Том 8, №2, 2016
РусскийEnglish

НАНОСИСТЕМЫ



DIRAC MATERIAL GRAPHENE

Elena F. Sheka


Russian Peoples' Friendship University of Russia, http://www.rudn.ru
117198 Moscow, Russin Federation
sheka@icp.ac.ru

Поступила в редакцию 14.10.2016


Аннотация. The paper presents an overview on the spin-rooted properties of graphene, supported by numerous experimental and calculation evidence. Correlation of odd pz electrons of the honeycomb lattice meets a strict demand “different orbitals for different spins”, which leads to spin polarization of electronic states, on the one hand, and generation of an impressive pool of local spins distributed over the lattice, on the other. These features characterize graphene as a peculiar semimetal with Dirac cone spectrum at particular points of the Brillouin zone. However, spin-orbit coupling (SOC), though small but available, supplemented by dynamic SOC caused by electron correlation, transforms graphene-semimetal into graphene-topological insulator (TI). The consequent topological non-triviality and local spins are proposed to discuss such peculiar properties of graphene as high temperature ferromagnetism and outstanding chemical behavior.The connection of these new findings with difficulties met at attempting to convert graphene-TI (usually taken as SM) into semiconductor one is discussed.

Ключевые слова: graphene, Dirac fermions, quasi-relativistic description, hexagonal honeycomb structure, local spins, open-shell molecules, spin-orbital coupling, quantum spin Hall insulator, high temperature ferromagnetism, chemical activity

