摘要
Free Access References Prof. Wolfram Hergert, Prof. Wolfram Hergert Martin Luther University Halle-Wittenberg, Von-Seckendorff-Platz 1, 06120 Halle, GermanySearch for more papers by this authorDr. R.Matthias Geilhufe, Dr. R.Matthias Geilhufe Nordita, Roslagstullsbacken 23, 10691 Stockholm, SwedenSearch for more papers by this author Book Author(s):Prof. Wolfram Hergert, Prof. Wolfram Hergert Martin Luther University Halle-Wittenberg, Von-Seckendorff-Platz 1, 06120 Halle, GermanySearch for more papers by this authorDr. R.Matthias Geilhufe, Dr. R.Matthias Geilhufe Nordita, Roslagstullsbacken 23, 10691 Stockholm, SwedenSearch for more papers by this author First published: 18 May 2018 https://doi.org/10.1002/9783527695799.refs AboutPDFPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShareShare a linkShare onFacebookTwitterLinked InRedditWechat References El-Batanouny, M. and Wooten, F. (2008) Symmetry and Condensed Matter Physics, Cambridge University Press. McClain, W. (2009) Symmetry Teory in Molecular Physics with Mathematica, Springer. Wigner, E. (1959) Group Teory: And its Application to the Quantum Mechanics of Atomic Spectra, Academic Press, New York . Haeckel, E. (2004) Kunstformen der Natur (reprint of 1904 edition), Marix, Wiesbaden. Wikipedia (2017) Chrysler building – Wikipedia, the free encyclopedia. https://de.wikipedia.org/wiki/Chrysler_Building (accessed 15 October 2017). Ernst, B. (1986) Der Zauberspiegel des M.C. Escher, Taco Verlagsgesellschaft, Berlin. Herfort, P. and Klotz, A. (1997) Orna-mente und Fraktale, Vieweg, Braunschweig. Shubnikov, A. and Koptsik, V. (1974) Symmetry in Science and Art, Plenum Press, New York and London. Weyl, H. (1980) Symmetry, Princeton University Press, Princeton. Altmann, S.L. (1992) Icons and Symmetries, Clarendon Press, Oxford. Gross, D.J. (1995) Symmetry in physics: Wigner 's lagacy. Physics Today, 48, 46– 50. Weyl, H. (1928) Gruppentheorie und Quantenmechanik, Hirzel, Leipzig. Pauli, W. (1926) Über das Wasser-stoffspektrum vom Standpunkt der neuen Quantenmechanik. Zeitschrift für Physik, 36, 336– 363. Valent, G. (2003) The hydrogen atom in electric and magnetic fields: Pauli's 1926 article. American Journal of Physics, 71 (2), 171– 175. Fock, V. (1935) Zur Theorie des Wasser-stoffatoms. Zeitschrift für Physik, 98, 145. Engel, E. and Dreizler, R.M. (2011) Density Functional Teory: An Advanced Course, Springer, Berlin. Fernandes, E., Donati, F., Patthey, F., Stavrić, S., Šljvančanin, V., and Brune, H. (2017) Adsorption sites of individual metal atoms on ultrathin MgO(100) films. Physical Review B, 96, 04519. Birner, A., Busch, K., and Müller, F. (1999) Photonische Kristalle – Mikrostrukturierte Festkörper eröffnen neue Wege zur Manipulation von Licht. Physikalische Blätter, 55 (4), 27– 33. Schmid, H. (2008) Some symmetry aspects of ferroics and single phase mul-tiferroics. Journal of Physics: Condensed Matter, 20, 434201. Saxena, A. and Lookman, T. (2011) Magnetic symmetry of low-dimensional multiferroics and ferroelastics. Phase Transitions, 84 (5/6), 421– 437. Maze, J.R., Gali, A., Togan, E., Chu, Y., Trifonov, A., Kaxiras, E., and Lukin, M.D. (2011) Properties of nitrogen-vacancy centers in diamond: The group theoretic approach. New Journal of Physics, 13, 025025. Bersuker I.B. (2012) Pseudo Jahn– Teller origin of perovskite multiferroics, magnetic-ferroelectric crossover, and magnetoelectric effects: The d 0-d 10 problem. Physical Review Letters, 108, 137202. Abergel, D., Apalkov, V., Berashevich, J., Ziegler, K., and Chakraborty, T. (2010) Properties of graphene: A theoretical perspective. Advances in Physics, 59 (4), 261– 482. Wehling, T., Black-Schaffer, A.M., and Balatsky, A.V. (2014) Dirac materials. Advances in Physics, 63 (1), 1– 76. Geilhufe, R.M., Borysov, S.S., Bouhon, A., and Balatsky, A.V. (2017) Data mining for three-dimensional organic Dirac materials: Focus on space group 19. Scientific Reports, 7 (1), 7298. Bradlyn, B., Cano, J., Wang, Z., Vergnio-ry, M., Felser, C., Cava, R., and Bernevig, B.A. (2016) Beyond Dirac and Weyl fermions: Unconventional quasiparti-cles in conventional crystals. Science, 353 (6299), 558. Sakoda, K. (2005) Optical Properties