Surface states and topological invariants in three-dimensional topological insulators: Application toBi1−xSbx
Open accessAbstract
We study the electronic surface states of the semiconducting alloy bismuth antimony $({\text{Bi}}_{1\ensuremath{-}x}{\text{Sb}}_{x})$. Using a phenomenological tight-binding model, we show that the Fermi surface for the 111 surface states encloses an odd number of time-reversal-invariant momenta (TRIM) in the surface Brillouin zone. This confirms that the alloy is a strong topological insulator in the (1;111) ${\mathbb{Z}}_{2}$ topological class. We go on to develop general arguments which show that spatial symmetries lead to additional topological structure of the bulk energy bands, and impose further constraints on the surface band structure. Inversion-symmetric band structures are characterized by eight ${\mathbb{Z}}_{2}$ ``parity invariants,'' which include the four ${\mathbb{Z}}_{2}$ invariants defined by time-reversal symmetry. The extra invariants determine the ``surface fermion parity,'' which specifies which surface TRIM are enclosed by an odd number of electron or hole pockets. We provide a simple proof of this result, which provides a direct link between the surface-state structure and the parity eigenvalues characterizing the bulk. Using this result, we make specific predictions for the surface-state structure for several faces of ${\text{Bi}}_{1\ensuremath{-}x}{\text{Sb}}_{x}$. We next show that mirror-invariant band structures are characterized by an integer ``mirror Chern number'' ${n}_{\mathcal{M}}$, which further constrains the surface states. We show that the sign of ${n}_{\mathcal{M}}$ in the topological insulator phase of ${\text{Bi}}_{1\ensuremath{-}x}{\text{Sb}}_{x}$ is related to a previously unexplored ${\mathbb{Z}}_{2}$ parameter in the $L$ point $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ theory of pure bismuth, which we refer to as the ``mirror chirality'' $\ensuremath{\eta}$. The value of $\ensuremath{\eta}$ predicted by the tight-binding model for bismuth disagrees with the value predicted by a more fundamental pseudopotential calculation. This explains a subtle disagreement between our tight-binding surface-state calculation and previous first-principles calculations of the surface states of bismuth. This suggests that the tight-binding parameters in the Liu-Allen model of bismuth need to be reconsidered. Implications for existing and future angle-resolved photoemission spectroscopy (ARPES) experiments and spin-polarized ARPES experiments will be discussed.
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
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.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The experimentally derived Mirror Chern number n_M = -2 agrees with the theoretical prediction for SnTe.
“and experimental derived topological invariant (Mirror Chern number 27,28 ) n M ¼ À 2 also agrees with theoretical prediction for SnTe 15 .”
From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [27]
The spin polarization configuration of the surface states corresponds to a mirror topological invariant, the mirror Chern number nM = -2.
“Theoretically expected spin polarization configuration of the surface states which corresponds to a mirror topological invariant (the mirror Chern number) n M ¼ À 2 (refs 27,28).”
From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [27]
Semiconducting Bi-Sb alloys are the only known topological insulator that has non-trivial weak invariants.
“and it is the only known topological insulator that has non-trivial weak invariants (15).”
