The DOI matches its Crossref record; 164 of the 164 references it cites were found in a registry or an index.
Z2Pack: Numerical implementation of hybrid Wannier centers for identifying topological materials
Open accessAbstract
The intense theoretical and experimental interest in topological insulators and semimetals has established band structure topology as a fundamental material property. Consequently, identifying band topologies has become an important, but often challenging, problem, with no exhaustive solution at the present time. In this work we compile a series of techniques, some previously known, that allow for a solution to this problem for a large set of the possible band topologies. The method is based on tracking hybrid Wannier charge centers computed for relevant Bloch states, and it works at all levels of materials modeling: continuous $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ models, tight-binding models, and ab initio calculations. We apply the method to compute and identify Chern, ${\mathbb{Z}}_{2}$, and crystalline topological insulators, as well as topological semimetal phases, using real material examples. Moreover, we provide a numerical implementation of this technique (the Z2Pack software package) that is ideally suited for high-throughput screening of materials databases for compounds with nontrivial topologies. We expect that our work will allow researchers to (a) identify topological materials optimal for experimental probes, (b) classify existing compounds, and (c) reveal materials that host novel, not yet described, topological states.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Generalized Gradient Approximation Made Simple
Perdew, J. P., Burke, K., & Ernzerhof, M. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.3865 · Cited by 215,824
Projector augmented-wave method
Blöchl, P. E. (1994) · Physical Review B · doi:10.1103/physrevb.50.17953 · Cited by 92,732
From ultrasoft pseudopotentials to the projector augmented-wave method
Kresse, G., & Joubert, D. (1999) · Physical Review B · doi:10.1103/physrevb.59.1758 · Cited by 85,307
Kresse, G., & Furthmüller, J. (1996) · Computational Materials Science · doi:10.1016/0927-0256(96)00008-0 · Cited by 75,638
Self-Consistent Equations Including Exchange and Correlation Effects
Kohn, W., & Sham, L. J. (1965) · Physical Review · doi:10.1103/physrev.140.a1133 · Cited by 64,135
Hohenberg, P., & Kohn, W. (1964) · Physical Review · doi:10.1103/physrev.136.b864 · Cited by 53,541
Matplotlib: a 2D graphics environment
Hunter, J. D. (2007) · Computing in Science & Engineering · doi:10.1109/mcse.2007.55 · Cited by 39,249
QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
Giannozzi, P., Baroni, S., Bonini, N., Calandra, M., Car, R., Cavazzoni, C., Ceresoli, D., Chiarotti, G. L., Cococcioni, M., Dabo, I., et al. (2009) · Journal of Physics: Condensed Matter · doi:10.1088/0953-8984/21/39/395502 · Cited by 29,281
Colloquium : Topological insulators
Hasan, M. Z., & Kane, C. L. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.3045 · Cited by 19,930
Hybrid functionals based on a screened Coulomb potential
Heyd, J., Scuseria, G. E., & Ernzerhof, M. (2003) · The Journal of Chemical Physics · doi:10.1063/1.1564060 · Cited by 19,629
Toward reliable density functional methods without adjustable parameters: The PBE0 model
Adamo, C., & Barone, V. (1999) · The Journal of Chemical Physics · doi:10.1063/1.478522 · Cited by 19,042
A new mixing of Hartree–Fock and local density-functional theories
Becke, A. D. (1993) · The Journal of Chemical Physics · doi:10.1063/1.464304 · Cited by 16,515
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
Fault-tolerant quantum computation by anyons
Kitaev, A. Y. (2003) · Annals of Physics · doi:10.1016/s0003-4916(02)00018-0 · Cited by 7,238
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
Self-citationQuantized 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
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
Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface
Zhang, H., Liu, C.-X., Qi, X.-L., Dai, X., Fang, Z., & Zhang, S.-C. (2009) · Nature Physics · doi:10.1038/nphys1270 · Cited by 6,359
Haldane, F. D. M. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.2015 · Cited by 6,301
Quantum Spin Hall Insulator State in HgTe Quantum Wells
König, M., Wiedmann, S., Brüne, C., Roth, A., Buhmann, H., Molenkamp, L. W., Qi, X.-L., & Zhang, S.-C. (2007) · Science · doi:10.1126/science.1148047 · Cited by 6,151
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 · cited 1×
“[30] Liang Fu and Charles L Kane, “Superconducting proximity effect and Majorana Fermions at the surface of a topological insulator,” Phys.”