of Photonic Crystals, Springer. Joannopoulos, J.D., Johnson, S.G., Winn, J.N., and Meade, R.D. (2008) Photonic Crystals – Molding the Flow of Light, Princeton University Press. Sakoda, K. (1995) Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices. Physical Review B, 52 (11), 7982. Reinke, C.M., Teofilo, M., Su, M.F., Sinclair, M.B., and El-Kady, I. (2011) Group-theory approach to tailored electromagnetic properties of metamaterials: An inverse-problem solution. Physical Review E, 83 (6), 066603. Colman, P., Combrié, S., Lehoucq, G., and De Rossi, A. (2012) Control of dispersion in photonic crystal waveguides using group symmetry theory. Optics Express, 20 (12), 13108– 13114. Mock, A., Lu, L., and O'Brien, J. (2010) Space group theory and Fourier space analysis of two-dimensional photonic crystal waveguides. Physical Review B, 81 (15), 155115. Vanwolleghem, M., Checoury, X., Śmi-gaj, W., Gralak, B., Magdenko, L., Posta-va, K., Dagens, B., Beauvillain, P., and Lourtioz, J.M.M. (2009) Unidirectional band gaps in uniformly magnetized two-dimensional magnetophotonic crystals. Physical Review B, 80 (12), 121102. Flashar, H. (2014) Aristoteles Lehrer des Abendlandes, Wissenschaftliche Buchgesellschaft, Darmstadt. Cornwell, J. (1969) Group Teory and Electronic Energy Bands in Solids, North-Holland Publishing Company. Cornwell, J. (1984) Group Teory in Physics, Academic Press. Inui, T., Tanabe, Y., and Onodera, Y. (1996) Group Teory and its Applications in Physics, Springer. Altmann, S.L. (2005) Rotations, Quaternions and Double Groups, Dover Publications, Inc., Mineola, New York. Morrison, M.A. and Parker, G.A. (1987) A Guide to Rotations in Quantum Mechanics. Australian Journal of Physics, 40, 465– 498. Hahn, T. and Wondratschek, H. (1994) Symmetry of Crystals – Introduction to International Tables for Crystallography Vol. A, Heron Press, Sofia. Greiner, W. (1979) Teoretische Physik: Ein Lehr- und Übungsbuch – Band 5: Quantenmechanik II Symmetrien, Ver-lag Harri Deutsch, Thun and Frankfurt/Main. Galois, E. (1846) Sur les conditions de résolubilité des équations par radicaux. Journal de Mathématiques Pures et Ap-pliquées, 11, 417– 444. Goethe, J.W. (1989) Wilhelm Meisters Wanderjahre, Deutscher Klassiker Ver-lag. Bilbao crystallographic server, www.cryst.ehu.es (accessed: 15 October 2017). International tables for crystallography, http://it.iucr.org (accessed: 15 October 2017). Crystallography open database, www.crystallography.net (accessed: 15 October 2017). Inorganic Crystal Structure Database (ICSD) FIZ Karlsruhe, https://icsd.fz-karlsruhe.de (accessed: 15 October 2017). Groom, C.R., Bruno, I.J., Lightfoot, M.P. and Ward, S.C. (2016) The Cambridge Structural Database, Acta Crystallo-graphica Section B, 72 (2), 171– 179 Visualization for Electronic and STructural Analysis (VESTA), http://jpminerals.org/vesta/en/ (accessed: 15 October 2017). T. Hahn (ed.) (1994) International Tables for Crystallography, Vol. A, Space-Group symmetry, Kluwer Academic Publishers. Terzibaschian, T. and Enderlein, B. (1986) The irreducible representations of the two-dimensional space groups of crystal surfaces. Theory and applications. Phys. Status Solidi B, 133, 443– 461. Boisen, M.B. and Gibbs, G.V. (1990) Mathematical Crystallography, vol. 15, in Reviews in Mineralogy, Mineralogical Society of America, Washington, DC. Stokes, H.T. and Hatch, D.M. (2005) FINDSYM: Program for identifying the space-group symmetry of a crystal. Journal of Applied Crystallography, 38 (1), 237– 238. Spek, A.L. (2003) Single-crystal structure validation with the program PLA-TON . Journal of Applied Crystallography, 36 (1), 7– 13. Le Page, Y. (1987) Computer derivation of the symmetry elements implied in a structure description. Journal of Applied Crystallography, 20 (3), 264– 269. Schönflies, A. (1923) Teorie der Kristallstruktur, Gebrüder Bornträger, Berlin. Henry, N. and Lonsdale, K. (1964) 1965. International Tables for X-ray Crystallography, 1, 6– 56. Zeller, R. (2014) Large scale supercell calculations for forces around substitu-tional defects in NiTi. Phys. Status Solidi B, 251 (10), 2048– 2054. Adeagbo, W.A., Fischer, G., Ernst, A., and Hergert, W. (2010) Magnetic