From Three-Dimensional Topological Insulators (2011) · cites this paper as [15]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
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 · see citing works
Self-citationQuantum 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 · see citing works
Kane, C. L., & Mele, E. J. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.146802 · Cited by 6,460 · see citing works
Self-citationQuantum 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 · see citing works
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 · see citing works
Self-citationTopological 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 · see citing works
Self-citationTopological insulators with inversion symmetry
Fu, L., & Kane, C. L. (2007) · Physical Review B · doi:10.1103/physrevb.76.045302 · Cited by 4,252 · see citing works
Self-citationA 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 · see citing works
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 · see citing works
Bernevig, B. A., & Zhang, S.-C. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.106802 · Cited by 2,164 · see citing works
Fu, L., & Kane, C. L. (2006) · Physical Review B · doi:10.1103/physrevb.74.195312 · Cited by 905 · see citing works
Self-citationStrong Spin-Orbit Splitting on Bi Surfaces
Koroteev, Y. M., Bihlmayer, G., Gayone, J. E., Chulkov, E. V., Blügel, S., Echenique, P. M., & Hofmann, P. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.046403 · Cited by 692 · see citing works
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 653 · see citing works
The surfaces of bismuth: Structural and electronic properties
Hofmann, P. (2006) · Progress in Surface Science · doi:10.1016/j.progsurf.2006.03.001 · Cited by 617 · see citing works
Effective g Factor of Electrons and Holes in Bismuth
Smith, G., Baraff, G. A., & Rowell, J. M. (1964) · Physical Review · doi:10.1103/physrev.135.a1118 · Cited by 375 · see citing works
Electronic structure of the semimetals Bi and Sb
Liu, Y., & Allen, R. E. (1995) · Physical Review B · doi:10.1103/physrevb.52.1566 · Cited by 375 · see citing works
Hirahara, T., Nagao, T., Matsuda, I., Bihlmayer, G., Chulkov, E. V., Koroteev, Y. M., Echenique, P. M., Saito, M., & Hasegawa, S. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.146803 · Cited by 313 · see citing works
Simple scheme for surface-band calculations. I
Lee, D. H., & Joannopoulos, J. D. (1981) · Physical review. B, Condensed matter · doi:10.1103/physrevb.23.4988 · Cited by 303 · see citing works
Transport properties of Bi-RICH Bi-Sb alloys
Lenoir, B., Cassart, M., Michenaud, J.-P., Scherrer, H., & Scherrer, S. (1996) · Journal of Physics and Chemistry of Solids · doi:10.1016/0022-3697(95)00148-4 · Cited by 281 · see citing works
Theg-factor and de haas-van alphen effect of electrons in bismuth
Cohen, M. H., & Blount, E. I. (1960) · Philosophical magazine · doi:10.1080/14786436008243294 · Cited by 248 · see citing works
Matrix elements and selection rules for the two-band model of bismuth
Wolff, P. A. (1964) · Journal of Physics and Chemistry of Solids · doi:10.1016/0022-3697(64)90128-3 · Cited by 235 · see citing works
Fermi Surface of Bi(111) Measured by Photoemission Spectroscopy
Ast, C. R., & Höchst, H. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.177602 · Cited by 230 · see citing works
First-principles investigation of structural and electronic properties of ultrathin Bi films
Koroteev, Y. M., Bihlmayer, G., Chulkov, E. V., & Blügel, S. (2008) · Physical Review B · doi:10.1103/physrevb.77.045428 · Cited by 218 · see citing works
Band Structure of Bismuth: Pseudopotential Approach
Golin, S. (1968) · Physical Review · doi:10.1103/physrev.166.643 · Cited by 212 · see citing works
Direct observation of spin splitting in bismuth surface states
