Wallpaper fermions and the nonsymmorphic Dirac insulator

Wieder, Benjamin J.; Bradlyn, Barry; Wang, Zhijun; Cano, Jennifer; Kim, Youngkuk; Kim, Hyeong-Seok D.; Rappe, Andrew M.; Kane, C. L.; Bernevig, B. Andrei

doi:10.1126/science.aan2802

Title: Wallpaper fermions and the nonsymmorphic Dirac insulator

Journal Article · 19 July 2018 · Science

DOI: https://doi.org/10.1126/science.aan2802 · OSTI ID:1460922

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Department of Physics, Princeton University, Princeton, NJ 08544, USA., Nordita, Center for Quantum Materials, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden., Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104-6323, USA.
Princeton Center for Theoretical Science, Princeton University, Princeton, NJ 08544, USA.
Department of Physics, Princeton University, Princeton, NJ 08544, USA.
Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104-6323, USA., Department of Physics, Sungkyunkwan University (SKKU), Suwon 16419, Korea.
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104-6323, USA., Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104-6323, USA.
Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104-6323, USA.
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104-6323, USA.
Department of Physics, Princeton University, Princeton, NJ 08544, USA., Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany., Max Planck Institute of Microstructure Physics, 06120 Halle, Germany.

Materials whose gapless surface states are protected by crystal symmetries include mirror topological crystalline insulators and nonsymmorphic hourglass insulators. There exists only a very limited set of possible surface crystal symmetries, captured by the 17 “wallpaper groups.” Here we show that a consideration of symmetry-allowed band degeneracies in the wallpaper groups can be used to understand previously described topological crystalline insulators and to predict phenomenologically distinct examples. In particular, the two wallpaper groups with multiple glide lines, pgg and p 4 g , allow for a topological insulating phase whose surface spectrum consists of only a single, fourfold-degenerate, true Dirac fermion, representing an exception to a symmetry-enhanced fermion-doubling theorem. We theoretically predict the presence of this phase in Sr ₂ Pb ₃ in space group 127 ( P 4 /mbm) .

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Sponsoring Organization:: USDOE

Grant/Contract Number:: NERSC; SC0016239

OSTI ID:: 1460922

Journal Information:: Science, Journal Name: Science Vol. 361 Journal Issue: 6399; ISSN 0036-8075

Publisher:: American Association for the Advancement of Science (AAAS)Copyright Statement

Country of Publication:: United States

Language:: English

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References (100)