BackgroundUnpaired Majorana fermions in quantum wires
Kitaev, A. Y. (2001) · Physics-Uspekhi · doi:10.1070/1063-7869/44/10s/s29 · Cited by 4,770
Maximally localized generalized Wannier functions for composite energy bands
Marzari, N., & Vanderbilt, D. (1997) · Physical Review B · doi:10.1103/physrevb.56.12847 · Cited by 4,758
Self-citationWan, X., Turner, A. M., Vishwanath, A., & Savrasov, S. Y. (2011) · Physical Review B · doi:10.1103/physrevb.83.205101 · Cited by 4,718
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
Theory of polarization of crystalline solids
King-Smith, R. D., & Vanderbilt, D. (1993) · Physical Review B · doi:10.1103/physrevb.47.1651 · Cited by 4,472
Self-citationAxial vector vertex in spinor electrodynamics
Adler, S. L. (1969) · Physical Review · doi:10.1103/physrev.177.2426 · Cited by 4,275
Topological insulators with inversion symmetry
Fu, L., & Kane, C. L. (2007) · Physical Review B · doi:10.1103/physrevb.76.045302 · Cited by 4,252
wannier90: A tool for obtaining maximally-localised Wannier functions
Mostofi, A. A., Yates, J. R., Lee, Y.-S., Souza, I., Vanderbilt, D., & Marzari, N. (2008) · Computer Physics Communications · doi:10.1016/j.cpc.2007.11.016 · Cited by 4,234
Self-citationIntroduction to Quantum Field Theory
Milonni, P. W. (1994) · The Quantum Vacuum · doi:10.1016/b978-0-08-057149-2.50014-x · Cited by 4,040
Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
Chang, C.-Z., Zhang, J., Feng, X., Shen, J., Zhang, Z., Guo, M., Li, K., Ou, Y., Wei, P., Wang, L.-L., et al. (2013) · Science · doi:10.1126/science.1234414 · Cited by 3,893
Observation of a large-gap topological-insulator class with a single Dirac cone on the surface
Xia, Y., Qian, D., Hsieh, D., Wray, L., Pal, A., Lin, H., Bansil, A., Grauer, D., Hor, Y. S., Cava, R. J., et al. (2009) · Nature Physics · doi:10.1038/nphys1274 · Cited by 3,765
Experimental Realization of a Three-Dimensional Topological Insulator, Bi 2 Te 3
Chen, Y. L., Analytis, J. G., Chu, J.-H., Liu, Z. K., Mo, S.-K., Qi, X. L., Zhang, H. J., Lu, D. H., Dai, X., Fang, Z., et al. (2009) · Science · doi:10.1126/science.1173034 · Cited by 3,585
A topological Dirac insulator in a quantum spin Hall phase
Hsieh, D., Qian, D., Wray, L., Xia, Y., Hor, Y. S., Cava, R. J., & Hasan, M. Z. (2008) · Nature · doi:10.1038/nature06843 · Cited by 3,523
Lutchyn, R. M., Sau, J. D., & Das Sarma, S. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.077001 · Cited by 3,435
Discovery of a Weyl fermion semimetal and topological Fermi arcs
Xu, S.-Y., Belopolski, I., Alidoust, N., Neupane, M., Bian, G., Zhang, C., Sankar, R., Chang, G., Yuan, Z., Lee, C.-C., et al. (2015) · Science · doi:10.1126/science.aaa9297 · Cited by 3,396 · cited 10×
“[161] Su-Yang Xu, Ilya Belopolski, Nasser Alidoust, Madhab Neupane, Guang Bian, Chenglong Zhang, Raman Sankar, Guoqing Chang, Zhujun Yuan, Chi-Cheng Lee, et al.”
BackgroundInfluentialTopological field theory of time-reversal invariant insulators
Qi, X.-L., Hughes, T. L., & Zhang, S.-C. (2008) · Physical Review B · doi:10.1103/physrevb.78.195424 · Cited by 3,329
Classification of topological insulators and superconductors in three spatial dimensions
Schnyder, A. P., Ryu, S., Furusaki, A., & Ludwig, A. W. W. (2008) · Physical Review B · doi:10.1103/physrevb.78.195125 · Cited by 3,322
A PCAC puzzle: π0→γγ in the σ-model
Bell, J. S., & Jackiw, R. (1969) · Il Nuovo Cimento A · doi:10.1007/bf02823296 · Cited by 3,284 · cited 1×
“In the presence of a magnetic field, Weyl points exhibit a chiral Landau level [36,141,142], which can be a source of the reduced or negative magnetoresistance observed in Weyl semimetals [43,143–145].”