Hirahara, T., Miyamoto, K., Matsuda, I., Kadono, T., Kimura, A., Nagao, T., Bihlmayer, G., Chulkov, E. V., Qiao, S., Shimada, K., et al. (2007) · Physical Review B · doi:10.1103/physrevb.76.153305 · Cited by 179 · see citing works
Role of Spin in Quasiparticle Interference
Pascual, J. I., Bihlmayer, G., Koroteev, Y. M., Rust, H. ‐., Ceballos, G., Hansmann, M., Horn, K., Chulkov, E. V., Blügel, S., Echenique, P. M., et al. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.196802 · Cited by 165 · see citing works
Electronic Band Structure of Arsenic. I. Pseudopotential Approach
Falicov, L. M., & Golin, S. (1965) · Physical Review · doi:10.1103/physrev.137.a871 · Cited by 138 · see citing works
Magnetic Energy Levels in the Bismuth Conduction Band
Baraff, G. A. (1965) · Physical Review · doi:10.1103/physrev.137.a842 · Cited by 89 · see citing works
The effect of reduced dimensionality on a semimetal: the electronic structure of the Bi(110) surface
Agergaard, S., Søndergaard, C. S., Li, H., Nielsen, M. B., Hoffmann, S. V., Li, Z., & Hofmann, P. (2001) · New Journal of Physics · doi:10.1088/1367-2630/3/1/315 · Cited by 79 · see citing works
Electronic structure and Fermi surface of Bi(100)
Hofmann, P., Gayone, J. E., Bihlmayer, G., Koroteev, Y. M., & Chulkov, E. V. (2005) · Physical Review B · doi:10.1103/physrevb.71.195413 · Cited by 62 · see citing works
Theory of Diamagnetism of Bismuth
Buot, F. A., & McClure, J. W. (1972) · Physical review. B, Solid state · doi:10.1103/physrevb.6.4525 · Cited by 43 · see citing works
Two-dimensional band structure and self-energy of Bi(111) near the Γ¯ point
Ast, C. R., & Höchst, H. (2002) · Physical review. B, Condensed matter · doi:10.1103/physrevb.66.125103 · Cited by 43 · see citing works
Photoemission study of the Bi(111) surface
Patthey, F., Schneider, W., & Micklitz, H. (1994) · Physical review. B, Condensed matter · doi:10.1103/physrevb.49.11293 · Cited by 38 · see citing works
Phase rule for the semiconductor-vacuum interface
Claro, F. H. (1978) · Physical review. B, Condensed matter · doi:10.1103/physrevb.17.699 · Cited by 19 · see citing works
Lack of electron–phonon coupling along two-dimensional bands in Bi1−xSbx single crystal alloys
Höchst, H., & Gorovikov, S. A. (2005) · Journal of Electron Spectroscopy and Related Phenomena · doi:10.1016/j.elspec.2005.01.163 · Cited by 8 · see citing works
Flagged first, then by citations
Research works printed but not linked: 1
- 36 B. Lenoir, et al., Proceedings of Fifteenth International Conference on Thermoelectrics, p. 1-12, (1996).
Cited by
Sorted by citations
<i>Colloquium</i> : Topological insulators
Hasan, M. Z., & Kane, C. L. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.3045 · Cited by 19,930 · see citing works
Self-citationTopological insulators and superconductors
Qi, X.-L., & Zhang, S.-C. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.1057 · Cited by 14,394 · see citing works
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 · see citing works
Classification of topological quantum matter with symmetries
Chiu, C., Teo, J. C. Y., Schnyder, A. P., & Ryu, S. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.035005 · Cited by 2,831 · see citing works
Self-citationTopological Insulator Materials
Ando, Y. (2013) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.82.102001 · Cited by 1,789 · see citing works
Higher-order topological insulators
Schindler, F., Cook, A. M., Vergniory, M. G., Wang, Z., Parkin, S., Bernevig, B. A., & Neupert, T. (2018) · Science Advances · doi:10.1126/sciadv.aat0346 · Cited by 1,634 · see citing works
Topological superconductors: a review
Sato, M., & Ando, Y. (2017) · Reports on Progress in Physics · doi:10.1088/1361-6633/aa6ac7 · Cited by 1,674 · see citing works
<i>Colloquium</i> : Topological band theory
Bansil, A., Lin, H., & Das, T. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.021004 · Cited by 1,587 · see citing works