effects of defect pair formation in ZnO. Journal of Physics: Condensed Matter, 22 (43), 436002. Wyckoff, R.W.G. (1922) Te Analytical Expression of the Results of the Teory of Space-groups, 318, Carnegie institution of Washington. Ludwig, W. and Falter, C. (2012) Symmetries in Physics: Group Teory Applied to Physical Problems, Springer Series in Solid-State Sciences, Springer, Berlin, Heidelberg. Ködderitzsch, D. (2003) Beschreibung der elektronischen Struktur von Über-gangsmetalloxiden mittels selbstwech-selwirkungskorrigierter Dichtefunk-tionaltheorie: Volumenkristalle, Ober-flächen und Punktdefekte, PhD thesis, Martin-Luther University Halle-Wittenberg. Vijayaraghavan, A. (2013) Graphene – Properties and characterization, in Springer Handbook of Nanomaterials, Springer, pp. 39– 82. Nanot, S., Thompson, N.A., Kim, J.H..H., Wang, X., Rice, W.D., Hároz, E.H., Ganesan, Y., Pint, C.L., and Kono, J. (2013) Single-walled carbon nan-otubes, in Springer Handbook of Nano-materials, Springer, pp. 105– 146. Terrones, H. (2013) Fullerenes and beyond: Complexity, morphology, and functionality in closed carbon nanos-tructures, in Springer Handbook of Nanomaterials, Springer, pp. 83– 104. Saito, R., Dresselhaus, G., and Dressel-haus, M.S. (1998) Physical Properties of Carbon Nanotubes, Imperial College Press, London. Contreras, M.L., Benítez, E., Alvarez, J., and Rozas, R. (2009) Algorithm for nanotubes computer generation with different configurations. Algorithms, 2 (1), 108– 120. Senn, P. (1995) Computation of the cartesian coordinates of Buckminster-fullerene. Journal of Chemical Education, 72 (4), 302. David, W.I., Ibberson, R.M., Matthew-man, J.C., Prassides, K., Dennis, T.J.S., Hare, J.P., Kroto, H.W., Taylor, R., and Walton, D.R. (1991) Crystal structure and bonding of ordered C60 . Nature, 353 (6340), 147– 149. Yannoni, C.S., Bernier, P.P., Bethune, D.S., Meijer, G., and Salem, J.R. (1991) NMR determination of the bond lengths in C60 . Journal of the American Chemical Society, 113 (8), 3190– 3192. Altmann, S. and Herzig, P. (1994) Point-group Teory Tables, Oxford Science Publications, Clarendon Press. Shirai, K. (1992) The basis functions and the matrix representations of the single and double icosahedral point group. Journal of the Physical Society of Japan, 61 (8), 2735– 2747. Dresselhaus, M.S., Dresselhaus, G., and Saito, R. (1993) Group theoretical concepts for C60 and other fullerenes. Materials Science and Engineering B, 19 (1), 122– 128. Balasubramanian, K. (1996) Double group of the icosahedral group (Ih) and its application to fullerenes. Chemical Physics Letters, 260 (3), 476– 484. Satpathy, S. (1986) Electronic structure of the truncated-icosahedral C60 cluster. Chemical Physics Letters, 130 (6), 545– 550. Laouini, N., Andersen, O.K., and Gun-narsson, O. (1995) Analytical molecular orbitals and band structures of solid C60 . Physical Review B, 51 (24), 17446. Lin, Y.-L. and Nori, F. (1996) Analytical application of the recursion and moments methods to the electronic structure of C60: Exact solution for the π and σ states. Physical Review B, 53 (3), 1641. Manousakis, E. (1991) Electronic structure of C60 within the tight-binding approximation. Physical Review B, 44 (19), 10991. Manousakis, E. (1993) Erratum: Electronic structure of C60 within the tight-binding approximation. Physical Review B, 48 (3), 2024. Tit, N. and Kumar, V. (1993) Empirical tight-binding parameters for solid C60 . Journal of Physics: Condensed Matter, 5 (44), 8255. Woo, S.J., Kim, E., and Lee, Y.H. (1993) Geometric, electronic, and vibrational structures of C50, C60, C70, and C80 . Physical Review B, 47 (11), 6721. Weyl, H. (1931) Gruppentheorie und Quantenmechanik, S.S. Hirzel, Leipzig, 1928; translated by H.P. Robertson. Te Teory of Groups and Quantum Mechanics, p. 91. Dresselhaus, M.S., Dresselhaus, G., and Jorio, A. (2008) Group Teory – Application to the Physics of Condensed Matter, Springer. Flodmark, S. and Blokker, E. (1967) A computer program for calculation of irreducible representations of finite groups. International Journal of Quantum Chemistry, 1 (S1), 703– 711. Flodmark, S. and Jansson, P.O. (1982) Irreducible representations