BackgroundHelical Liquids and Majorana Bound States in Quantum Wires
Oreg, Y., Refael, G., & von Oppen, F. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.177002 · Cited by 3,167
ABINIT: First-principles approach to material and nanosystem properties
Gonze, X., Amadon, B., Anglade, P.-M., Beuken, J.-M., Bottin, F., Boulanger, P., Bruneval, F., Caliste, D., Caracas, R., Côté, M., et al. (2009) · Computer Physics Communications · doi:10.1016/j.cpc.2009.07.007 · Cited by 2,701
The Universe in a Helium Droplet
Volovik, G. E. (2009) · doi:10.1093/acprof:oso/9780199564842.001.0001 · Cited by 2,632
Soluyanov, A. A., Gresch, D., Wang, Z., Wu, Q., Troyer, M., Dai, X., & Bernevig, B. A. (2015) · Nature · doi:10.1038/nature15768 · Cited by 2,526
Self-citationAn updated version of wannier90: A tool for obtaining maximally-localised Wannier functions
Mostofi, A. A., Yates, J. R., Pizzi, G., Lee, Y.-S., Souza, I., Vanderbilt, D., & Marzari, N. (2014) · Computer Physics Communications · doi:10.1016/j.cpc.2014.05.003 · Cited by 2,474
Self-citationExperimental Discovery of Weyl Semimetal TaAs
Lv, B. Q., Weng, H. M., Fu, B. B., Wang, X. P., Miao, H., Ma, J., Richard, P., Huang, X. C., Zhao, L. X., Chen, G. F., et al. (2015) · Physical Review X · doi:10.1103/physrevx.5.031013 · Cited by 2,399
Unpaired majorana fermions in quantum wiresPreprint
Kitaev, A. Y. (2000) · Cited by 2,399
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
Discovery of a Three-Dimensional Topological Dirac Semimetal, Na 3 Bi
Liu, Z. K., Zhou, B., Zhang, Y., Wang, Z. J., Weng, H. M., Prabhakaran, D., Mo, S.-K., Shen, Z. X., Fang, Z., Dai, X., et al. (2014) · Science · doi:10.1126/science.1245085 · Cited by 2,328
Weyl Semimetal in a Topological Insulator Multilayer
Burkov, A. A., & Balents, L. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.127205 · Cited by 2,289
Quantized Anomalous Hall Effect in Magnetic Topological Insulators
Yu, R., Zhang, W., Zhang, H.-J., Zhang, S.-C., Dai, X., & Fang, Z. (2010) · Science · doi:10.1126/science.1187485 · Cited by 2,267
Topological Crystalline Insulators
Fu, L. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.106802 · Cited by 2,095
Berry’s phase for energy bands in solids
Zak, J. (1989) · Physical Review Letters · doi:10.1103/physrevlett.62.2747 · Cited by 1,950
Dirac semimetal and topological phase transitions in A 3 Bi ( A = Na , K, Rb)
Wang, Z., Sun, Y., Chen, X.-Q., Franchini, C., Xu, G., Weng, H., Dai, X., & Fang, Z. (2012) · Physical Review B · doi:10.1103/physrevb.85.195320 · Cited by 1,900
Weyl Semimetal Phase in Noncentrosymmetric Transition-Metal Monophosphides
Weng, H., Fang, C., Fang, Z., Bernevig, B. A., & Dai, X. (2015) · Physical Review X · doi:10.1103/physrevx.5.011029 · Cited by 1,889
Self-citationAryasetiawan, F., & Gunnarsson, O. (1998) · Reports on Progress in Physics · doi:10.1088/0034-4885/61/3/002 · Cited by 1,816
Appearance of Gauge Structure in Simple Dynamical Systems
Wilczek, F., & Zee, A. (1984) · Physical Review Letters · doi:10.1103/physrevlett.52.2111 · Cited by 1,775
Quantization of particle transport
Thouless, D. J. (1983) · Physical Review B · doi:10.1103/physrevb.27.6083 · Cited by 1,767
The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal
Nielsen, H. B., & Ninomiya, M. (1983) · Physics Letters B · doi:10.1016/0370-2693(83)91529-0 · Cited by 1,708
Periodic table for topological insulators and superconductors
Kitaev, A., Lebedev, V., & Feigel’man, M. (2009) · AIP Conference Proceedings · doi:10.1063/1.3149495 · Cited by 1,699
Burkov, A. A., Hook, M. D., & Balents, L. (2011) · Physical Review B · doi:10.1103/physrevb.84.235126 · Cited by 1,677
Large, non-saturating magnetoresistance in WTe2
Ali, M. N., Xiong, J., Flynn, S., Tao, J., Gibson, Q. D., Schoop, L. M., Liang, T., Haldolaarachchige, N., Hirschberger, M., Ong, N. P., et al. (2014) · Nature · doi:10.1038/nature13763 · Cited by 1,673
Three-dimensional Dirac semimetal and quantum transport in Cd3As2
Wang, Z., Weng, H., Wu, Q., Dai, X., & Fang, Z. (2013) · Physical Review B · doi:10.1103/physrevb.88.125427 · Cited by 1,649
Geometry, Topology and Physics
Nakahara, M. (1990) · doi:10.1887/0750306068 · Cited by 1,620
A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class
Huang, S.-M., Xu, S.-Y., Belopolski, I., Lee, C.-C., Chang, G., Wang, B., Alidoust, N., Bian, G., Neupane, M., Zhang, C., et al. (2015) · Nature Communications · doi:10.1038/ncomms8373 · Cited by 1,576
Observation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal TaAs
Huang, X., Zhao, L., Long, Y., Wang, P., Chen, D., Yang, Z., Liang, H., Xue, M., Weng, H., Fang, Z., et al. (2015) · Physical Review X · doi:10.1103/physrevx.5.031023 · Cited by 1,528 · cited 1×
“[43] Xiaochun Huang, Lingxiao Zhao, Yujia Long, Peipei Wang, Dong Chen, Zhanhai Yang, Hui Liang, Mianqi Xue, Hongming Weng, Zhong Fang, et al.”
BackgroundUltrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd3As2
Liang, T., Gibson, Q., Ali, M. N., Liu, M., Cava, R. J., & Ong, N. P. (2015) · Nature Materials · doi:10.1038/nmat4143 · Cited by 1,494
A stable three-dimensional topological Dirac semimetal Cd3As2
Liu, Z. K., Jiang, J., Zhou, B., Wang, Z. J., Zhang, Y., Weng, H. M., Prabhakaran, D., Mo, S.-K., Peng, H., Dudin, P., et al. (2014) · Nature Materials · doi:10.1038/nmat3990 · Cited by 1,491
Chern Semimetal and the Quantized Anomalous Hall Effect in HgCr 2 Se 4
Xu, G., Weng, H., Wang, Z., Dai, X., & Fang, Z. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.186806 · Cited by 1,483
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 · cited 2×
“The mirror Chern number was predicted to be nM = 2 for this material [122].”
BackgroundObservation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2
Neupane, M., Xu, S.-Y., Sankar, R., Alidoust, N., Bian, G., Liu, C., Belopolski, I., Chang, T.-R., Jeng, H.-T., Lin, H., et al. (2014) · Nature Communications · doi:10.1038/ncomms4786 · Cited by 1,399
Chiral anomaly and classical negative magnetoresistance of Weyl metals
Son, D. T., & Spivak, B. Z. (2013) · Physical Review B · doi:10.1103/physrevb.88.104412 · Cited by 1,378
A brief introduction to the ABINIT software package
Gonze, X. (2005) · Zeitschrift für Kristallographie - Crystalline Materials · doi:10.1524/zkri.220.5.558.65066 · Cited by 1,261
Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
Bradlyn, B., Cano, J., Wang, Z., Vergniory, M. G., Felser, C., Cava, R. J., & Bernevig, B. A. (2016) · Science · doi:10.1126/science.aaf5037 · Cited by 1,252
Self-citationObservation of Unconventional Quantum Spin Textures in Topological Insulators
Hsieh, D., Xia, Y., Wray, L., Qian, D., Pal, A., Dil, J. H., Osterwalder, J., Meier, F., Bihlmayer, G., Kane, C. L., et al. (2009) · Science · doi:10.1126/science.1167733 · Cited by 1,239
Negative magnetoresistance without well-defined chirality in the Weyl semimetal TaP
Arnold, F., Shekhar, C., Wu, S.-C., Sun, Y., dos Reis, R. D., Kumar, N., Naumann, M., Ajeesh, M. O., Schmidt, M., Grushin, A. G., et al. (2016) · Nature Communications · doi:10.1038/ncomms11615 · Cited by 1,224
Majorana fermions in a tunable semiconductor device
Alicea, J. (2010) · Physical Review B · doi:10.1103/physrevb.81.125318 · Cited by 1,205
Experimental Realization of a Three-Dimensional Dirac Semimetal
Borisenko, S., Gibson, Q., Evtushinsky, D., Zabolotnyy, V., Büchner, B., & Cava, R. J. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.027603 · Cited by 1,175
Effects of Electron-Electron and Electron-Phonon Interactions on the One-Electron States of Solids
Hedin, L., & Lundqvist, S. (1970) · Solid State Physics · doi:10.1016/s0081-1947(08)60615-3 · Cited by 1,134
Analytic Properties of Bloch Waves and Wannier Functions
Kohn, W. (1959) · Physical Review · doi:10.1103/physrev.115.809 · Cited by 1,132
Experimental observation of Weyl points
Lu, L., Wang, Z., Ye, D., Ran, L., Fu, L., Joannopoulos, J. D., & Soljačić, M. (2015) · Science · doi:10.1126/science.aaa9273 · Cited by 1,067
Periodic table for topological insulators and superconductorsPreprint
Kitaev, A. (2009) · Cited by 1,059
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
Topological phases and the quantum spin Hall effect in three dimensions
Roy, R. (2009) · Physical Review B · doi:10.1103/physrevb.79.195322 · Cited by 973
Magnetoelectric Polarizability and Axion Electrodynamics in Crystalline Insulators
Essin, A. M., Moore, J. E., & Vanderbilt, D. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.146805 · Cited by 947
Self-citationTopological response in Weyl semimetals and the chiral anomaly
Zyuzin, A. A., & Burkov, A. A. (2012) · Physical Review B · doi:10.1103/physrevb.86.115133 · Cited by 906
Topological invariant and the quantization of the Hall conductance
Kohmoto, M. (1985) · Annals of Physics · doi:10.1016/0003-4916(85)90148-4 · Cited by 905
Time reversal polarization and a Z 2 adiabatic spin pump
Fu, L., & Kane, C. L. (2006) · Physical Review B · doi:10.1103/physrevb.74.195312 · Cited by 905