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 · see citing works
Self-citationBenalcazar, W. A., Bernevig, B. A., & Hughes, T. L. (2017) · Physical Review B · doi:10.1103/physrevb.96.245115 · Cited by 1,389 · see citing works
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 · see citing works
Observation 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 · see citing works
Self-citationSpintronics and pseudospintronics in graphene and topological insulators
Pesin, D. A., & MacDonald, A. H. (2012) · Nature Materials · doi:10.1038/nmat3305 · Cited by 1,099 · see citing works
Topological surface states protected from backscattering by chiral spin texture
Roushan, P., Seo, J., Parker, C. V., Hor, Y. S., Hsieh, D., Qian, D., Richardella, A., Hasan, M. Z., Cava, R. J., & Yazdani, A. (2009) · Nature · doi:10.1038/nature08308 · Cited by 1,052 · see citing works
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 969 · see citing works
Yu, R., Qi, X. L., Bernevig, B. A., Fang, Z., & Dai, X. (2011) · Physical Review B · doi:10.1103/physrevb.84.075119 · Cited by 869 · see citing works
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 · see citing works
Higher-order topology in bismuth
Schindler, F., Wang, Z., Vergniory, M. G., Cook, A. M., Murani, A., Sengupta, S., Kasumov, A. Y., Deblock, R., Jeon, S., Drozdov, I., et al. (2018) · Nature Physics · doi:10.1038/s41567-018-0224-7 · Cited by 834 · see citing works
Benalcazar, W. A., Li, T., & Hughes, T. L. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.99.245151 · Cited by 764 · see citing works
Experimental Demonstration of Topological Surface States Protected by Time-Reversal Symmetry
Zhang, T., Cheng, P., Chen, X., Jia, J.-F., Ma, X., He, K., Wang, L., Zhang, H., Dai, X., Fang, Z., et al. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.266803 · Cited by 744 · see citing works
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 · see citing works
Self-citationXu, S.-Y., Liu, C., Alidoust, N., Neupane, M., Qian, D., Belopolski, I., Denlinger, J. D., Wang, Y. J., Lin, H., Wray, L. A., et al. (2012) · Nature Communications · doi:10.1038/ncomms2191 · Cited by 691 · see citing works
Topological Classification of Crystalline Insulators through Band Structure Combinatorics
Kruthoff, J., Jan De Boer, A., van Wezel, J., Kane, C. L., & Slager, R.-J. (2017) · Physical Review X · doi:10.1103/physrevx.7.041069 · Cited by 690 · see citing works
Self-citationThree-Dimensional Topological Insulators
Hasan, M. Z., & Moore, J. E. (2011) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-062910-140432 · Cited by 699 · see citing works
The space group classification of topological band-insulators
Slager, R.-J., Mesaroš, A., Juričić, V., & Zaanen, J. (2012) · Nature Physics · doi:10.1038/nphys2513 · Cited by 631 · see citing works
Miransky, V. A., & Shovkovy, I. A. (2015) · Physics Reports · doi:10.1016/j.physrep.2015.02.003 · Cited by 644 · see citing works
Topological band engineering of graphene nanoribbons
Rizzo, D. J., Veber, G., Cao, T., Bronner, C., Chen, T., Zhao, F., Rodriguez, H., Louie, S. G., Crommie, M. F., & Fischer, F. R. (2018) · Nature · doi:10.1038/s41586-018-0376-8 · Cited by 648 · see citing works
Topological superconductors: a review
Sato, M., & Ando, Y. (2017) · Kölner Universitäts PublikationsServer (Universität zu Köln) · Cited by 728 · see citing works
Massive Dirac fermions and spin physics in an ultrathin film of topological insulator
Lu, H.-Z., Shan, W.-Y., Yao, W., Niu, Q., & Shen, S.-Q. (2010) · Physical Review B · doi:10.1103/physrevb.81.115407 · Cited by 607 · see citing works
Two-dimensional surface state in the quantum limit of a topological insulator
Analytis, J. G., McDonald, R. D., Riggs, S. C., Chu, J.-H., Boebinger, G. S., & Fisher, I. R. (2010) · Nature Physics · doi:10.1038/nphys1861 · Cited by 595 · see citing works