Generalized Gradient Approximation Made Simple Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868 https://doi.org/10.1103/PhysRevLett.77.3865	journal	October 1996
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
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
Projector augmented-wave method Blöchl, P. E. Physical Review B, Vol. 50, Issue 24, p. 17953-17979 https://doi.org/10.1103/PhysRevB.50.17953	journal	December 1994
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
Condensed-Matter Simulation of a Three-Dimensional Anomaly Semenoff, Gordon W. Physical Review Letters, Vol. 53, Issue 26 https://doi.org/10.1103/PhysRevLett.53.2449	journal	December 1984
Hourglass fermions Wang, Zhijun; Alexandradinata, A.; Cava, R. J. Nature, Vol. 532, Issue 7598 https://doi.org/10.1038/nature17410	journal	April 2016
The Hg-Sr (Mercury-Strontium) System Gumiński, C. Journal of Phase Equilibria and Diffusion, Vol. 26, Issue 1 https://doi.org/10.1007/s11669-005-0070-z	journal	February 2005
Three-dimensional Dirac semimetal and quantum transport in Cd 3 As 2 Wang, Zhijun; Weng, Hongming; Wu, Quansheng Physical Review B, Vol. 88, Issue 12 https://doi.org/10.1103/PhysRevB.88.125427	journal	September 2013
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
QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials Giannozzi, Paolo; Baroni, Stefano; Bonini, Nicola Journal of Physics: Condensed Matter, Vol. 21, Issue 39, Article No. 395502 https://doi.org/10.1088/0953-8984/21/39/395502	journal	September 2009
Classification of stable three-dimensional Dirac semimetals with nontrivial topology Yang, Bohm-Jung; Nagaosa, Naoto Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms5898	journal	September 2014
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
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
Anomalies and odd dimensions Alvarez-Gaumé, L.; Della Pietra, S.; Moore, G. Annals of Physics, Vol. 163, Issue 2 https://doi.org/10.1016/0003-4916(85)90383-5	journal	September 1985
Existence of bulk chiral fermions and crystal symmetry Mañes, J. L. Physical Review B, Vol. 85, Issue 15 https://doi.org/10.1103/PhysRevB.85.155118	journal	April 2012
Dirac Semimetal in Three Dimensions Young, S. M.; Zaheer, S.; Teo, J. C. Y. Physical Review Letters, Vol. 108, Issue 14 https://doi.org/10.1103/PhysRevLett.108.140405	journal	April 2012
Tunable Luttinger Liquid Physics in Biased Bilayer Graphene Killi, Matthew; Wei, Tzu-Chieh; Affleck, Ian Physical Review Letters, Vol. 104, Issue 21 https://doi.org/10.1103/PhysRevLett.104.216406	journal	May 2010
Topological Insulators and Topological Superconductors Bernevig, B. Andrei Princeton University Press https://doi.org/10.1515/9781400846733	book	January 2013
Topological crystalline insulators in the SnTe material class Hsieh, Timothy H.; Lin, Hsin; Liu, Junwei Nature Communications, Vol. 3, Article No. 982 https://doi.org/10.1038/ncomms1969	journal	January 2012
The electronic properties of graphene Castro Neto, A. H.; Guinea, F.; Peres, N. M. R. Reviews of Modern Physics, Vol. 81, Issue 1, p. 109-162 https://doi.org/10.1103/RevModPhys.81.109	journal	January 2009
Unconventional Chiral Fermions and Large Topological Fermi Arcs in RhSi Chang, Guoqing; Xu, Su-Yang; Wieder, Benjamin J. Physical Review Letters, Vol. 119, Issue 20 https://doi.org/10.1103/PhysRevLett.119.206401	journal	November 2017
Topological semimetals with helicoid surface states Fang, Chen; Lu, Ling; Liu, Junwei Nature Physics, Vol. 12, Issue 10 https://doi.org/10.1038/nphys3782	journal	June 2016
