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Higher-order topological insulators and superconductors protected by inversion symmetry
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Here, higher-order topological insulators and superconductors protected by inversion symmetry are investigated. These phases are characterized by gapped bulk and surface with gapless modes confined to hinges or corners of the sample. Such surface states can be understood as topological defects that are globally stabilized by inversion. They can be built using a layer construction that embeds a standard topological insulator/superconductor into a higher dimension by symmetrically adding to it copies of itself. Using this procedure, a complete classification of such states in any dimension is obtained and several examples for possible physical realizations are provided.
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Cites
Colloquium : Topological insulators
Hasan, M. Z., & Kane, C. L. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.3045 · Cited by 19,930
Topological insulators and superconductors
Qi, X.-L., & Zhang, S.-C. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.1057 · Cited by 14,394
Quantum Spin Hall Effect in Graphene
Kane, C. L., & Mele, E. J. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.226801 · Cited by 8,197
Klitzing, K. V., Dorda, G., & Pepper, M. (1980) · Physical Review Letters · doi:10.1103/physrevlett.45.494 · Cited by 7,119
Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
Bernevig, B. A., Hughes, T. L., & Zhang, S.-C. (2006) · Science · doi:10.1126/science.1133734 · Cited by 7,090
Quantized Hall Conductance in a Two-Dimensional Periodic Potential
Thouless, D. J., Kohmoto, M., Nightingale, M. P., & den Nijs, M. (1982) · Physical Review Letters · doi:10.1103/physrevlett.49.405 · Cited by 6,973
Su, W. P., Schrieffer, J. R., & Heeger, A. J. (1979) · Physical Review Letters · doi:10.1103/physrevlett.42.1698 · Cited by 6,783
Z 2 Topological Order and the Quantum Spin Hall Effect
Kane, C. L., & Mele, E. J. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.146802 · Cited by 6,460
Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator
Fu, L., & Kane, C. L. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.096407 · Cited by 4,868
Topological Insulators in Three Dimensions
Fu, L., Kane, C. L., & Mele, E. J. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.106803 · Cited by 4,651
Read, N., & Green, D. (2000) · Physical Review B · doi:10.1103/physrevb.61.10267 · Cited by 3,476
The Universe in a Helium Droplet
Volovik, G. E. (2009) · doi:10.1093/acprof:oso/9780199564842.001.0001 · Cited by 2,632
Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures
Altland, A., & Zirnbauer, M. R. (1997) · Physical Review B · doi:10.1103/physrevb.55.1142 · Cited by 2,402
Topological invariants of time-reversal-invariant band structures
Moore, J. E., & Balents, L. (2007) · Physical Review B · doi:10.1103/physrevb.75.121306 · Cited by 2,350
Solitons with fermion number ½
Jackiw, R., & Rebbi, C. (1976) · Physical Review D · doi:10.1103/physrevd.13.3398 · Cited by 2,243
Topological Crystalline Insulators
Fu, L. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.106802 · Cited by 2,095
Topological insulators and superconductors: tenfold way and dimensional hierarchy
Ryu, S., Schnyder, A. P., Furusaki, A., & Ludwig, A. W. W. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/6/065010 · Cited by 2,045
Quantized electric multipole insulators
Benalcazar, W. A., Bernevig, B. A., & Hughes, T. L. (2017) · Science · doi:10.1126/science.aah6442 · Cited by 2,029
Non-Abelian Statistics of Half-Quantum Vortices inp-Wave Superconductors
Ivanov, D. A. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.268 · Cited by 1,930
Bradlyn, B., Elcoro, L., Cano, J., Vergniory, M. G., Wang, Z., Felser, C., Aroyo, M. I., & Bernevig, B. A. (2017) · Nature · doi:10.1038/nature23268 · Cited by 1,624
Topological superconductors: a review
Sato, M., & Ando, Y. (2017) · Reports on Progress in Physics · doi:10.1088/1361-6633/aa6ac7 · Cited by 1,614
Topological crystalline insulators in the SnTe material class
Hsieh, T. H., Lin, H., Liu, J., Duan, W., Bansil, A., & Fu, L. (2012) · Nature Communications · doi:10.1038/ncomms1969 · Cited by 1,449
Benalcazar, W. A., Bernevig, B. A., & Hughes, T. L. (2017) · Physical Review B · doi:10.1103/physrevb.96.245115 · Cited by 1,389
(d−2) -Dimensional Edge States of Rotation Symmetry Protected Topological States
Song, Z., Fang, Z., & Fang, C. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.246402 · Cited by 1,039
Experimental realization of a topological crystalline insulator in SnTe
Tanaka, Y., Ren, Z., Sato, T., Nakayama, K., Souma, S., Takahashi, T., Segawa, K., & Ando, Y. (2012) · Nature Physics · doi:10.1038/nphys2442 · Cited by 1,004
Observation of a phononic quadrupole topological insulator
Serra-Garcia, M., Peri, V., Süsstrunk, R., Bilal, O. R., Larsen, T., Villanueva, L. G., & Huber, S. D. (2018) · Nature · doi:10.1038/nature25156 · Cited by 982
Reflection-Symmetric Second-Order Topological Insulators and Superconductors
Langbehn, J., Peng, Y., Trifunovic, L., von Oppen, F., & Brouwer, P. W. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.246401 · Cited by 973