of finite groups. Physica A: Statistical Mechanics and its Applications, 114 (1–3), 485– 492. Artin, M. (2011) Algebra, Pearson Education. Holt, D., Eick, B., and O'Brien, E. (2005) Handbook of Computational Group Te-ory, Discrete Mathematics and Its Applications, Taylor & Francis. Bethe, H. (1929) Termaufspaltung in Kristallen. Annalen der Physik, 395 (2), 133– 208. Bouckaert, L.P., Smoluchowski, R., and Wigner, E. (1936) Theory of Brillouin zones and symmetry properties of wave functions in crystals. Physical Review, 50, 58– 67. (1955) Report on notation for the spectra of polyatomic molecules. Te Journal of Chemical Physics, 23 (11), 1997– 2011. Mulliken, R.S. (1956) Erratum: Report on notation for the spectra of polyatomic molecules. Te Journal of Chemical Physics, 24 (5), 1118– 1118. Mathiak, K. and Stingl, P. (1968) Grup-pentheorie für Chemiker, Physiko-Chemiker, Mineralogen, Hochschul-Studienbuch, F. Vieweg. Howarth, D. and Jones, H. (1952) The cellular method of determining electronic wave functions and eigenvalues in crystals, with applications to sodium. Proceedings of the Physical Society. Section A, 65 (5), 355. Bell, D.G. (1954) Group Theory and Crystal Lattices. Reviews of Modern Physics, 26 (3), 311. Vandenbroek, P.M. and Cornwell, J.F. (1978) Clebsch–Gordan coefficients of symmetry groups. Physica Status Solidi B, 90 (1), 211– 224. Heisenberg, W. (2006) Physik und Philosophie, S. Hirzel Verlag. Born, M. and von Karman, T. (1912) On fluctuations in spatial grids. Physikali-sche Zeitschrift der Sowjetunion, 13, 297– 309. Zak, J. (1960) Method to obtain the character tables of nonsymmorphic space groups. Journal of Mathematical Physics, 1 (3), 165– 171. Aroyo, M.I., Kirov, A., Capillas, C., Perez-Mato, J., and Wondratschek, H. (2006) Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups. Acta Crystallographica Section A: Foundations of Crystallography, 62 (2), 115– 128. Bradley, C. and Cracknell, A. (2010) Te Mathematical Teory of Symmetry in Solids: Representation Teory for Point Groups and Space Groups, Oxford University Press. Geilhufe, R.M., Bouhon, A., Borysov, S.S., and Balatsky, A.V. (2017) Three-dimensional organic Dirac-line materials due to nonsymmorphic symmetry: A data mining approach. Physical Review B, 95, 041103. Young, S.M. and Kane, C.L. (2015) Dirac semimetals in two dimensions. Physical Review Letters, 115, 126803. Wieder, B.J., Kim, Y., Rappe, A., and Kane, C. (2016) Double Dirac semimet-als in three dimensions. Physical Review Letters, 116 (18), 186402. Feynman, R., Leighton, R., and Sands, M. (1979) Te Feynman Lectures on Physics: Vol. 3: Quantum Mechanics, Addison-Wesley. Kohn, W. (1999) Nobel lecture: Electronic structure of matter–wave functions and density functionals. Reviews of Modern Physics, 71 (5), 1253. Jones, R.O. (2015) Density functional theory: Its origins, rise to prominence, and future. Reviews of Modern Physics, 87, 897– 923. Hanwell, M.D., Curtis, D.E., Lonie, D.C., Vandermeersch, T., Zurek, E., and Hutchison, G.R. (2012) Avogadro: An advanced semantic chemical editor, visualization, and analysis platform. Journal of Cheminformatics, 4, 17. Momma, K. and Izumi, F. (2011) VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data. Journal of Applied Crystallography, 44 (6), 1272– 1276. Mulak, J. and Gajek, Z. (2000) Te Effective Crystal Field Potential, Elsevier Science. Danielsen, O. and Lindgård, P.A. (1972) Quantum mechanical operator equivalents used in the theory of magnetism, Denmark. Forskningscenter Risø. Risø-R; No. 259. Wybourne, B.C. (1965) Spectroscopic Properties of Rare Earths, John Wiley, New York. Smith, D. and Thornley, J.H.M. (1966) The use of 'operator equivalents'. Proceedings of the Physical Society, 89 (4), 779. Stevens, K.W.H. (1952) Matrix elements and operator equivalents connected with the magnetic properties of rare earth ions. Proceedings of the Physical Society. Section A, 65 (3), 209. Forstreuter, J., Steinbeck, L., Richter, M., and Eschrig, H. (1997) Density-functional calculations for rare-earth atoms and ions. Physical Review B, 55, 9415– 9421. Pauli, W. (1925) Über den Zusam-menhang des Abschlusses der Elek-tronengruppen im Atom mit der