Yu, R., Qi, X. L., Bernevig, A., Fang, Z., & Dai, X. (2011) · Physical Review B · doi:10.1103/physrevb.84.075119 · Cited by 884
Classification of stable three-dimensional Dirac semimetals with nontrivial topology
Yang, B.-J., & Nagaosa, N. (2014) · Nature Communications · doi:10.1038/ncomms5898 · Cited by 864
Abrikosov, A. A. (1998) · Physical Review B · doi:10.1103/physrevb.58.2788 · Cited by 848
Teo, J. C. Y., Fu, L., & Kane, C. L. (2008) · Physical Review B · doi:10.1103/physrevb.78.045426 · Cited by 761
Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
Haldane, F. D. M. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.206602 · Cited by 760
Quantum Anomalous Hall Effect inHg1−yMnyTeQuantum Wells
Liu, C.-X., Qi, X.-L., Dai, X., Fang, Z., & Zhang, S.-C. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.146802 · Cited by 736
Multi-Weyl Topological Semimetals Stabilized by Point Group Symmetry
Fang, C., Gilbert, M. J., Dai, X., & Bernevig, B. A. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.266802 · Cited by 698
Self-citationQuantum anomalous Hall effect in graphene from Rashba and exchange effects
Qiao, Z., Yang, S. A., Feng, W., Tse, W.-K., Ding, J., Yao, Y., Wang, J., & Niu, Q. (2010) · Physical Review B · doi:10.1103/physrevb.82.161414 · Cited by 689
Antiferromagnetic topological insulators
Mong, R. S. K., Essin, A. M., & Moore, J. E. (2010) · Physical Review B · doi:10.1103/physrevb.81.245209 · Cited by 663
Quantum Spin-Hall Effect and Topologically Invariant Chern Numbers
Sheng, D. N., Weng, Z. Y., Sheng, L., & Haldane, F. D. M. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.036808 · Cited by 642
van Rossum, G. (2006) · USENIX Annual Technical Conference · Cited by 581
Computing topological invariants without inversion symmetry
Soluyanov, A. A., & Vanderbilt, D. (2011) · Physical Review B · doi:10.1103/physrevb.83.235401 · Cited by 574
Self-citationBzdušek, T., Wu, Q., Rüegg, A., Sigrist, M., & Soluyanov, A. A. (2016) · Nature · doi:10.1038/nature19099 · Cited by 528
Self-citationLandau quantization and quasiparticle interference in the three-dimensional Dirac semimetal Cd3As2
Jeon, S., Zhou, B. B., Gyenis, A., Feldman, B. E., Kimchi, I., Potter, A. C., Gibson, Q. D., Cava, R. J., Vishwanath, A., & Yazdani, A. (2014) · Nature Materials · doi:10.1038/nmat4023 · Cited by 489
Wannier representation ofZ2topological insulators
Soluyanov, A. A., & Vanderbilt, D. (2011) · Physical Review B · doi:10.1103/physrevb.83.035108 · Cited by 445
Self-citationBlount, E. I. (1962) · Solid State Physics · doi:10.1016/s0081-1947(08)60459-2 · Cited by 445
MoTe2: A Type-II Weyl Topological Metal
Wang, Z., Gresch, D., Soluyanov, A. A., Xie, W., Kushwaha, S., Dai, X., Troyer, M., Cava, R. J., & Bernevig, B. A. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.056805 · Cited by 428
Self-citationExponential Localization of Wannier Functions in Insulators
Brouder, C., Panati, G., Calandra, M., Mourougane, C., & Marzari, N. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.046402 · Cited by 409
Hedgehog spin texture and Berry’s phase tuning in a magnetic topological insulator
Xu, S.-Y., Neupane, M., Liu, C., Zhang, D., Richardella, A., Andrew Wray, L., Alidoust, N., Leandersson, M., Balasubramanian, T., Sánchez-Barriga, J., et al. (2012) · Nature Physics · doi:10.1038/nphys2351 · Cited by 388
Wilson-loop characterization of inversion-symmetric topological insulators
Alexandradinata, A., Dai, X., & Bernevig, B. A. (2014) · Physical Review B · doi:10.1103/physrevb.89.155114 · Cited by 388
Self-citationLocalized edge states in two-dimensional topological insulators: Ultrathin Bi films
Wada, M., Murakami, S., Freimuth, F., & Bihlmayer, G. (2011) · Physical Review B · doi:10.1103/physrevb.83.121310 · Cited by 368
Half-Heusler Compounds as a New Class of Three-Dimensional Topological Insulators
Xiao, D., Yao, Y., Feng, W., Wen, J., Zhu, W., Chen, X.-Q., Stocks, G. M., & Zhang, Z. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.096404 · Cited by 363
Double Dirac Semimetals in Three Dimensions.