Topological insulator on the kagome lattice
Guo, H., & Franz, M. (2009) · Physical Review B · doi:10.1103/physrevb.80.113102 · Cited by 554 · see citing works
Khang, N. H. D., Ueda, Y., & Hai, P. N. (2018) · Nature Materials · doi:10.1038/s41563-018-0137-y · Cited by 514 · see citing works
Topology of crystalline insulators and superconductors
Shiozaki, K., & Sato, M. (2014) · Physical Review B · doi:10.1103/physrevb.90.165114 · Cited by 506 · see citing works
Analytis, J. G., Chu, J., Chen, Y., Corredor, F., McDonald, R., Shen, Z., & Fisher, I. R. (2010) · Physical Review B · doi:10.1103/physrevb.81.205407 · Cited by 467 · see citing works
Z2Pack: Numerical implementation of hybrid Wannier centers for identifying topological materials
Gresch, D., Autès, G., Yazyev, O. V., Troyer, M., Vanderbilt, D. H., Bernevig, B. A., & Soluyanov, A. A. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.95.075146 · Cited by 435 · see citing works
Wang, Z., Alexandradinata, A., Cava, R. J., & Bernevig, B. A. (2016) · Nature · doi:10.1038/nature17410 · Cited by 421 · see citing works
One-dimensional topologically protected modes in topological insulators with lattice dislocations
Ran, Y., Zhang, Y., & Vishwanath, A. (2009) · Nature Physics · doi:10.1038/nphys1220 · Cited by 421 · see citing works
Kim, H.-J., Kim, K.-S., Wang, J.-F., Sasaki, M., Satoh, N., Ohnishi, A., Kitaura, M., Yang, M., & Li, L. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.246603 · Cited by 425 · see citing works
Zhang, W., Yu, R., Zhang, H.-J., Dai, X., & Fang, Z. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/6/065013 · Cited by 423 · see citing works
Yan, B., & Zhang, S. (2012) · Reports on Progress in Physics · doi:10.1088/0034-4885/75/9/096501 · Cited by 412 · see citing works
One-dimensional topological edge states of bismuth bilayers
Drozdov, I., Alexandradinata, A., Jeon, S., Nadj-Perge, S., Ji, H., Cava, R. J., Bernevig, B. A., & Yazdani, A. (2014) · Nature Physics · doi:10.1038/nphys3048 · Cited by 401 · see citing works
Second-order topological insulators and superconductors with an order-two crystalline symmetry
Geier, M., Trifunovic, L., Hoskam, M. S. M., & Brouwer, P. W. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.97.205135 · Cited by 409 · see citing works
Shan, W.-Y., Lu, H.-Z., & Shen, S.-Q. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/4/043048 · Cited by 398 · see citing works
Fragile Topology and Wannier Obstructions
Po, H. C., Watanabe, H., & Vishwanath, A. (2018) · Physical Review Letters · doi:10.1103/physrevlett.121.126402 · Cited by 377 · see citing works
Interacting topological insulators: a review
Rachel, S. (2018) · Reports on Progress in Physics · doi:10.1088/1361-6633/aad6a6 · Cited by 383 · see citing works
Ca3P2 and other topological semimetals with line nodes and drumhead surface states
Chan, Y., Chiu, C., Chou, M. Y., & Schnyder, A. P. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.93.205132 · Cited by 384 · see citing works
Liu, J., Hsieh, T. H., Wei, P., Duan, W., Moodera, J. S., & Fu, L. (2013) · Nature Materials · doi:10.1038/nmat3828 · Cited by 356 · see citing works
Self-citationClassification of topological insulators and superconductors in the presence of reflection symmetry
Chiu, C., Yao, H., & Ryu, S. (2013) · Physical Review B · doi:10.1103/physrevb.88.075142 · Cited by 346 · see citing works
New topological invariants in non-Hermitian systems
Ghatak, A., & Das, T. (2019) · Journal of Physics Condensed Matter · doi:10.1088/1361-648x/ab11b3 · Cited by 350 · see citing works
Wang, Z., Wieder, B. J., Li, J., Yan, B., & Bernevig, B. A. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.186401 · Cited by 348 · see citing works
Classification of reflection-symmetry-protected topological semimetals and nodal superconductors