Kom-plexstruktur der Spektren. Zeitschrift für Physik, 31 (1), 765– 783. Pauli, W. (1927) Zur Quantenmechanik des magnetischen Elektrons. Zeitschrift für Physik, 43 (9), 601– 623. Damhus, T. (1984) Double group as symmetry groups for spin–orbit coupling Hamiltonians. MATCH Communications in Mathematical and in Computer Chemistry. Stover, C. and Weisstein, E.W.: Matrix inverse, WolframMathWorld, http://mathworld.wolfram.com/MatrixInverse.html (accessed: 15 October 2017). Opechowski, W. (1940) Sur les groupes cristallographiques ‹doubles›. Physica, 7 (6), 552– 562. Eddington, A. (2012) New Pathways in Science: Messenger Lectures (1934), Cambridge University Press. Burdick, G.A. (1963) Energy band structure of copper. Physical Review, 129, 138– 150. Löwdin, P.O. (1950) On the non-orthogonality problem connected with the use of atomic wave functions in the theory of molecules and crystals. Te Journal of Chemical Physics, 18 (3), 365– 375. Mercer Jr., J.L. and Chou, M.Y. (1994) Tight-binding model with intra-atomic matrix elements. Physical Review B, 49 (12), 8506. Cohen, R.E., Stixrude, L., and Wasser-man, E. (1997) Tight-binding computations of elastic anisotropy of Fe, Xe, and Si under compression. Physical Review B, 56 (14), 8575. Podolskiy, A.V. and Vogl, P. (2004) Compact expression for the angular dependence of tight-binding hamiltonian matrix elements. Physical Review B, 69, 233 101. Slater, J.C. and Koster, G.F. (1954) Simplified LCAO method for the periodic potential problem. Physical Review, 94, 1498– 1524. Geim, A.K. and Novoselov, K.S. (2007) The rise of graphene. Nature materials, 6 (3), 183– 191. Novoselov, K.S., Geim, A.K., Moro-zov, S., Jiang, D., Katsnelson, M., Grig-orieva, I., Dubonos, S., and Firsov, A. (2005) Two-dimensional gas of mass-less Dirac fermions in graphene. Nature, 438 (7065), 197– 200. Min, H., Hill, J.E., Sinitsyn, N.A., Sahu, B.R., Kleinman, L., and MacDonald, A.H. (2006) Intrinsic and Rashba spin– orbit interactions in graphene sheets. Physical Review B, 74 (16), 165310. Egorov, R.F., Reser, B.I., and Shi-rokovskii, V.P. (1968) Consistent treatment of symmetry in the tight binding approximation. Phys. Status Solidi B, 26, 391– 408. Wannier, G.H. (1937) The structure of electronic excitation levels in insulating crystals. Physical Review, 52 (3), 191. Marzari, N., Mostofi, A.A., Yates, J.R., Souza, I., and Vanderbilt, D. (2012) Maximally localized Wannier functions: Theory and applications. Reviews of Modern Physics, 84 (4), 1419. Mostofi, A.A., Yates, J.R., Pizzi, G., Lee, Y.S., Souza, I., Vanderbilt, D., and Marzari, N. (2014) An updated version of wannier90: A tool for obtaining maximally-localised Wannier functions. Computer Physics Communications, 185 (8), 2309– 2310. wannier90 (v2.1.0) (2017) www.wannier.org (accessed: 15 October 2017). Yu, P. and Cardona, M. (2010) Fundamentals of Semiconductors, Physics and Materials Properties, Springer. Rössler, U. (2009), Solid State Theory – An Introduction. Springer-Verlag. Martin, R.M. (2004) Electronic Structure: Basic Teory and Practical Methods, Cambridge University Press, Cambridge, New York. Chen, A.B. and Sher, A. (1995) Semiconductor Alloys – Physics and Materials Engineering, Plenum Press. Fritsch, D., Schmidt, H., and Grund-mann, M. (2003) Band-structure pseu-dopotential calculation of zinc-blende and wurtzite AlN, GaN, and InN. Physical Review B, 67 (23), 235205. Fritsch, D., Schmidt, H., and Grund-mann, M. (2004) Band dispersion relations of zinc-blende and wurtzite InN. Physical Review B, 69 (16), 165204. Böhm, G. and Unger, K. (1999) Selfcon-sistent calculation of disorder-induced corrections to the VCA band-structures of Al x Ga1- x As and Al x Ga1- x P. Phys. Status Solidi B, 216 (2), 961– 973. Cohen, M.L. and Bergstresser, T.K. (1966) Band structures and pseudopo-tential form factors for fourteen semiconductors of the diamond and zinc-blende structures. Physical Review, 141 (2), 789. Levine, Z.H. and Louie, S.G. (1982) New model dielectric function and exchange-correlation potential for semiconductors and insulators. Physical Review B, 25 (10), 6310. Papaconstantopoulos, D.A. (1986) Handbook of the Band Structure of Elemental Solids, Plenum Press, New York. Papaconstantopoulos, D.A. (2015) Handbook of the Band Structure of Elemental Solids, Springer, New York, Heidelberg, Dordrecht, London. Christensen, N.E. and Seraphin, B.O. (1971) Relativistic band calculation and the optical properties of gold. Physical Review B, 4 (10), 3321. Eckardt, H., Fritsche, L., and Noffke, J. (1984) Self-consistent relativistic band structure of the noble metals. Journal of Physics F: Metal Physics, 14 (1), 97. Rangel, T., Kecik, D., Trevisanutto, P.E., Rignanese, G.