Wieder, B. J., Kim, Y., Rappe, A. M., & Kane, C. L. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.186402 · Cited by 345
Robustness of the spin-Chern number
Prodan, E. (2009) · Physical Review B · doi:10.1103/physrevb.80.125327 · Cited by 343
Triple Point Topological Metals
Zhu, Z., Winkler, G. W., Wu, Q., Li, J., & Soluyanov, A. A. (2016) · ETH Zurich · doi:10.3929/ethz-b-000118301 · Cited by 333
Self-citationPossible States for a Three-Dimensional Electron Gas in a Strong Magnetic Field
Halperin, B. I. (1987) · Japanese Journal of Applied Physics · doi:10.7567/jjaps.26s3.1913 · Cited by 321
Triple Point Topological Metals
Zhu, Z., Winkler, G. W., Wu, Q., Li, J., & Soluyanov, A. A. (2016) · Physical Review X · doi:10.1103/physrevx.6.031003 · Cited by 310
Self-citationZ2classification of quantum spin Hall systems: An approach using time-reversal invariance
Roy, R. (2009) · Physical Review B · doi:10.1103/physrevb.79.195321 · Cited by 299
Characteristic Classes of Hermitian Manifolds
Chern, S.-S. (1946) · The Annals of Mathematics · doi:10.2307/1969037 · Cited by 293 · cited 1×
“In 2D, or on a 2D cut of the 3D BZ, one can define a Chern number [91] of a single isolated band as [23]”
BackgroundClassification of Topological Insulators and Superconductors
Schnyder, A. P., Ryu, S., Furusaki, A., Ludwig, A. W. W., Lebedev, V., & Feigel’man, M. (2009) · AIP Conference Proceedings · doi:10.1063/1.3149481 · Cited by 289
Spin-orbit coupling with ultrasoft pseudopotentials: Application to Au and Pt
Corso, A. D., & Conte, A. M. (2005) · Physical Review B · doi:10.1103/physrevb.71.115106 · Cited by 289
An Aharonov-Bohm interferometer for determining Bloch band topology
Duca, L., Li, T., Reitter, M., Bloch, I., Schleier-Smith, M., & Schneider, U. (2015) · Science · doi:10.1126/science.1259052 · Cited by 259
Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator
Fu, L., & Kane, C. L. (2009) · Topologica · doi:10.3731/topologica.2.013 · Cited by 257
Adler-Bell-Jackiw anomaly in Weyl semimetals: Application to pyrochlore iridates
Aji, V. (2012) · Physical Review B · doi:10.1103/physrevb.85.241101 · Cited by 250
(1997) · De Gruyter eBooks · doi:10.1515/9783110805055 · Cited by 246
Disordered topological insulators via C * -algebras
Loring, T. A., & Hastings, M. B. (2010) · EPL (Europhysics Letters) · doi:10.1209/0295-5075/92/67004 · Cited by 226
Helical edge and surface states in HgTe quantum wells and bulk insulators
Dai, X., Hughes, T. L., Qi, X.-L., Fang, Z., & Zhang, S.-C. (2008) · Physical Review B · doi:10.1103/physrevb.77.125319 · Cited by 211
Brauer, G., & Zintl, E. (1937) · Zeitschrift für Physikalische Chemie · doi:10.1515/zpch-1937-3725 · Cited by 211
Wannier center sheets in topological insulators
Taherinejad, M., Garrity, K. F., & Vanderbilt, D. (2014) · Physical Review B · doi:10.1103/physrevb.89.115102 · Cited by 205
Self-citationRobust Type-II Weyl Semimetal Phase in Transition Metal DiphosphidesXP2(X=Mo, W)
Autès, G., Gresch, D., Troyer, M., Soluyanov, A. A., & Yazyev, O. V. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.066402 · Cited by 193
Self-citationTopological order and absence of band insulators at integer filling in non-symmorphic crystals
Parameswaran, S. A., Turner, A. M., Arovas, D. P., & Vishwanath, A. (2013) · Nature Physics · doi:10.1038/nphys2600 · Cited by 184
Kivelson, S. (1982) · Physical Review B · doi:10.1103/physrevb.26.4269 · Cited by 171