Two new compounds, β-ScTe and Y ₃ Au ₂ , and a reassessment of Y ₂ Au Chai, Ping; Corbett, John D. Acta Crystallographica Section C Crystal Structure Communications, Vol. 67, Issue 11 https://doi.org/10.1107/S010827011103589X	journal	October 2011
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
Absence of neutrinos on a lattice Nielsen, H. B.; Ninomiya, M. Nuclear Physics B, Vol. 185, Issue 1 https://doi.org/10.1016/0550-3213(81)90361-8	journal	July 1981
On the Sr-Pb system Bruzzone, G.; Franceschi, E.; Merlo, F. Journal of the Less Common Metals, Vol. 81, Issue 1 https://doi.org/10.1016/0022-5088(81)90278-2	journal	September 1981
Z2 Topological Order and the Quantum Spin Hall Effect Kane, C. L.; Mele, E. J. Physical Review Letters, Vol. 95, Issue 14, Article No. 146802 https://doi.org/10.1103/PhysRevLett.95.146802	journal	September 2005
Topological valley transport at bilayer graphene domain walls Ju, Long; Shi, Zhiwen; Nair, Nityan Nature, Vol. 520, Issue 7549 https://doi.org/10.1038/nature14364	journal	April 2015
Solitons with fermion number ½ Jackiw, R.; Rebbi, C. Physical Review D, Vol. 13, Issue 12 https://doi.org/10.1103/PhysRevD.13.3398	journal	June 1976
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Kresse, G.; Furthmüller, J. Physical Review B, Vol. 54, Issue 16, p. 11169-11186 https://doi.org/10.1103/PhysRevB.54.11169	journal	October 1996
Filling-Enforced Magnetic Dirac Semimetals in Two Dimensions Young, Steve M.; Wieder, Benjamin J. Physical Review Letters, Vol. 118, Issue 18 https://doi.org/10.1103/PhysRevLett.118.186401	journal	May 2017
FINDSYM : program for identifying the space-group symmetry of a crystal Stokes, Harold T.; Hatch, Dorian M. Journal of Applied Crystallography, Vol. 38, Issue 1 https://doi.org/10.1107/S0021889804031528	journal	January 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
Dirac semimetal and topological phase transitions in A 3 Bi ( A = Na , K, Rb) Wang, Zhijun; Sun, Yan; Chen, Xing-Qiu Physical Review B, Vol. 85, Issue 19 https://doi.org/10.1103/PhysRevB.85.195320	journal	May 2012
Computing topological invariants without inversion symmetry Soluyanov, Alexey A.; Vanderbilt, David Physical Review B, Vol. 83, Issue 23 https://doi.org/10.1103/PhysRevB.83.235401	journal	June 2011
Möbius Kondo insulators Chang, Po-Yao; Erten, Onur; Coleman, Piers Nature Physics, Vol. 13, Issue 8 https://doi.org/10.1038/nphys4092	journal	April 2017
Organizing symmetry-protected topological phases by layering and symmetry reduction: A minimalist perspective Xiong, Charles Zhaoxi; Alexandradinata, A. Physical Review B, Vol. 97, Issue 11 https://doi.org/10.1103/PhysRevB.97.115153	journal	March 2018
( d − 2 ) -Dimensional Edge States of Rotation Symmetry Protected Topological States Song, Zhida; Fang, Zhong; Fang, Chen Physical Review Letters, Vol. 119, Issue 24 https://doi.org/10.1103/PhysRevLett.119.246402	journal	December 2017
Controlling the Electronic Structure of Bilayer Graphene Ohta, Taisuke; Bostwick, Aaron; Seyller, Thomas Science, Vol. 313, Issue 5789 https://doi.org/10.1126/science.1130681	journal	August 2006
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
Gravitational anomalies Alvarez-Gaumé, Luis; Witten, Edward Nuclear Physics B, Vol. 234, Issue 2 https://doi.org/10.1016/0550-3213(84)90066-X	journal	April 1984
Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property Haldane, F. D. M. Physical Review Letters, Vol. 93, Issue 20 https://doi.org/10.1103/PhysRevLett.93.206602	journal	November 2004
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
Self-consistent effective-mass theory for intralayer screening in graphite intercalation compounds DiVincenzo, D. P.; Mele, E. J. Physical Review B, Vol. 29, Issue 4 https://doi.org/10.1103/PhysRevB.29.1685	journal	February 1984