-M., Van Swygenhoven, H., and Olevano, V. (2012) Band structure of gold from many-body perturbation theory. Physical Review B, 86 (12), 125125. XCrySDen (1.5.60) (2015) www.xcrysden.org (accessed: 15 October 2017). Harrison, W.A. (1960) Electronic structure of polyvalent metals. Physical Review, 118, 1190– 1208. Biswas, C. and Lee, Y.H. (2011) Graphene versus carbon nanotubes in electronic devices. Advanced Functional Materials, 21 (20), 3806– 3826. Wong, H.S.P. and Akinwande, D. (2011) Carbon Nanotube and Graphene Device Physics, Cambridge University Press. Pettifor, D.G. and Weaire, D.L. (2012) The Recursion Method and its Applications: Proceedings of the Conference, Imperial College , London, England September 13–14, 1984, vol. 58, Springer. Godin, T.J. and Haydock, R. (1991) The block recursion library: Accurate calculation of resolvent submatrices using the block recursion method. Computer Physics Communications, 64 (1), 123– 130. Haydock, R. (1980) The recursive solution of the Schrödinger equation. Computer Physics Communications, 20 (1), 11– 16. Vogl, P., Hjalmarson, H.P., and Dow, J.D. (1983) A semi-empirical tight-binding theory of the electronic structure of semiconductors. Journal of Physics and Chemistry of Solids, 44, 365– 378. Strasser, T. et al. (2001) One-step photoemission calculations for ideal GaAs(001) and AlAs(001) surfaces and (GaAs) m (AlAs) n superlattices. Physical Review B, 63, 195321. Jancu, J.M., Scholz, R., Beltram, F., and Bassani, F. (1998) Empirical spds* tight-binding calculation for cubic semiconductors: General method and material parameters. Physical Review B, 57 (11), 6493. Chadi, D.J. (1977) Spin-orbit splitting in crystalline and compositionally disordered semiconductors. Physical Review B, 16 (2), 790. Cardona, M., Shaklee, K.L., and Pol-lak, F.H. (1967) Electroreflectance at a semiconductor-electrolyte interface. Physical Review, 154 (3), 696. Awschalom, D.D. and Flatté, M.E. (2007) Challenges for semiconductor spintron-ics. Nature Physics, 3 (3), 153– 159. Xia, J., Ge, W., and Chang, K. (2012) Semiconductor Spintronics, World Scientific, Singapore. Schäpers, T. (2016) Semiconductor Spin-tronics, Walter de Gruyter GmbH & Co KG. Tan, Y., Povolotskyi, M., Kubis, T., He, Y., Jiang, Z., Klimeck, G., and Boykin, T.B. (2013) Empirical tight binding parameters for GaAs and MgO with explicit basis through DFT mapping. Journal of Computational Electronics, 12 (1), 56– 60. Cohen, R.E. (1992) Origin of ferroelec-tricity in perovskite oxides. Nature, 358 (6382), 136– 138. Junquera, J. and Ghosez, P. (2003) Critical thickness for ferroelectricity in perovskite ultrathin films. Nature, 422 (6931), 506– 509. Fong, D.D., Stephenson, G.B., Streiffer, S.K., Eastman, J.A., Auciello, O., Fuoss, P.H., and Thompson, C. (2004) Ferro-electricity in ultrathin perovskite films. Science, 304 (5677), 1650– 1653. Müller, K.A. and Burkard, H. (1979) SrTiO3: An intrinsic quantum paraelec-tric below 4 K. Physical Review B, 19, 3593– 3602. Schooley, J.F., Hosler, W.R., and Cohen, M.L. (1964) Superconductivity in semiconducting SrTiO3 . Physical Review Letters, 12, 474– 475. Fert, A. (2008) Nobel lecture: Origin, development, and future of spintronics. Reviews of Modern Physics, 80, 1517– 1530. Felser, C., Fecher, G.H., and Balke, B. (2007) Spintronics: A challenge for materials science and solid-state chemistry. Angewandte Chemie International Edition, 46 (5), 668– 699. Wolfram, T. and Ellialtioglu, S. (2006) Electronic and Optical Properties of d-band Perovskites, Cambridge University Press. Rößler, W. (2007) Eine kleine Nacht-physik: Geschichten aus der Physik, Springer. Johnson, S. and