Chiu, C.-K., & Schnyder, A. P. (2014) · Physical Review B · doi:10.1103/physrevb.90.205136 · Cited by 339 · see citing works
Topological Crystalline Insulators and Topological Superconductors: From Concepts to MaterialsPreprint
Ando, Y., & Fu, L. (2015) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 391 · see citing works
Self-citationPressure-induced superconductivity in topological parent compound Bi 2 Te 3
Zhang, J. L., Zhang, S. J., Weng, H., Zhang, W., Yang, L., Liu, Q. Q., Feng, S. M., Wang, X., Yu, R., Cao, L., et al. (2010) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1014085108 · Cited by 334 · see citing works
Quantitative mappings between symmetry and topology in solids
Song, Z., Zhang, T., Fang, Z., & Fang, C. (2018) · Nature Communications · doi:10.1038/s41467-018-06010-w · Cited by 316 · see citing works
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 312 · see citing works
Topological insulators and Mott physics from the Hubbard interaction
Rachel, S., & Hur, K. L. (2010) · Physical Review B · doi:10.1103/physrevb.82.075106 · Cited by 305 · see citing works
Classification of topological phonons in linear mechanical metamaterials
Süsstrunk, R., & Huber, S. D. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1605462113 · Cited by 308 · see citing works
Edge states and the bulk-boundary correspondence in Dirac Hamiltonians
Mong, R. S. K., & Shivamoggi, V. (2011) · Physical Review B · doi:10.1103/physrevb.83.125109 · Cited by 298 · see citing works
Topological classification with additional symmetries from Clifford algebras
Morimoto, T., & Furusaki, A. (2013) · Physical Review B · doi:10.1103/physrevb.88.125129 · Cited by 272 · see citing works
Building blocks of topological quantum chemistry: Elementary band representations
Cano, J., Bradlyn, B., Wang, Z., Elcoro, L., Vergniory, M. G., Felser, C., Aroyo, M. I., & Bernevig, B. A. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.97.035139 · Cited by 261 · see citing works
Exciton Condensation and Charge Fractionalization in a Topological Insulator Film
Seradjeh, B., Moore, J. E., & Franz, M. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.066402 · Cited by 267 · see citing works
Bouhon, A., Black‐Schaffer, A. M., & Slager, R.-J. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.100.195135 · Cited by 251 · see citing works
New classes of three-dimensional topological crystalline insulators: Nonsymmorphic and magnetic
Fang, C., & Fu, L. (2015) · Physical Review B · doi:10.1103/physrevb.91.161105 · Cited by 237 · see citing works
Self-citationAb initio tight-binding Hamiltonian for transition metal dichalcogenides
Fang, S., Defo, R. K., Shirodkar, S. N., Lieu, S., Tritsaris, G. A., & Kaxiras, E. (2015) · Physical Review B · doi:10.1103/physrevb.92.205108 · Cited by 232 · see citing works
Two types of surface states in topological crystalline insulators
Liu, J., Duan, W., & Fu, L. (2013) · Physical Review B · doi:10.1103/physrevb.88.241303 · Cited by 229 · see citing works
Self-citationDirect Evidence for the Dirac-Cone Topological Surface States in the Ternary Chalcogenide TlBiSe2
Sato, T., Segawa, K., Guo, H., Sugawara, K., Souma, S., Takahashi, T., & Ando, Y. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.136802 · Cited by 223 · see citing works
Strong and fragile topological Dirac semimetals with higher-order Fermi arcs
Wieder, B. J., Wang, Z., Cano, J., Dai, X., Schoop, L. M., Bradlyn, B., & Bernevig, B. A. (2020) · Nature Communications · doi:10.1038/s41467-020-14443-5 · Cited by 246 · see citing works
Zero-gap materials for future spintronics, electronics and optics
Wang, X. L., Dou, S. X., & Zhang, C. (2010) · NPG Asia Materials · doi:10.1038/asiamat.2010.7 · Cited by 217 · see citing works
A fractional corner anomaly reveals higher-order topology