Wannier functions for magnetic sub-bands
Thouless, D. J. (1984) · Journal of Physics C: Solid State Physics · doi:10.1088/0022-3719/17/12/003 · Cited by 170
Quantum anomalous Hall effect with tunable Chern number in magnetic topological insulator film
Jiang, H., Qiao, Z., Liu, H., & Niu, Q. (2012) · Physical Review B · doi:10.1103/physrevb.85.045445 · Cited by 164
Three-Dimensional Topological Insulators inI−III−VI2andII−IV−V2Chalcopyrite Semiconductors
Feng, W., Xiao, D., Ding, J., & Yao, Y. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.016402 · Cited by 161
Electron localization in the insulating state: Application to crystalline semiconductors
Sgiarovello, C., Peressi, M., & Resta, R. (2001) · Physical Review B · doi:10.1103/physrevb.64.115202 · Cited by 158
Spin-Orbit-Free Topological Insulators without Time-Reversal Symmetry
Alexandradinata, A., Fang, C., Gilbert, M. J., & Bernevig, B. A. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.116403 · Cited by 133
Self-citationTilted Dirac FermionsPreprint
Muechler, L., Alexandradinata, A., Neupert, T., & Car, R. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1604.01398 · Cited by 116
Triviality of Bloch and Bloch-Dirac bundlesPreprint
Panati, G. (2007) · Cited by 115
Non-commutative tools for topological insulators
Prodan, E. V. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/6/065003 · Cited by 113
Chern Insulators from Heavy Atoms on Magnetic Substrates
Garrity, K. F., & Vanderbilt, D. H. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.116802 · Cited by 112
Self-citationExperimental Realization of a Three-Dimensional Topological Insulator, Bi 2Te3
Siemons, W. (2010) · Physical Review B · Cited by 111
Smooth gauge for topological insulators
Soluyanov, A. A., & Vanderbilt, D. H. (2012) · Physical Review B · doi:10.1103/physrevb.85.115415 · Cited by 109
Self-citationTopological Phases in InAs 1 − x Sb x : From Novel Topological Semimetal to Majorana Wire
Winkler, G. W., Wu, Q., Troyer, M., Krogstrup, P., & Soluyanov, A. A. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.076403 · Cited by 108
Self-citationTopological insulators with commensurate antiferromagnetism
Fang, C., Gilbert, M. J., & Bernevig, B. A. (2013) · Physical Review B · doi:10.1103/physrevb.88.085406 · Cited by 104
Self-citationChiral degeneracies and Fermi-surface Chern numbers in bcc Fe
Gosálbez-Martínez, D., Souza, I., & Vanderbilt, D. H. (2015) · Physical Review B · doi:10.1103/physrevb.92.085138 · Cited by 101
Self-citationElectric Polarization in a Chern Insulator
Coh, S., & Vanderbilt, D. H. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.107603 · Cited by 94
Self-citationBerry-phase description of topological crystalline insulators
Alexandradinata, A., & Bernevig, B. A. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.93.205104 · Cited by 91
Self-citationMagnetically doped semiconducting topological insulators
Kou, X., Jiang, W., Lang, M., Xiu, F., He, L., Wang, Y., Wang, Y., Yu, X., Fedorov, A. V., Zhang, P., et al. (2012) · Journal of Applied Physics · doi:10.1063/1.4754452 · Cited by 85
Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi
Chen, Y.-C., Liu, Z., Zhou, B., Zhang, Y., Wang, Z. J., Weng, H., Prabhakran, D., Mo, S., Shen, Z., Fang, Z., et al. (2014) · Bulletin of the American Physical Society · Cited by 81
On the Arsenides and Antimonides of Tantalum.