Joannopoulos, J. (2001) Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis. Optics Express, 8 (3), 173– 190. MIT Photonic-Bands (v1.6.1) (2018) https://mpb.readthedocs.io/en/latest/ (accessed: 4 April 2018). Prather, D.W. (2009) Photonic Crystals: Teory, Applications, and Fabrication, John Wiley & Sons, Inc., Hoboken. Sukhoivanov, I.A. and Guryev, I.V. (2009) Photonic Crystals: Physics and Practical Modeling, vol. 152, Springer. Shen, L., Ye, Z., and He, S. (2003) Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm. Physical Review B, 68 (3), 035109. Birner, A., Grüning, U., Ottow, S., Schneider, A., Müller, F., Lehmann, V., Föll, H., and Gösele, U. (1998) Macro-porous silicon: A two-dimensional photonic bandgap material suitable for the near-infrared spectral range. Phys. Status Solidi A, 165 (1), 111– 117. Hillebrand, R. and Hergert, W. (2000) Band gap studies of triangular 2d photonic crystals with varying pore roundness. Solid State Communications, 115 (5), 227– 232. Hillebrand, R., Hergert, W., and Harms, W. (2000) Theoretical band gap studies of two-dimensional photonic crystals with varying column roundness. Phys. Status Solidi B, 217 (2), 981– 990. Heisenberg, W. (1976) Der Teil und das Ganze, Piper, München. Sakoda, K. and Shiroma, H. (1997) Numerical method for localized defect modes in photonic lattices. Physical Review B, 56 (8), 4830. Sakoda, K. (1998) Numerical study on localized defect modes in two-dimensional triangular photonic crystals. Journal of Applied Physics, 84 (3), 1210– 1214. Robertson, W.M., Arjavalingam, G., Meade, R.D., Brommer, K.D., Rappe, A.M., and Joannopoulos, J.D. (1992) Measurement of photonic band structure in a two-dimensional periodic dielectric array. Physical Review Letters, 68 (13), 2023– 2026. Robertson, W.M., Arjavalingam, G., Meade, R.D., Brommer, K.D., Rappe, A.M., and Joannopoulos, J.D. (1993) Measurement of the photon dispersion relation in two-dimensional ordered dielectric arrays. Journal of the Optical Society of America B, 10 (2), 322– 327. Wada, M., Doi, Y., Inoue, K., and Haus, J.W. (1997) Far-infrared transmittance and band-structure correspondence in two-dimensional air-rod photonic crystals. Physical Review B, 55 (16), 10443. Stefanou, N., Karathanos, V., and Modi-nos, A. (1992) Scattering of electromagnetic waves by periodic structures. Journal of Physics: Condensed Matter, 4 (36), 7389. Weyl, H. and Bechtolsheim, L. (1981) Symmetrie, Birkhäuser, Basel. Sakoda, K. (1997) Group-theoretical classification of eigenmodes in three-dimensional photonic lattices. Physical Review B, 55, 15345– 15348. Ho, K.M., Chan, C.T., and Soukoulis, C.M. (1990) Existence of a photonic gap in periodic dielectric structures. Physical Review Letters, 65 (25), 3152. Ohtaka, K. and Tanabe, Y. (1996) Photonic band using vector spherical waves. I. Various properties of bloch electric fields and heavy photons. Journal of the Physical Society of Japan, 65 (7), 2265– 2275. Ohtaka, K. and Tanabe, Y. (1996) Photonic bands using vector spherical waves. II. Reflectivity, coherence and local field. Journal of the Physical Society of Japan, 65 (7), 2276– 2284. Ohtaka, K. and Tanabe, Y. (1996) Photonic bands using vector spherical waves. III. Group-theoretical treatment. Journal of the Physical Society of Japan, 65 (8), 2670– 2684. Ohtaka, K., Ueta, T., and Tanabe, Y. (1996) Photonic bands using vector spherical waves. IV. Analogy of optics of photonic crystals to that of anisotropic crystals. Journal of the Physical Society of Japan, 65 (9), 3068– 3077. Moroz, A. (1995) Density-of-states calculations and multiple-scattering theory for photons. Physical Review B, 51 (4), 2068. Weinberger, P. (1990) Electron Scattering Teory for Ordered and Disordered Matter, Clarendon Press, Oxford. Zabloudil, J., Hammerling, R., Szunyo-gh, L., and Weinberger, P. (2005) Electron Scattering in Solid Matter: A Te-oretical and Computational Treatise, Springer, Berlin, New York. Mie, G. (1908) Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösun-gen. Annalen der Physik, 330 (3), 377– 445. Rennert, P. (1990) The Mie scattering at an inhomogeneous and arbitrary shaped inclusion. Annalen der Physik, 502 (1), 27– 40. Bohren, C.F. and