Peterson, C. W., Li, T., Benalcazar, W. A., Hughes, T. L., & Bahl, G. (2020) · Science · doi:10.1126/science.aba7604 · Cited by 206 · see citing works
Topological Aspect and Quantum Magnetoresistance of β−Ag2Te
Zhang, W., Yu, R., Feng, W., Yao, Y., Weng, H., Dai, X., & Fang, Z. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.156808 · Cited by 209 · see citing works
Topological materials discovery from crystal symmetry
Wieder, B. J., Bradlyn, B., Cano, J., Wang, Z., Vergniory, M. G., Elcoro, L., Soluyanov, A. A., Felser, C., Neupert, T., Regnault, N., et al. (2021) · Nature Reviews Materials · doi:10.1038/s41578-021-00380-2 · Cited by 209 · see citing works
All topological bands of all nonmagnetic stoichiometric materials
Vergniory, M. G., Wieder, B. J., Elcoro, L., Parkin, S., Felser, C., Bernevig, B. A., & Regnault, N. (2022) · Science · doi:10.1126/science.abg9094 · Cited by 215 · see citing works
Topological superconductivity in two-dimensional altermagnetic metals
Zhu, D., Zhuang, Z.-Y., Wu, Z., & Yan, Z. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.108.184505 · Cited by 203 · see citing works
Eto, K., Ren, Z., Taskin, A. A., Segawa, K., & Ando, Y. (2010) · Physical Review B · doi:10.1103/physrevb.81.195309 · Cited by 200 · see citing works
Disordered topological insulators: a non-commutative geometry perspective
Prodan, E. V. (2011) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/44/11/113001 · Cited by 198 · see citing works
Benalcazar, W. A., Teo, J. C. Y., & Hughes, T. L. (2014) · Physical Review B · doi:10.1103/physrevb.89.224503 · Cited by 191 · see citing works
Self-citationYokoyama, T., Tanaka, Y., & Nagaosa, N. (2010) · Physical Review B · doi:10.1103/physrevb.81.121401 · Cited by 197 · see citing works
Strong and fragile topological Dirac semimetals with higher-order Fermi arcs
Wieder, B. J., Wang, Z., Cano, J., Dai, X., Schoop, L. M., Bradlyn, B., & Bernevig, B. A. (2020) · Refubium (Universitätsbibliothek der Freien Universität Berlin) · doi:10.17169/refubium-26770 · Cited by 191 · see citing works
Quantum oscillations in a topological insulator Bi1−xSbx
Taskin, A. A., & Ando, Y. (2009) · Physical Review B · doi:10.1103/physrevb.80.085303 · Cited by 181 · see citing works
Second-order topological non-Hermitian skin effects
Okugawa, R., Takahashi, R., & Yokomizo, K. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.102.241202 · Cited by 183 · see citing works
Two-dimensional surface charge transport in topological insulators
Culcer, D., Hwang, E. H., Stanescu, T. D., & Sarma, S. D. (2010) · Physical Review B · doi:10.1103/physrevb.82.155457 · Cited by 183 · see citing works
Large linear magnetoresistance in the Dirac semimetal TlBiSSe
Novak, M., Sasaki, S., Segawa, K., & Ando, Y. (2015) · Physical Review B · doi:10.1103/physrevb.91.041203 · Cited by 183 · see citing works
Axial anomaly and longitudinal magnetoresistance of a generic three dimensional metal
Goswami, P., Pixley, J. H., & Das Sarma, S. (2015) · Physical Review B · doi:10.1103/physrevb.92.075205 · Cited by 180 · see citing works
Topological Crystalline Kondo Insulator in Mixed Valence Ytterbium Borides
Weng, H., Zhao, J., Wang, Z., Fang, Z., & Dai, X. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.016403 · Cited by 175 · see citing works
Teo, J. C. Y., & Hughes, T. L. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.047006 · Cited by 174 · see citing works
Self-citationWallpaper fermions and the nonsymmorphic Dirac insulator
Wieder, B. J., Bradlyn, B., Wang, Z., Cano, J., Kim, Y., Kim, H.-S. D., Rappe, A. M., Kane, C. L., & Bernevig, B. A. (2018) · Science · doi:10.1126/science.aan2802 · Cited by 172 · see citing works
Self-citationTopological Superconductivity in Dirac Semimetals
Kobayashi, S., & Sato, M. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.187001 · Cited by 171 · see citing works
