Topology of Disconnected Elementary Band Representations

Cano, Jennifer; Bradlyn, Barry; Wang, Zhijun; Elcoro, L.; Vergniory, M. G.; Felser, C.; Aroyo, M. I.; Bernevig, B. Andrei

doi:10.1103/PhysRevLett.120.266401

Title: Topology of Disconnected Elementary Band Representations

Journal Article · 26 June 2018 · Physical Review Letters

DOI: https://doi.org/10.1103/PhysRevLett.120.266401 · OSTI ID:1457495

Cano, Jennifer; Bradlyn, Barry; Wang, Zhijun; Elcoro, L.; Vergniory, M. G.; Felser, C.; Aroyo, M. I.; Bernevig, B. Andrei

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0016239

OSTI ID:: 1457495

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 26 Vol. 120; ISSN 0031-9007; ISSN PRLTAO

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (47)

Duals of crystallographic groups. Band and quasi-band representations Bacry, Henri Communications in Mathematical Physics, Vol. 153, Issue 2 https://doi.org/10.1007/BF02096648	journal	April 1993
Elementary energy bands in crystals are connected Michel, L. Physics Reports, Vol. 341, Issue 1-6 https://doi.org/10.1016/S0370-1573(00)00093-4	journal	February 2001
Hourglass fermions Wang, Zhijun; Alexandradinata, A.; Cava, R. J. Nature, Vol. 532, Issue 7598 https://doi.org/10.1038/nature17410	journal	April 2016
Topological quantum chemistry Bradlyn, Barry; Elcoro, L.; Cano, Jennifer Nature, Vol. 547, Issue 7663 https://doi.org/10.1038/nature23268	journal	July 2017
Direct measurement of the Zak phase in topological Bloch bands Atala, Marcos; Aidelsburger, Monika; Barreiro, Julio T. Nature Physics, Vol. 9, Issue 12 https://doi.org/10.1038/nphys2790	journal	November 2013
Topological Thouless pumping of ultracold fermions Nakajima, Shuta; Tomita, Takafumi; Taie, Shintaro Nature Physics, Vol. 12, Issue 4 https://doi.org/10.1038/nphys3622	journal	January 2016
Symmetry-based indicators of band topology in the 230 space groups Po, Hoi Chun; Vishwanath, Ashvin; Watanabe, Haruki Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/s41467-017-00133-2	journal	June 2017
The \mathbb{Z}_{2} network model for the quantum spin Hall effect: two-dimensional Dirac fermions, topological quantum numbers and corner multifractality Ryu, Shinsei; Mudry, Christopher; Obuse, Hideaki New Journal of Physics, Vol. 12, Issue 6 https://doi.org/10.1088/1367-2630/12/6/065005	journal	June 2010
Simplified LCAO Method for the Periodic Potential Problem Slater, J. C.; Koster, G. F. Physical Review, Vol. 94, Issue 6 https://doi.org/10.1103/PhysRev.94.1498	journal	June 1954
Band representations of space groups Zak, J. Physical Review B, Vol. 26, Issue 6 https://doi.org/10.1103/PhysRevB.26.3010	journal	September 1982
Connectivity of energy bands in crystals Michel, L.; Zak, J. Physical Review B, Vol. 59, Issue 9 https://doi.org/10.1103/PhysRevB.59.5998	journal	March 1999
Time reversal polarization and a Z 2 adiabatic spin pump Fu, Liang; Kane, C. L. Physical Review B, Vol. 74, Issue 19 https://doi.org/10.1103/PhysRevB.74.195312	journal	November 2006
Topological invariants of time-reversal-invariant band structures Moore, J. E.; Balents, L. Physical Review B, Vol. 75, Issue 12, Article No. 121306(R) https://doi.org/10.1103/PhysRevB.75.121306	journal	March 2007
Topological insulators with inversion symmetry Fu, Liang; Kane, C. L. Physical Review B, Vol. 76, Issue 4 https://doi.org/10.1103/PhysRevB.76.045302	journal	July 2007