Furuseth, S., Selte, K., Kjekshus, A., Gronowitz, S., Hoffman, R. A., & Westerdahl, A. (1965) · Acta Chemica Scandinavica · doi:10.3891/acta.chem.scand.19-0095 · Cited by 79
Proposal for Direct Measurement of Topological Invariants in Optical Lattices
Wang, L., Soluyanov, A. A., & Troyer, M. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.166802 · Cited by 75
Self-citationTopological charges of three-dimensional Dirac semimetals with rotation symmetry
Yang, B., Morimoto, T., & Furusaki, A. (2015) · Physical Review B · doi:10.1103/physrevb.92.165120 · Cited by 75
Measuring Z2 topological invariants in optical lattices using interferometry
Grusdt, F., Abanin, D. A., & Demler, E. (2014) · Physical Review A · doi:10.1103/physreva.89.043621 · Cited by 62
Bloch Bundles, Marzari-Vanderbilt Functional and Maximally Localized Wannier Functions
Panati, G., & Pisante, A. (2013) · Communications in Mathematical Physics · doi:10.1007/s00220-013-1741-y · Cited by 58
Chiral anomaly induced negative magnetoresistance in topological Weyl semimetal NbAs
Yang, X., Liu, Y., Wang, Z., Zheng, Y., & Xu, Z.-A. (2015) · arXiv · doi:10.48550/arxiv.1506.03190 · Cited by 52
An analog of the quantum Hall effect in a superfluid 3He film
Воловик, Г. Е. (1988) · Journal of Experimental and Theoretical Physics · Cited by 51
Adiabatic Pumping of Chern-Simons Axion Coupling
Taherinejad, M., & Vanderbilt, D. H. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.096401 · Cited by 48
Self-citationSmooth gauge and Wannier functions for topological band structures in arbitrary dimensions
Winkler, G. W., Soluyanov, A. A., & Troyer, M. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.93.035453 · Cited by 36
Self-citationConstruction of Real-Valued Localized Composite Wannier Functions for Insulators
Fiorenza, D., Monaco, D., & Panati, G. (2015) · Annales Henri Poincaré · doi:10.1007/s00023-015-0400-6 · Cited by 34
Niu, C., Dai, Y., Yu, L., Guo, M., Ma, Y., & Huang, B. (2011) · Applied Physics Letters · doi:10.1063/1.3645624 · Cited by 31
Engineering quantum anomalous Hall phases with orbital and spin degrees of freedom
Zhang, H., Freimuth, F., Bihlmayer, G., Ležaić, M., Blügel, S., & Mokrousov, Y. (2013) · Physical Review B · doi:10.1103/physrevb.87.205132 · Cited by 26
Fermions with cubic and quartic spectrum
Heikkilä, T. T., & Воловик, Г. Е. (2010) · Journal of Experimental and Theoretical Physics Letters · doi:10.1134/s0021364010220091 · Cited by 25
Quantum Anomalous Hall Effect in Magnetic Topological Insulator GdBiTe3Preprint
Zhang, H., Zhang, X., & Zhang, S. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1108.4857 · Cited by 15
Topological aspects of band theory
Soluyanov, A. A. (2012) · Rutgers University Community Repository (Rutgers University) · doi:10.7282/t3n0159g · Cited by 8
Self-citationThree-Dimensional Topological Insulators in I-III-VI$_2$ and II-IV-V$_2$ Chalcopyrite Semiconductors
Xiao, D., Feng, W., Ding, J., & Yao, Y. (2011) · Bulletin of the American Physical Society · Cited by 5
Cited by
WannierTools: An open-source software package for novel topological materials
Wu, Q., Zhang, S., Song, H.-F., Troyer, M., & Soluyanov, A. A. (2018) · Computer Physics Communications · doi:10.1016/j.cpc.2017.09.033 · Cited by 2,724
Self-citationMounet, N., Gibertini, M., Schwaller, P., Campi, D., Merkys, A., Marrazzo, A., Sohier, T., Castelli, I. E., Cepellotti, A., Pizzi, G., et al. (2018) · Nature Nanotechnology · doi:10.1038/s41565-017-0035-5 · Cited by 1,863
From DFT to machine learning: recent approaches to materials science–a review
Schleder, G. R., Padilha, A. C. M., Acosta, C. M., Costa, M., & Fazzio, A. (2019) · Journal of Physics: Materials · doi:10.1088/2515-7639/ab084b · Cited by 852
Electronic Structure: Basic Theory and Practical Methods
Martin, R. M. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108555586 · Cited by 269
Topological Semimetals from First Principles
Gao, H., Venderbos, J. W. F., Kim, Y., & Rappe, A. M. (2019) · Annual Review of Materials Research · doi:10.1146/annurev-matsci-070218-010049 · Cited by 263
Metadata
- Authors
- Gresch, D., Autès, G., Yazyev, O. V., Troyer, M., Vanderbilt, D., Bernevig, B. A., & Soluyanov, A. A.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2017-02-23
- Volume
- 95
- Issue
- 7
- ISSN
- 2469-9950 (ISSN-L)
- 2469-9969
- OpenAlex
- W2542129052
- Cited by
- 438
- References
- 164
- FWCI
- 28.19
- Type
- journal article
- Language
- en
- Open access
- green
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.