Optimized pseudopotentials Rappe, Andrew M.; Rabe, Karin M.; Kaxiras, Efthimios Physical Review B, Vol. 41, Issue 2 https://doi.org/10.1103/PhysRevB.41.1227	journal	January 1990
Maximally localized Wannier functions for entangled energy bands Souza, Ivo; Marzari, Nicola; Vanderbilt, David Physical Review B, Vol. 65, Issue 3 https://doi.org/10.1103/PhysRevB.65.035109	journal	December 2001
Highly convergent schemes for the calculation of bulk and surface Green functions Sancho, M. P. Lopez; Sancho, J. M. Lopez; Sancho, J. M. L. Journal of Physics F: Metal Physics, Vol. 15, Issue 4 https://doi.org/10.1088/0305-4608/15/4/009	journal	April 1985
Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe Xu, Su-Yang; Liu, Chang; Alidoust, N. Nature Communications, Vol. 3, Issue 1 https://doi.org/10.1038/ncomms2191	journal	January 2012
Filling constraints for spin-orbit coupled insulators in symmorphic and nonsymmorphic crystals Watanabe, Haruki; Po, Hoi Chun; Vishwanath, Ashvin Proceedings of the National Academy of Sciences, Vol. 112, Issue 47 https://doi.org/10.1073/pnas.1514665112	journal	November 2015
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
Solitons in Polyacetylene Su, W. P.; Schrieffer, J. R.; Heeger, A. J. Physical Review Letters, Vol. 42, Issue 25 https://doi.org/10.1103/PhysRevLett.42.1698	journal	June 1979
Higher-order topological insulators Schindler, Frank; Cook, Ashley M.; Vergniory, Maia G. Science Advances, Vol. 4, Issue 6 https://doi.org/10.1126/sciadv.aat0346	journal	June 2018
Topological nonsymmorphic crystalline insulators Liu, Chao-Xing; Zhang, Rui-Xing; VanLeeuwen, Brian K. Physical Review B, Vol. 90, Issue 8 https://doi.org/10.1103/PhysRevB.90.085304	journal	August 2014
wannier90: A tool for obtaining maximally-localised Wannier functions Mostofi, Arash A.; Yates, Jonathan R.; Lee, Young-Su Computer Physics Communications, Vol. 178, Issue 9 https://doi.org/10.1016/j.cpc.2007.11.016	journal	May 2008
Critical behavior of four-terminal conductance of bilayer graphene domain walls Wieder, Benjamin J.; Zhang, Fan; Kane, C. L. Physical Review B, Vol. 92, Issue 8 https://doi.org/10.1103/PhysRevB.92.085425	journal	August 2015
Maximally localized generalized Wannier functions for composite energy bands Marzari, Nicola; Vanderbilt, David Physical Review B, Vol. 56, Issue 20 https://doi.org/10.1103/PhysRevB.56.12847	journal	November 1997
Topological Crystalline Insulators Fu, Liang Physical Review Letters, Vol. 106, Issue 10 https://doi.org/10.1103/PhysRevLett.106.106802	journal	March 2011
Anomalous topological pumps and fractional Josephson effects Zhang, Fan; Kane, C. L. Physical Review B, Vol. 90, Issue 2 https://doi.org/10.1103/PhysRevB.90.020501	journal	July 2014
Author Correction: Higher-order topology in bismuth Schindler, Frank; Wang, Zhijun; Vergniory, Maia G. Nature Physics, Vol. 14, Issue 10 https://doi.org/10.1038/s41567-018-0308-4	journal	September 2018
Topological crystalline insulator states in Pb1−xSnxSe Dziawa, P.; Kowalski, B. J.; Dybko, K. Nature Materials, Vol. 11, Issue 12 https://doi.org/10.1038/nmat3449	journal	September 2012
A topological Dirac insulator in a quantum spin Hall phase Hsieh, D.; Qian, D.; Wray, L. Nature, Vol. 452, Issue 7190, p. 970-974 https://doi.org/10.1038/nature06843	journal	April 2008
Dirac Fermions in Solids: From High-T _c Cuprates and Graphene to Topological Insulators and Weyl Semimetals Vafek, Oskar; Vishwanath, Ashvin Annual Review of Condensed Matter Physics, Vol. 5, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031113-133841	journal	March 2014
