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For over 100 years, the group-theoretic characterization of crystalline solids has provided the foundational language for diverse problems in physics and chemistry.
Über die reellen Darstellungen der endlichen Gruppen: Über die Äquivalenz der Gruppen linearer Substitutionen. Von G. Frobenius und I. Schur
Frobenius, G. & Schur, I · 1906
Earlier work this paper cites.
A 1D lattice model for the boundary of the quantum spin-Hall insulator
Metlitski, M. A · 1908
Earlier work this paper cites.
Termaufspaltung in kristallen
Bethe, H · 1929
Earlier work this paper cites.
Über die operation der zeitumkehr in der quantenmechanik
Wigner, E. P · 1932
Earlier work this paper cites.
Theory of the Variations in Paramagnetic Anisotropy Among Different Salts of the Iron Group
Van Vleck, J. H · 1932
Earlier work this paper cites.
Electronic Structures of Polyatomic Molecules and Valence. IV. Electronic States, Quantum Theory of the Double Bond
Mulliken, R. S · 1933
Earlier work this paper cites.
On the theory of phase transitions
Landau, L · 1937
Earlier work this paper cites.
Magnetic scattering of slow neutrons
Halpern, O. & Johnson, M. H · 1937
Earlier work this paper cites.
Character tables for two space groups
Herring, C · 1942
Earlier work this paper cites.
Symmetry and Antisymmetry of Finite Figures (USSR Academy of Sciences, Moscow, USSR, 1951)
Shubnikov, A. V · 1951
Earlier work this paper cites.
Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid
Watson, J. D. & Crick, F. H. C · 1953
Earlier work this paper cites.
Generalization of Fedorov Groups
Zamorzaev, A. M · 1953
Earlier work this paper cites.
The 1651 Shubnikov groups
Belov, N., Neronova, N. & Smirnova, T · 1955
Earlier work this paper cites.
Shubnikov groups
Belov, N. & Neronova, T., N.N .and Smirnova · 1957
Earlier work this paper cites.
Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra (Academic Press, 1959)
Wigner, E. & Griffin, J · 1959
Earlier work this paper cites.
Two soluble models of an antiferromagnetic chain
Lieb, E., Schultz, T. & Mattis, D · 1961
Earlier work this paper cites.
Irreducible representations of magnetic groups
Dimmock, J. & Wheeler, R · 1962
Earlier work this paper cites.
Colored Symmetry (Macmillan, 1964)
Shubnikov, A. & Belov, N · 1964
Earlier work this paper cites.
Superconductivity in a strong spin-exchange field
Fulde, P. & Ferrell, R. A · 1964
Earlier work this paper cites.
Nonuniform state of superconductors
Larkin, A. & Ovchinnikov, Y. N · 1965
Earlier work this paper cites.
Magnetism, Ch. 3 , vol. 2A (New York: Academic Press, 1965)
Opechowski, W. & Guccione, R · 1965
Earlier work this paper cites.
Subgroups of black–white point groups
Ascher, E. & Janner, A · 1965
Earlier work this paper cites.
Tables of Irreducible Representations of Space Groups and Corepresentations of Magnetic Space Groups (1967)
Miller, S. & Love, W · 1967
Earlier work this paper cites.
The application of Landau’s theory of continuous phase transitions to magnetic phase transitions
Cracknell, A. P · 1971
Earlier work this paper cites.
The Mathematical Theory of Symmetry in Solids: Representation Theory for Point Groups and Space Groups (Clarendon Press, 1972)
Bradley, C. & Cracknell, A · 1972
Earlier work this paper cites.
Cubic harmonics as linear combinations of spherical harmonics
Muggli, J · 1972
Earlier work this paper cites.
Band representations and symmetry types of bands in solids
Zak, J · 1981
Earlier work this paper cites.
Band representations of space groups
Zak, J · 1982
Earlier work this paper cites.
Wannier functions for magnetic sub-bands
Thouless, D. J · 1984
Earlier work this paper cites.
Gravitational anomalies
Alvarez-Gaumé, L. & Witten, E · 1984
Earlier work this paper cites.
Gauge noninvariance and parity nonconservation of three-dimensional fermions
Redlich, A. N · 1984
Earlier work this paper cites.
Fractional charge and zero modes for planar systems in a magnetic field
Jackiw, R · 1984
Earlier work this paper cites.
Two applications of axion electrodynamics
Wilczek, F · 1987
Earlier work this paper cites.
Symmetry and classification of energy bands in crystals
Bacry, H., Michel, L. & Zak, J · 1988
Earlier work this paper cites.
Band corepresentations of magnetic space groups
Evarestov, R. A., Smirnov, V. P. & Egorov, S. A · 1989
Earlier work this paper cites.
Berry’s phase for energy bands in solids
Zak, J · 1989
Earlier work this paper cites.
Representation Theory: A First Course
Fulton, W., Harris, W. & Harris, J · 1991
Earlier work this paper cites.
Theory of polarization of crystalline solids
King-Smith, R. D. & Vanderbilt, D · 1993
Earlier work this paper cites.
Linear Representations of Finite Groups
Scott, L. & Serre, J · 1996
Earlier work this paper cites.
Maximally localized generalized Wannier functions for composite energy bands
Marzari, N. & Vanderbilt, D · 1997
Earlier work this paper cites.
Physical Chemistry: A Molecular Approach (University Science Books, 1997)
McQuarrie, D. A. & Simon, J. D · 1997
Earlier work this paper cites.