Higher-Order Topological Insulators and Semimetals on the Breathing Kagome and Pyrochlore Lattices
Ezawa, M. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.026801 · Cited by 864
Topological phases of fermions in one dimension
Fidkowski, L., & Kitaev, A. (2011) · Physical Review B · doi:10.1103/physrevb.83.075103 · Cited by 860
A quantized microwave quadrupole insulator with topologically protected corner states
Peterson, C. W., Benalcazar, W. A., Hughes, T. L., & Bahl, G. (2018) · Nature · doi:10.1038/nature25777 · Cited by 818
Odd-Parity Topological Superconductors: Theory and Application toCuxBi2Se3
Fu, L., & Berg, E. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.097001 · Cited by 802
Díaz-Cruz, J. L., Hernández‐Sánchez, J., Moretti, S., & Rosado, A. (2008) · AIP conference proceedings · Cited by 800
Topological defects and gapless modes in insulators and superconductors
Teo, J. C. Y., & Kane, C. L. (2010) · Physical Review B · doi:10.1103/physrevb.82.115120 · Cited by 798
Symmetry-based indicators of band topology in the 230 space groups
Po, H. C., Vishwanath, A., & Watanabe, H. (2017) · Nature Communications · doi:10.1038/s41467-017-00133-2 · Cited by 791
Topological superconductors: a review
Sato, M., & Ando, Y. (2017) · Kölner Universitäts PublikationsServer (Universität zu Köln) · Cited by 728
Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
Ando, Y., & Fu, L. (2015) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-031214-014501 · Cited by 723
Effects of interactions on the topological classification of free fermion systems
Fidkowski, L., & Kitaev, A. (2010) · Physical Review B · doi:10.1103/physrevb.81.134509 · Cited by 577
Topology of crystalline insulators and superconductors
Shiozaki, K., & Sato, M. (2014) · Physical Review B · doi:10.1103/physrevb.90.165114 · Cited by 507
Moore, J. (2009) · Nature Physics · doi:10.1038/nphys1294 · Cited by 444
Second-order topological insulators and superconductors with an order-two crystalline symmetry
Geier, M., Trifunovic, L., Hoskam, M., & Brouwer, P. W. (2018) · Physical Review B · doi:10.1103/physrevb.97.205135 · Cited by 410
Topological Crystalline Insulators and Topological Superconductors: From Concepts to MaterialsPreprint
Ando, Y., & Fu, L. (2015) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 391
Symmetry-based indicators of band topology in the 230 space groups
Po, H. C., Vishwanath, A., & Watanabe, H. (2017) · RePEc: Research Papers in Economics · Cited by 332
Interacting fermionic topological insulators/superconductors in three dimensions
Wang, C., & Senthil, T. (2014) · Physical Review B · doi:10.1103/physrevb.89.195124 · Cited by 288
Topological odd-parity superconductors
Sato, M. (2010) · Physical Review B · doi:10.1103/physrevb.81.220504 · Cited by 275
Classification of Interacting Electronic Topological Insulators in Three Dimensions
Wang, C., Potter, A. C., & Senthil, T. (2014) · Science · doi:10.1126/science.1243326 · Cited by 253
ADVANCES IN THEORETICAL PHYSICS: Landau Memorial Conference
Lebedev, V., & Feigel'man, M. V. (2009) · Cited by 236
Interacting topological phases and modular invariance
Ryu, S., & Zhang, S.-C. (2012) · Physical Review B · doi:10.1103/physrevb.85.245132 · Cited by 213
Topological Phases Protected by Point Group Symmetry
Song, H., Huang, S.-J., Fu, L., & Hermele, M. (2017) · Physical Review X · doi:10.1103/physrevx.7.011020 · Cited by 200
Building crystalline topological phases from lower-dimensional states
Huang, S.-J., Song, H., Huang, Y.-P., & Hermele, M. (2017) · Physical Review B · doi:10.1103/physrevb.96.205106 · Cited by 186
Zhu, X. (2018) · Physical Review B · doi:10.1103/physrevb.97.205134 · Cited by 173
Gu, Z., & Levin, M. (2014) · Physical Review B · doi:10.1103/physrevb.89.201113 · Cited by 169
Interaction effect on topological classification of superconductors in two dimensions
Yao, H., & Ryu, S. (2013) · Physical Review B · doi:10.1103/physrevb.88.064507 · Cited by 165
Qi, X.-L. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/6/065002 · Cited by 158
Sitte, M., Rosch, A., Altman, E., & Fritz, L. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.126807 · Cited by 140
Theory of interacting topological crystalline insulators
Isobe, H., & Fu, L. (2015) · Physical Review B · doi:10.1103/physrevb.92.081304 · Cited by 116
Morimoto, T., Furusaki, A., & Mudry, C. (2015) · Physical Review B · doi:10.1103/physrevb.92.125104 · Cited by 109
(2013) · Contemporary concepts of condensed matter science · doi:10.1016/b978-0-444-63314-9.00012-3 · Cited by 87
Topological superfluid 3He-B in magnetic field and ising variable
Воловик, Г. Е. (2010) · Journal of Experimental and Theoretical Physics Letters · doi:10.1134/s0021364010040090 · Cited by 74
Interaction-enabled topological crystalline phases
Lapa, M. F., Teo, J. C. Y., & Hughes, T. L. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.93.115131 · Cited by 33
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Metadata
- Authors
- Khalaf, E.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2018-05-25
- Volume
- 97
- Issue
- 20
- ISSN
- 2469-9950 (ISSN-L)
- 2469-9969
- OpenAlex
- W2787634402
- Cited by
- 528
- References
- 59
- FWCI
- 30.96
- Type
- journal article
- Language
- en
- Open access
- green
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