Huffman, D.R. (1983) Absorption and Scattering of Light by Small Particles, John Wiley & Sons, New York . Altmann, S.L. (1991) Band Teory of Solids: An Introduction from the Point of View of Symmetry, Clarendon Press, Oxford. Reddy, K.V. (2009) Symmetry and Spec-troscopy of Molecules, New Age International (P), New Delhi. Srivastava, G.P. (1990) Te Physics of Phonons, CRC Press. Brüesch, P. (1982) Phonons I, Springer, Berlin, Heidelberg. Czycholl, G. (2015) Teoretische Fest-körperphysik Band 1: Grundlagen: Phononen und Elektronen in Kristallen, Springer. Fujii, Y., Lurie, N.A., Pynn, R., and Shi-rane, G. (1974) Inelastic neutron scattering from solid 36Ar. Physical Review B, 10, 3647– 3659. Henshaw, D.G. (1958) Atomic distribution in liquid and solid neon and solid argon by neutron diffraction. Physical Review, 111, 1470– 1475. Heisenberg, W. (1976) Schritte über Grenzen. Gesammelte Reden und Auf-sätze, Piper, München. Tolédano, J.C. and Tolédano, P. (1987) Te Landau Teory of Phase Transitions: Application to Structural, Incommensurate, Magnetic, and Liquid Crystal Systems, World Scientific, Singapore, Teaneck, N.J. Ljubarski, G.J. (1962) Anwendungen der Gruppentheorie in der Physik, VEB Deutscher Verlag der Wissenschaften. Izyumov, Y.A. and Syromyatnikov, V. (1990) Phase Transitions and Crystal Symmetry, Kluwer Academic Publishers, Dordrecht, Boston, London. Birman, J.L. (1966) Simplified theory of symmetry change in second-order phase transitions: Application to V3Si. Physical Review Letters, 17 (24), 1216. Stokes, H.T. and Hatch, D.M. (1984) Group-subgroup structural phase transitions: A comparison with existing tables. Physical Review B, 30 (9), 4962. Hatch, D.M. and Stokes, H.T. (1984) Symmetry-restricted phase transitions in two-dimensional solids. Physical Review B, 30 (9), 5156. Sakhnenko, V.P. and Chechin, G.M. (1988) Symmetry methods and space group representations in the theory of phase transitions. Computers & Mathematics with Applications, 16 (5), 453– 464. Volovik, G. and Gor'kov, L. (1984) An unusual superconductivity in UBe13 . JETP Letters, 39 (12), 550– 553. Volovik, G. and Gor'kov, L. (1985) Superconducting classes in heavy-fermion systems. Soviet Physics, Journal of Experimental and Teoretical Physics, 61 (4), 843– 854. Blount, E. (1985) Symmetry properties of triplet superconductors. Physical Review B, 32 (5), 2935. Sigrist, M. and Ueda, K. (1991) Phe-nomenological theory of unconventional superconductivity. Reviews of Modern Physics, 63 (2), 239. Geilhufe, R.M. and Balatsky, A.V. (2018) Symmetry analysis of odd- and even-frequency superconducting gap symmetries for time-reversal symmetric interactions, Phys. Rev. B, 97, 024507 Beraha, L., Steurer, W., and Perez-Mato, J.M. (2001) The quasicrystal-to-crystal transformation. II. Landau theory. Zeit-schrift für Kristallographie – Crystalline Materials, 216 (11), 573– 585. Janssen, T. (2007) Phase transitions in aperiodic crystals. Ferroelectrics, 354 (1), 44– 51. Bronstein, I. and Semendjajew, K. (2008) Taschenbuch der Mathematik, Harri Deutsch. Kobayashi, A., Sankey, O.F., Volz, S.M., and Dow, J.D. (1983) Semiempiri-cal tight-binding band structures of wurtzite semiconductors: AlN, CdS, CdSe, ZnS, and ZnO. Physical Review B, 28, 935. Chelikowsky, J., Chadi, D.J., and Cohen, M.L. (1973) Calculated valence-band densities of states and photoemission spectra of diamond and zinc-blende semiconductors. Physical Review B, 8 (6), 2786. Perdew, J.P. and Zunger, A. (1981) Self-interaction correction to density-functional approximations for many-electron systems. Physical Review B, 23 (10), 5048. Vis5d+ (v1.2.0) (2002) http://vis5d.sourceforge.net (accessed: 15 October 2017). ParaView (v5.4.1) (2017) www.paraview.org (accessed: 15 October 2017). Hall, S.R., Allen, F.H., and Brown, I.D. (1991) The crystallographic information file (CIF): A new standard archive file for crystallography. Acta Crystallographica Section A, 47 (6), 655– 685. Kresse, G. and Furthmüller, J. (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Physical Review B, 54, 11169– 11186. Group Theory in Solid State Physics and Photonics: Problem Solving with Mathematica ReferencesRelatedInformation