basics
Examples
Topological Physics – Phenomena in physics controlled by the topology (often: the homotopy theory) of the physical system.
General theory:
In metamaterials:
topological phononics (sound waves?)
For quantum computation:
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.
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:
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)
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
Last revised on June 19, 2024 at 06:21:53. See the history of this page for a list of all contributions to it.