Surface states and topological invariants in three-dimensional topological insulators: Application to Bi1−xSbx Teo, Jeffrey C. Y.; Fu, Liang; Kane, C. L. Physical Review B, Vol. 78, Issue 4, Article No. 045426 https://doi.org/10.1103/PhysRevB.78.045426	journal	July 2008
Topological phases and the quantum spin Hall effect in three dimensions Roy, Rahul Physical Review B, Vol. 79, Issue 19 https://doi.org/10.1103/PhysRevB.79.195322	journal	May 2009
Wannier representation of Z 2 topological insulators Soluyanov, Alexey A.; Vanderbilt, David Physical Review B, Vol. 83, Issue 3 https://doi.org/10.1103/PhysRevB.83.035108	journal	January 2011
Equivalent expression of Z 2 topological invariant for band insulators using the non-Abelian Berry connection Yu, Rui; Qi, Xiao Liang; Bernevig, Andrei Physical Review B, Vol. 84, Issue 7 https://doi.org/10.1103/PhysRevB.84.075119	journal	August 2011
Smooth gauge for topological insulators Soluyanov, Alexey A.; Vanderbilt, David Physical Review B, Vol. 85, Issue 11 https://doi.org/10.1103/PhysRevB.85.115415	journal	March 2012
Symmetry classification of energy bands in graphene Kogan, E.; Nazarov, V. U. Physical Review B, Vol. 85, Issue 11 https://doi.org/10.1103/PhysRevB.85.115418	journal	March 2012
Wannier center sheets in topological insulators Taherinejad, Maryam; Garrity, Kevin F.; Vanderbilt, David Physical Review B, Vol. 89, Issue 11 https://doi.org/10.1103/PhysRevB.89.115102	journal	March 2014
Wilson-loop characterization of inversion-symmetric topological insulators Alexandradinata, A.; Dai, Xi; Bernevig, B. Andrei Physical Review B, Vol. 89, Issue 15 https://doi.org/10.1103/PhysRevB.89.155114	journal	April 2014
Compactly supported Wannier functions and algebraic K -theory Read, N. Physical Review B, Vol. 95, Issue 11 https://doi.org/10.1103/PhysRevB.95.115309	journal	March 2017
Topological crystalline materials: General formulation, module structure, and wallpaper groups Shiozaki, Ken; Sato, Masatoshi; Gomi, Kiyonori Physical Review B, Vol. 95, Issue 23 https://doi.org/10.1103/PhysRevB.95.235425	journal	June 2017
Band connectivity for topological quantum chemistry: Band structures as a graph theory problem Bradlyn, Barry; Elcoro, L.; Vergniory, M. G. Physical Review B, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevB.97.035138	journal	January 2018
Building blocks of topological quantum chemistry: Elementary band representations Cano, Jennifer; Bradlyn, Barry; Wang, Zhijun Physical Review B, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevB.97.035139	journal	January 2018
Graph theory data for topological quantum chemistry Vergniory, M. G.; Elcoro, L.; Wang, Zhijun Physical Review E, Vol. 96, Issue 2 https://doi.org/10.1103/PhysRevE.96.023310	journal	August 2017
Topological Surface States in Three-Dimensional Magnetic Insulators Moore, Joel E.; Ran, Ying; Wen, Xiao-Gang Physical Review Letters, Vol. 101, Issue 18 https://doi.org/10.1103/PhysRevLett.101.186805	journal	October 2008
Topological Crystalline Insulators Fu, Liang Physical Review Letters, Vol. 106, Issue 10 https://doi.org/10.1103/PhysRevLett.106.106802	journal	March 2011
Flat Chern Band in a Two-Dimensional Organometallic Framework Liu, Zheng; Wang, Zheng-Fei; Mei, Jia-Wei Physical Review Letters, Vol. 110, Issue 10 https://doi.org/10.1103/PhysRevLett.110.106804	journal	March 2013
Spin-Orbit-Free Topological Insulators without Time-Reversal Symmetry Alexandradinata, A.; Fang, Chen; Gilbert, Matthew J. Physical Review Letters, Vol. 113, Issue 11 https://doi.org/10.1103/PhysRevLett.113.116403	journal	September 2014
