$]$

• Timothy H Hsieh, Hsin Lin, Junwei Liu, Wenhui Duan, Arun Bansil, Liang Fu, Topological crystalline insulators in the SnTe material class, Nature Communications 3 (2012) 982 $[$doi:10.1038/ncomms1969$]$

• M. Zahid Hasan et al., Observation of Dirac Node Formation and Mass Acquisition in a Topological Crystalline Insulator, Science 341 1496 (2013) $[$doi:10.1126/science.1239451$]$

• M. Zahid Hasan et al., Mapping the unconventional orbital texture in topological crystalline insulators, Nature Physics 10 (2014) 572–577 $[$doi:10.1038/nphys3012$]$

• Wenhui Fan, Simin Nie, Cuixiang Wang, Binbin Fu, Changjiang Yi, Shunye Gao, Zhicheng Rao, Dayu Yan, Junzhang Ma, Ming Shi, Yaobo Huang, Youguo Shi, Zhijun Wang, Tian Qian, Hong Ding,

  Discovery of Ĉ2 rotation anomaly in topological crystalline insulator SrPb, Nature Communications 12 2052 (2021) $[$doi:10.1038/s41467-021-22350-6$]$