Nernst and magnetothermal conductivity in a lattice model of Weyl fermions
Sharma, G., Goswami, P., & Tewari, S. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.93.035116 · Cited by 168 · see citing works
Ferroelectric Order Control of the Dirac‐Semimetal Phase in GeTe‐Sb2Te3 Superlattices
Tominaga, J., Kolobov, A. V., Fons, P., Nakano, T., & Murakami, S. (2013) · Advanced Materials Interfaces · doi:10.1002/admi.201300027 · Cited by 170 · see citing works
Direct mapping of the spin-filtered surface bands of a three-dimensional quantum spin Hall insulator
Nishide, A., Taskin, A. A., Takeichi, Y., Okuda, T., Kakizaki, A., Hirahara, T., Nakatsuji, K., Komori, F., Ando, Y., & Matsuda, I. (2010) · Physical Review B · doi:10.1103/physrevb.81.041309 · Cited by 166 · see citing works
Hsieh, T. H., & Fu, L. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.107005 · Cited by 166 · see citing works
Self-citationTopology of nonsymmorphic crystalline insulators and superconductors
Shiozaki, K., Sato, M., & Gomi, K. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.93.195413 · Cited by 162 · see citing works
Topological crystalline insulators and Dirac octets in antiperovskites
Hsieh, T. H., Liu, J., & Fu, L. (2014) · Physical Review B · doi:10.1103/physrevb.90.081112 · Cited by 165 · see citing works
Self-citationFractional disclination charge in two-dimensional Cn -symmetric topological crystalline insulators
Li, T., Zhu, P., Benalcazar, W. A., & Hughes, T. L. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.101.115115 · Cited by 159 · see citing works
Trapped fractional charges at bulk defects in topological insulators
Peterson, C. W., Li, T., Jiang, W., Hughes, T. L., & Bahl, G. (2021) · Nature · doi:10.1038/s41586-020-03117-3 · Cited by 167 · see citing works
Single-layer MoS 2 on Au(111): Band gap renormalization and substrate interaction
Bruix, A., Miwa, J. A., Hauptmann, N., Wegner, D., Ulstrup, S., Grønborg, S. S., Sanders, C. E., Dendzik, M., Čabo, A. G., Bianchi, M., et al. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.93.165422 · Cited by 162 · see citing works
Two-dimensional Stiefel-Whitney insulators in liganded Xenes
Pan, M., Li, D., Fan, J., & Huang, H. (2022) · npj Computational Materials · doi:10.1038/s41524-021-00695-2 · Cited by 161 · see citing works
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 154 · see citing works
Robustness of Topologically Protected Surface States in Layering of Bi2Te3 Thin Films
Park, K., Heremans, J. J., Scarola, V. W., & Minić, D. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.186801 · Cited by 150 · see citing works
Dispersion of Fermi arcs in Weyl semimetals and their evolutions to Dirac cones
Okugawa, R., & Murakami, S. (2014) · Physical Review B · doi:10.1103/physrevb.89.235315 · Cited by 150 · see citing works
- Authors
- Teo, J. C. Y., Fu, L., & Kane, C. L.
- Affiliations
- University of Pennsylvania (US)
- ORCID
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2008-07-23
- Volume
- 78
- Issue
- 4
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W2171464705
- Cited by
- 761
- References
- 35
- Citations by year
- 2026: 18 · 2025: 40 · 2024: 38 · 2023: 37 · 2022: 54 · 2021: 45 · 2020: 59 · 2019: 51 · 2018: 56 · 2017: 49 · 2016: 57 · 2015: 61 · 2014: 48 · 2013: 38 · 2012: 35
- FWCI
- 14.52
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- APS
- Bulletin of the American Physical Society
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Surface and Thin Film Phenomena
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Keywords
- Bi1-xSbx, bismuth-antimony alloys, topological insulators, surface states, Z2 topological invariant, surface Brillouin zone, parity invariant, mirror Chern number, inversion symmetry, mirror symmetry, Fermi surface
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
