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Symmetry protected topological (SPT) phases are gapped phases of matter that cannot be deformed to a trivial phase without breaking the symmetry or closing the bulk gap.
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2018
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2013
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Marcos Atala, Monika Aidelsburger, Julio T. Barreiro, Dmitry Abanin, Takuya Kitagawa, Eugene Demler, and Immanuel Bloch, “Direct measurement of the zak phase in topological bloch bands,” Nature Physics 9
2013
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Wladimir A. Benalcazar, Jeffrey C. Y. Teo, and Taylor L. Hughes, “Classification of two-dimensional topological crystalline superconductors and majorana bound states at disclinations,” Phys. Rev. B 89
2014
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2014
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M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimbène, N. R. Cooper, I. Bloch, and N. Goldman, “Measuring the chern number of hofstadter bands with ultracold bosonic atoms,” Nature Physics 11
2015
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M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, “Observation of chiral edge states with neutral fermions in synthetic hall ribbons,” Science 349
2015
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A. Alexandradinata, Zhijun Wang, and B. Andrei Bernevig, “Topological insulators from group cohomology,” Phys. Rev. X 6
2016
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Benjamin J. Wieder and C. L. Kane, “Spin-orbit semimetals in the layer groups,” Phys. Rev. B 94
2016
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2018
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Christopher W. Peterson, Wladimir A. Benalcazar, Taylor L. Hughes, and Gaurav Bahl, “A quantized microwave quadrupole insulator with topologically protected corner states,” Nature 555
2018
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Stefan Imhof, Christian Berger, Florian Bayer, Johannes Brehm, Laurens W. Molenkamp, Tobias Kiessling, Frank Schindler, Ching Hua Lee, Martin Greiter, Titus Neupert, and Ronny Thomale, “Topolectrical-circuit realization of topological corner modes,” Nature Physics 14
2018
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2018
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2018
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2018
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Luka Trifunovic and Piet W. Brouwer, “Higher-order bulk-boundary correspondence for topological crystalline phases,” Phys. Rev. X 9
2019
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Wladimir A. Benalcazar, Tianhe Li, and Taylor L. Hughes, “Quantization of fractional corner charge in C n {C}_{n} -symmetric higher-order topological crystalline insulators,” Phys. Rev. B 99
2019
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Shang Liu, Ashvin Vishwanath, and Eslam Khalaf, “Shift insulators: Rotation-protected two-dimensional topological crystalline insulators,” Phys. Rev. X 9
2019
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2019
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Yoonseok Hwang, Junyeong Ahn, and Bohm-Jung Yang, “Fragile topology protected by inversion symmetry: Diagnosis, bulk-boundary correspondence, and wilson loop,” Phys. Rev. B 100
2019
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2019
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Takahiro Fukui, “Dirac fermion model associated with a second-order topological insulator,” Physical Review B 99
2019
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Heejae Kim, Ken Shiozaki, and Shuichi Murakami, “Glide-symmetric magnetic topological crystalline insulators with inversion symmetry,” Phys. Rev. B 100
2019
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Marc Serra-Garcia, Roman Süsstrunk, and Sebastian D. Huber, “Observation of quadrupole transitions and edge mode topology in an lc circuit network,” Phys. Rev. B 99
2019
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S. N. Kempkes, M. R. Slot, J. J. van den Broeke, P. Capiod, W. A. Benalcazar, D. Vanmaekelbergh, D. Bercioux, I. Swart, and C. Morais Smith, “Robust zero-energy modes in an electronic higher-order topological insulator,” Nature Materials 18
2019
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Sunil Mittal, Venkata Vikram Orre, Guanyu Zhu, Maxim A. Gorlach, Alexander Poddubny, and Mohammad Hafezi, “Photonic quadrupole topological phases,” Nature Photonics 13
2019
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2019
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Christopher W. Peterson, Tianhe Li, Wladimir A. Benalcazar, Taylor L. Hughes, and Gaurav Bahl, “A fractional corner anomaly reveals higher-order topology,” Science 368
2020
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2020
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Benjamin J Wieder, Zhijun Wang, Jennifer Cano, Xi Dai, Leslie M Schoop, Barry Bradlyn, and B Andrei Bernevig, “Strong and fragile topological Dirac semimetals with higher-order Fermi arcs,” Nature Communications 11
2020
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2020
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