Evaluation of the rotation matrices in the basis of real spherical harmonics
Blanco, M. A., Flórez, M. & Bermejo, M · 1997
Earlier work this paper cites.
Connectivity of energy bands in crystals
Michel, L. & Zak, J · 1999
Earlier work this paper cites.
Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect
Read, N. & Green, D · 2000
Earlier work this paper cites.
Elementary energy bands in crystals are connected
Michel, L. & Zak, J · 2001
Earlier work this paper cites.
The Pin Groups in Physics: C, P and T
Berg, M., De Witt-Morette, C., Gwo, S. & Kramer, E · 2001
Earlier work this paper cites.
International Tables for Crystallography,Volume E: Subperiodic Groups
Kopsky, V. & Litvin, D · 2002
Earlier work this paper cites.
Order parameter symmetry in ferromagnetic superconductors
Samokhin, K. V. & Walker, M. B · 2002
Earlier work this paper cites.
Deconfined quantum critical points
Senthil, T., Vishwanath, A., Balents, L., Sachdev, S. & Fisher, M. P. A · 2004
Earlier work this paper cites.
Slave-rotor mean-field theories of strongly correlated systems and the Mott transition in finite dimensions
Florens, S. & Georges, A · 2004
Earlier work this paper cites.
Quantum Spin Hall Effect in Graphene
Kane, C. L. & Mele, E. J · 2005
Earlier work this paper cites.
Fundamentals of Semiconductors: Physics and Materials Properties
Yu, P. & Cardona, M · 2005
Earlier work this paper cites.
Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
Bernevig, B. A., Hughes, T. L. & Zhang, S.-C · 2006
Earlier work this paper cites.
Bilbao Crystallographic Server: I. Databases and crystallographic computing programs
Aroyo, M. I. et al · 2006
Earlier work this paper cites.
Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups
Aroyo, M. I., Kirov, A., Capillas, C., Perez-Mato, J. M. & Wondratschek, H · 2006
Earlier work this paper cites.
Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups
Aroyo, M. I., Kirov, A., Capillas, C., Perez-Mato, J. M. & Wondratschek, H · 2006
Earlier work this paper cites.
Field dependence of the magnetic spectrum in anisotropic and Dzyaloshinskii-Moriya antiferromagnets. II. Raman spectroscopy
Benfatto, L. et al · 2006
Earlier work this paper cites.
Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
Qi, X.-L., Wu, Y.-S. & Zhang, S.-C · 2006
Earlier work this paper cites.
Time reversal polarization and a Z 2 {Z}_{2} adiabatic spin pump
Fu, L. & Kane, C. L · 2006
Earlier work this paper cites.
Topological insulators in three dimensions
Fu, L., Kane, C. L. & Mele, E. J · 2007
Earlier work this paper cites.
Topological insulators with inversion symmetry
Fu, L. & Kane, C. L · 2007
Earlier work this paper cites.
Topological invariants of time-reversal-invariant band structures
Moore, J. E. & Balents, L · 2007
Earlier work this paper cites.
Topological field theory of time-reversal invariant insulators
Qi, X.-L., Hughes, T. L. & Zhang, S.-C · 2008
Earlier work this paper cites.
A topological Dirac insulator in a quantum spin Hall phase
Hsieh, D. et al · 2008
Earlier work this paper cites.
The Symmetries of Things
Conway, J., Burgiel, H. & Goodman-Strauss, C · 2008
Earlier work this paper cites.
Surface states and topological invariants in three-dimensional topological insulators: Application to Bi 1 − x Sb x {\text{Bi}}_{1-x}{\text{Sb}}_{x}
Teo, J. C. Y., Fu, L. & Kane, C. L · 2008
Earlier work this paper cites.
Odd parity and line nodes in nonsymmorphic superconductors
Micklitz, T. & Norman, M. R · 2009
Earlier work this paper cites.
Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
Essin, A. M., Moore, J. E. & Vanderbilt, D · 2009
Earlier work this paper cites.
Periodic table for topological insulators and superconductors
Kitaev, A · 2009
Earlier work this paper cites.
Unlocking of time reversal, space-time inversion and rotation invariants in magnetic materials
Yang, J., Liu, Z.-X. & Fang, C · 2009
Earlier work this paper cites.
IrRep: symmetry eigenvalues and irreducible representations of ab initio band structures
Iraola, M. et al · 2009
Earlier work this paper cites.
Quantized Anomalous Hall Effect in Magnetic Topological Insulators
Yu, R. et al · 2010
Earlier work this paper cites.
Antiferromagnetic topological insulators
Mong, R. S. K., Essin, A. M. & Moore, J. E · 2010
Earlier work this paper cites.
Mott physics and band topology in materials with strong spin–orbit interaction
Pesin, D. & Balents, L · 2010
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High-throughput electronic band structure calculations: Challenges and tools
Setyawan, W. & Curtarolo, S · 2010
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Topological crystalline insulators
Fu, L · 2011
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Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates
Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y · 2011
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Point-Group Theory Tables (University of Vienna, 2011), 2 edn
Altmann, S. & Herzig, P · 2011
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Higher-order topology in bismuth
Schindler, F. et al · 2018
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Weyl and Dirac semimetals in three-dimensional solids
Armitage, N. P., Mele, E. J. & Vishwanath, A · 2018
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Fragile Topology and Wannier Obstructions
Po, H. C., Watanabe, H. & Vishwanath, A · 2018
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Cano, J. et al · 2018
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