Topological field theory of time-reversal invariant insulators Qi, Xiao-Liang; Hughes, Taylor L.; Zhang, Shou-Cheng Physical Review B, Vol. 78, Issue 19, Article No. 195424 https://doi.org/10.1103/PhysRevB.78.195424	journal	November 2008
New classes of three-dimensional topological crystalline insulators: Nonsymmorphic and magnetic Fang, Chen; Fu, Liang Physical Review B, Vol. 91, Issue 16 https://doi.org/10.1103/PhysRevB.91.161105	journal	April 2015
Gauge Noninvariance and Parity Nonconservation of Three-Dimensional Fermions Redlich, A. N. Physical Review Letters, Vol. 52, Issue 1 https://doi.org/10.1103/PhysRevLett.52.18	journal	January 1984
Gate-induced insulating state in bilayer graphene devices Oostinga, Jeroen B.; Heersche, Hubert B.; Liu, Xinglan Nature Materials, Vol. 7, Issue 2 https://doi.org/10.1038/nmat2082	journal	December 2007
Refinement of the Crystal Structure of Sr3Hg2 Druska, Ch.; Doert, Th.; B�ttcher, P. Zeitschrift f�r anorganische und allgemeine Chemie, Vol. 622, Issue 3 https://doi.org/10.1002/zaac.19966220304	journal	March 1996
Topological insulators avoid the parity anomaly Mulligan, Michael; Burnell, F. J. Physical Review B, Vol. 88, Issue 8 https://doi.org/10.1103/PhysRevB.88.085104	journal	August 2013
Quick iterative scheme for the calculation of transfer matrices: application to Mo (100) Sancho, M. P. Lopez; Sancho, J. M. Lopez; Rubio, J. Journal of Physics F: Metal Physics, Vol. 14, Issue 5 https://doi.org/10.1088/0305-4608/14/5/016	journal	May 1984
Berry-phase description of topological crystalline insulators Alexandradinata, A.; Bernevig, B. Andrei Physical Review B, Vol. 93, Issue 20 https://doi.org/10.1103/PhysRevB.93.205104	journal	May 2016
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
Spontaneous Quantum Hall States in Chirally Stacked Few-Layer Graphene Systems Zhang, Fan; Jung, Jeil; Fiete, Gregory A. Physical Review Letters, Vol. 106, Issue 15 https://doi.org/10.1103/PhysRevLett.106.156801	journal	April 2011
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
Critical behavior of a point contact in a quantum spin Hall insulator Teo, Jeffrey C. Y.; Kane, C. L. Physical Review B, Vol. 79, Issue 23 https://doi.org/10.1103/PhysRevB.79.235321	journal	June 2009
Triple point fermions in a minimal symmorphic model Fulga, I. C.; Stern, Ady Physical Review B, Vol. 95, Issue 24 https://doi.org/10.1103/PhysRevB.95.241116	journal	June 2017
Discovery of a Three-Dimensional Topological Dirac Semimetal, Na3Bi Liu, Z. K.; Zhou, B.; Zhang, Y. Science, Vol. 343, Issue 6173 https://doi.org/10.1126/science.1245085	journal	January 2014
Gate-controlled topological conducting channels in bilayer graphene Li, Jing; Wang, Ke; McFaul, Kenton J. Nature Nanotechnology, Vol. 11, Issue 12 https://doi.org/10.1038/nnano.2016.158	journal	August 2016
Designed nonlocal pseudopotentials for enhanced transferability Ramer, Nicholas J.; Rappe, Andrew M. Physical Review B, Vol. 59, Issue 19 https://doi.org/10.1103/PhysRevB.59.12471	journal	May 1999
Experimental realization of a topological crystalline insulator in SnTe Tanaka, Y.; Ren, Zhi; Sato, T. Nature Physics, Vol. 8, Issue 11 https://doi.org/10.1038/nphys2442	journal	September 2012
Topology of nonsymmorphic crystalline insulators and superconductors Shiozaki, Ken; Sato, Masatoshi; Gomi, Kiyonori Physical Review B, Vol. 93, Issue 19 https://doi.org/10.1103/PhysRevB.93.195413	journal	May 2016
Double Dirac Semimetals in Three Dimensions Wieder, Benjamin J.; Kim, Youngkuk; Rappe, A. M. Physical Review Letters, Vol. 116, Issue 18 https://doi.org/10.1103/PhysRevLett.116.186402	journal	May 2016