Symmetry Specification of Bands in Solids Zak, J. Physical Review Letters, Vol. 45, Issue 12 https://doi.org/10.1103/PhysRevLett.45.1025	journal	September 1980
Symmetry and Analyticity of Energy Bands in Solids Bacry, H.; Michel, L.; Zak, J. Physical Review Letters, Vol. 61, Issue 8 https://doi.org/10.1103/PhysRevLett.61.1005	journal	August 1988
Berry’s phase for energy bands in solids Zak, J. Physical Review Letters, Vol. 62, Issue 23 https://doi.org/10.1103/PhysRevLett.62.2747	journal	June 1989
Quantum Spin Hall Effect in Graphene Kane, C. L.; Mele, E. J. Physical Review Letters, Vol. 95, Issue 22 https://doi.org/10.1103/PhysRevLett.95.226801	journal	November 2005
Topological Insulators in Three Dimensions Fu, Liang; Kane, C. L.; Mele, E. J. Physical Review Letters, Vol. 98, Issue 10, Article No. 106803 https://doi.org/10.1103/PhysRevLett.98.106803	journal	March 2007
Flat Bands and Wigner Crystallization in the Honeycomb Optical Lattice Wu, Congjun; Bergman, Doron; Balents, Leon Physical Review Letters, Vol. 99, Issue 7 https://doi.org/10.1103/PhysRevLett.99.070401	journal	August 2007
Topological Insulators from Group Cohomology Alexandradinata, A.; Wang, Zhijun; Bernevig, B. Andrei Physical Review X, Vol. 6, Issue 2 https://doi.org/10.1103/PhysRevX.6.021008	journal	April 2016
Topological Phases Protected by Point Group Symmetry Song, Hao; Huang, Sheng-Jie; Fu, Liang Physical Review X, Vol. 7, Issue 1 https://doi.org/10.1103/PhysRevX.7.011020	journal	February 2017
Maximally localized Wannier functions: Theory and applications Marzari, Nicola; Mostofi, Arash A.; Yates, Jonathan R. Reviews of Modern Physics, Vol. 84, Issue 4 https://doi.org/10.1103/RevModPhys.84.1419	journal	October 2012
Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups Aroyo, Mois I.; Kirov, Asen; Capillas, Cesar Acta Crystallographica Section A Foundations of Crystallography, Vol. 62, Issue 2 https://doi.org/10.1107/S0108767305040286	journal	March 2006
Double crystallographic groups and their representations on the Bilbao Crystallographic Server Elcoro, Luis; Bradlyn, Barry; Wang, Zhijun Journal of Applied Crystallography, Vol. 50, Issue 5 https://doi.org/10.1107/S1600576717011712	journal	September 2017
Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells Bernevig, B. A.; Hughes, T. L.; Zhang, S.-C. Science, Vol. 314, Issue 5806, p. 1757-1761 https://doi.org/10.1126/science.1133734	journal	December 2006
Quantized electric multipole insulators Benalcazar, Wladimir A.; Bernevig, B. Andrei; Hughes, Taylor L. Science, Vol. 357, Issue 6346 https://doi.org/10.1126/science.aah6442	journal	July 2017
Bismuthene on a SiC substrate: A candidate for a high-temperature quantum spin Hall material Reis, F.; Li, G.; Dudy, L. Science, Vol. 357, Issue 6348 https://doi.org/10.1126/science.aai8142	journal	June 2017
Physical Equivalence of Energy Bands in Solids Michel, L.; Zak, J. Europhysics Letters (EPL), Vol. 18, Issue 3 https://doi.org/10.1209/0295-5075/18/3/009	journal	February 1992
Bilbao Crystallographic Server: I. Databases and crystallographic computing programs Aroyo, Mois Ilia; Perez-Mato, Juan Manuel; Capillas, Cesar Zeitschrift für Kristallographie - Crystalline Materials, Vol. 221, Issue 1 https://doi.org/10.1524/zkri.2006.221.1.15	journal	January 2006

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