Data for "Wallpaper Fermions and the Nonsymmorphic Dirac Insulator" University), Kim, Youngkuk (Department Of Physics, Sungkyunkwan Harvard Dataverse https://doi.org/10.7910/DVN/EUGQDU	dataset	January 2018
Commentary: The Materials Project: A materials genome approach to accelerating materials innovation Jain, Anubhav; Ong, Shyue Ping; Hautier, Geoffroy APL Materials, Vol. 1, Issue 1 https://doi.org/10.1063/1.4812323	journal	July 2013
Experimental evidence of hourglass fermion in the candidate nonsymmorphic topological insulator KHgSb Ma, Junzhang; Yi, Changjiang; Lv, Baiqing Science Advances, Vol. 3, Issue 5 https://doi.org/10.1126/sciadv.1602415	journal	May 2017
Classification of topological crystalline insulators based on representation theory Dong, Xiao-Yu; Liu, Chao-Xing Physical Review B, Vol. 93, Issue 4 https://doi.org/10.1103/PhysRevB.93.045429	journal	January 2016
Topological quantum chemistry Bradlyn, Barry; Elcoro, L.; Cano, Jennifer Nature, Vol. 547, Issue 7663 https://doi.org/10.1038/nature23268	journal	July 2017
Dirac Semimetals in Two Dimensions Young, Steve M.; Kane, Charles L. Physical Review Letters, Vol. 115, Issue 12 https://doi.org/10.1103/PhysRevLett.115.126803	journal	September 2015
Helical Liquid and the Edge of Quantum Spin Hall Systems Wu, Congjun; Bernevig, B. Andrei; Zhang, Shou-Cheng Physical Review Letters, Vol. 96, Issue 10 https://doi.org/10.1103/PhysRevLett.96.106401	journal	March 2006
Model Characterization of Gapless Edge Modes of Topological Insulators Using Intermediate Brillouin-Zone Functions Fidkowski, Lukasz; Jackson, T. S.; Klich, Israel Physical Review Letters, Vol. 107, Issue 3 https://doi.org/10.1103/PhysRevLett.107.036601	journal	July 2011
Z 2 topology in nonsymmorphic crystalline insulators: Möbius twist in surface states Shiozaki, Ken; Sato, Masatoshi; Gomi, Kiyonori Physical Review B, Vol. 91, Issue 15 https://doi.org/10.1103/PhysRevB.91.155120	journal	April 2015
The Quantum Theory of Fields Weinberg, Steven https://doi.org/10.1017/CBO9781139644167	book	May 2013
Landau-Level Degeneracy and Quantum Hall Effect in a Graphite Bilayer McCann, Edward; Fal’ko, Vladimir I. Physical Review Letters, Vol. 96, Issue 8 https://doi.org/10.1103/PhysRevLett.96.086805	journal	March 2006
Experimental Realization of a Three-Dimensional Dirac Semimetal Borisenko, Sergey; Gibson, Quinn; Evtushinsky, Danil Physical Review Letters, Vol. 113, Issue 2 https://doi.org/10.1103/PhysRevLett.113.027603	journal	July 2014
Fractional charge and zero modes for planar systems in a magnetic field Jackiw, R. Physical Review D, Vol. 29, Issue 10 https://doi.org/10.1103/PhysRevD.29.2375	journal	May 1984
Sr5Al2Sb6 und Ba5In2Sb6: Zwei neue Zintlphasen mit unterschiedlichen Bänderanionen / Sr5Al2Sb6 and Ba5In2Sb6: Two New Zintl Phases with Different Chain Anions Cordier, Gerhard; Stelter, Michael Zeitschrift für Naturforschung B, Vol. 43, Issue 4 https://doi.org/10.1515/znb-1988-0413	journal	April 1988
Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals Bradlyn, Barry; Cano, Jennifer; Wang, Zhijun Science, Vol. 353, Issue 6299 https://doi.org/10.1126/science.aaf5037	journal	July 2016
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
Bulk Dirac Points in Distorted Spinels Steinberg, Julia A.; Young, Steve M.; Zaheer, Saad Physical Review Letters, Vol. 112, Issue 3 https://doi.org/10.1103/PhysRevLett.112.036403	journal	January 2014
Spin-orbit semimetals in the layer groups Wieder, Benjamin J.; Kane, C. L. Physical Review B, Vol. 94, Issue 15 https://doi.org/10.1103/PhysRevB.94.155108	journal	October 2016

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