PACS: 51.05.ue

Библиография – 79 ссылок

РЭНСИТ, 2016, 8(2):131-153 DOI: 10.17725/rensit.2016.08.131
ЛИТЕРАТУРА
  • Graphene Science Handbook: 6-volume set. Eds. Aliofkhazraei M, Ali N, Miln WI, Ozkan CS, Mitura S, Gervasoni J. CRC Press, Taylor and Francis Group, Boca Raton, 2016.
  • Löwdin P-O. Correlation problem in many-electron quantum mechanics. 1. Review of different approaches and discussion of some current ideas. Adv. Chem. Phys., 1958, 2:209-322.
  • Sheka EF. The uniqueness of physical and chemical natures of graphene: Their coherence and conflicts. Int. J. Quant. Chem., 2014, 114:1079-1095.
  • Sheka EF. Computational strategy for graphene: Insight from odd electrons correlation. Int. J. Quant. Chem., 2012, 112:3076-3090.
  • Sheka EF, Chernozatonskii LA. Chemical reactivity and magnetism of graphene. Int. J. Quant. Chem., 2010, 110:1938-1946.
  • Sheka EF, Popova NA, Popova VA, Nikitina EA, Shaymardanova LKh. Structure-sensitive mechanism of nanographene failure. J. Exp. Theor. Phys., 2011, 112:602-611.
  • Sheka EF. Spin effects of sp2 nanocarbons in light of unrestricted Hartree-Fock approach and spin-orbit coupling theory. In: Advances in Quantum Methods and Applications in Chemistry, Physics, and Biology (Tadjer, A., Brändas, E.J., Maruani, J., Delgado-Barrio, G., ed.). Progress in Theoretical Chemistry and Physics 31, Springer, Switzerland, 2016:xxx-yyy.
  • Wallace PR. The band theory of graphite. Phys. Rev., 1947, 71:622-634.
  • Kane CL, Mele EJ. Quantum spin Hall effect in graphene. Phys. Rev. Lett., 2005, 95:226801.
  • Guzmàn-Verri GG. Electronic Properties of Silicon-Based Nanostructures. MS thesis, Wright State University, Dayton, 2006.
  • Slonczewski JC, Weiss PR. Band structure of graphite. Phys. Rev., 1957, 109:272-279.
  • Katsnelson MI. Graphene: carbon in two dimensions. Materials Today, 2007, 10:20-27.
  • Geim AK, Novoselov KS. The rise of graphene. Nat. Mat., 2007, 6:183-191.
  • Kim P. Graphene and relativistic quantum physics. Matiere de Dirac, Seminaire Poincare XVIII, 2014:1-21.
  • Hwang C, Siegel DA, Mo S-K, Regan W, Ismach A, Zhang Y, Zettl A, Lanzara A. Fermi velocity engineering in graphene by substrate modification. Sci. Rep., 2012, 2:590.
  • Kara A, Enriquez H, Seitsonen AP, Lew Yan Voon LC, Vizzini S, Aufray B, Oughaddou H. A review on silicene − new candidate for electronics. Surf Sci. Rep., 2012, 67:1-18.
  • Sheka EF. Silicene is a material phantom. Nanosyst. Phys. Chem. Math., 2016, 7:983-1001.
  • Zhang R-W, Ji W-X, Zhang C-W, Li P, Wang P-J. Prediction of flatness-driven quantum spin Hall effect in functionalized germanene and stanene. Phys. Chem. Chem. Phys., 2016, 18:28134-28139.
  • Gomes KK, Mar W, Ko W, Guinea F, Manoharan HC. Designer Dirac fermions and topological phases in molecular graphene. Nature, 2012, 483:307-311.
  • Tarruell L, Greif D, Uehlinger T, Jotzu G, Esslinger T. (2012). Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice. Nature, 2012, 483:302-306.
  • Bhimanapati GR, Lin Z, Meunier V, Jung Y, Cha J, Das S, Xiao D, Son Y, Strano MS, Cooper VR, Liang L, Louie SG, Ringe E, Zhou W, Sumpter BG, Terrones H, Xia F, Wang Y, Zhu J, Akinwande D, Alem N, Schuller JA, Schaak RE, Terrones M, Robinson JA. (2015). Recent advances in two-dimensional materials beyond graphene, ACS Nano, 2015, 9:11509-11539.
  • Xu L-C, Du A, Kou L. Hydrogenated borophene as a stable two-dimensional Dirac material with an ultrahigh Fermi velocity. Phys. Chem. Chem. Phys., 2016, 18:27284-27289.
  • Wang C, Xia Q, Nie Y, Rahman M, Guo G. Strain engineering band gap, effective mass and anisotropic Dirac-like cone in monolayer arsenene. AIP Advances, 2016, 6:035204.
  • Wang A, Zhang X, Zhao M. Topological insulator states in a honeycomb lattice of s-triazines. Nanoscale, 2014, 6:11157-11162.
  • Zhang X, Wang A, Zhao M. Spin-gapless semiconducting graphitic carbon nitrides: A theoretical design from first principles. Carbon, 2015, 84:1-8.
  • Wei L, Zhang X, Zhao M. Spin-polarized Dirac cones and topological nontriviality in a metal-organic framework Ni2C24S6H12. Phys. Chem. Chem. Phys., 2016, 18:8059-8064.
  • Zhang H, Li Y, Hou J, Du A, Chen Z. Dirac state in the FeB2 monolayer with graphene-like boron sheet. Nano Lett., 2016, 16:6124-6129.
  • Si C, Jin K-H, Zhou J, Sun Z, Liu F. Large-gap quantum spin hall state in MXenes: d-Band topological order in a triangular lattice. Nano Lett., 2016, DOI: 10.1021/acs.nanolett.6b03118.
  • Naguib M, Mochalin VN, Barsoum MW, Gogotsi Y. 25th Anniversary Article: MXenes: A new family of two-dimensional materials. Adv. Mat., 2014, 26:992-1005.
  • Bandurin DA, Tyurnina AV, Yu GL, Mishchenko A, Zólyomi V, Morozov SV, Kumar RK, Gorbachev RV, Kudrynskyi ZR, Pezzini S, Kovalyuk ZD, Zeitler U, Novoselov KS, Patanè A, Eaves L, Grigorieva IV, Fal’ko VI, Geim AK, Cao Y. High electron mobility, quantum Hall effect and anomalous optical response in atomically thin InSe. Nat. Nanotech., 2016, DOI: 10.1038/NNANO.2016.242.
  • Sheka EF. Stretching and breaking of chemical иonds, correlation of electrons, and radical properties of covalent species, Adv. Quant. Chem., 2015, 70:111-161.
  • Hohenadler M, Assaad FF. Correlation effects in two-dimensional topological insulators, J. Phys.: Condens. Matter, 2013, 25:143201 (31pp).
  • Mayorov AS, Elias DC, Mukhin IS, Morozov SV, Ponomarenko LA, Novoselov KS, Geim AK, Gorbachev RV. How close can one approach the Dirac point in graphene experimentally? Nano Letters, 2012, 12:4629-4634.
  • Topological Insulators: Fundamentals and Perspective. Eds. Ortmann F, Roche S, Valenzuela SO, Molenkamp LW. Wiley: Chichester, 2015.
  • Schüler M, Rösner M, Wehling TO, Lichtenstein AI, Katsnelson MI. Optimal Hubbard models for materials with nonlocal Coulomb interactions: graphene, silicene and benzene. Phys. Rev. Lett., 2013, 111:036601.
  • Bučinský L, Malček M, Biskupič S, Jayatilaka D, Büchel GE, Arion VB. Spin contamination analogy, Kramers pairs symmetry and spin density representations at the 2-component unrestricted Hartree–Fock level of theory. Comp. Theor. Chem., 2015, 1065:27-41.
  • Yazyev OV. Emergence of magnetism in graphene materials and nanostructures. Rep. Prog. Phys., 2010, 73:05650130.
  • Esquinazi P, Spemann D, Hohne R, Setzer A, Han KH, Butz T. Induced magnetic ordering by proton irradiation in graphite. Phys. Rev. Lett., 2003, 91:227201.
  • Sepioni M, Nair RR, Rablen S, Narayanan J, Tuna F, Winpenny R, Geim AK, Grigorieva IV. Limits on intrinsic magnetism in graphene, Phys. Rev. Lett., 2010, 105:207205.
  • Nair RR, Sepioni M, Tsai I-L, Lehtinen O, Keinonen J, Krasheninnikov AV, Thomson T, Geim AK, Grigorieva IV. Spin-half paramagnetism in graphene induced by point defects. Nat. Phys., 2012, 8:199-202.
  • Eng AYS, Poh HL, Sanek F, Marysko M, Matejkova S, Sofer Z. Pumera M. Searching for magnetism in hydrogenated graphene: Using highly hydrogenated graphene prepared via birch reduction of graphite oxides. ACS Nano, 2013, 7:5930-5939.
  • Nair RR, Tsai I-L, Sepioni M, Lehtinen O, Keinonen J, Krasheninnikov AV, Castro Neto AH, Katsnelson MI, Geim AK, Grigorieva IV. Dual origin of defect magnetism in graphene and its reversible switching by molecular doping. Nat. Commn., 2013, 4:2010.
  • Tada K, Haruyama J, Yang HX, Chshiev M, Matsui T, Fukuyama H. Ferromagnetism in hydrogenated graphene nanopore arrays.Phys. Rev. Lett., 2011, 107:217203.
  • Ning G, Xu C, Hao L, Kazakova O, Fan Z, Wang H, Wang K, Gao J, Qian W, Wei F. Ferromagnetism in nanomesh graphene. Carbon, 2013, 51:390-396.
  • Van Fleck JH. The Theory of Electric and Magnetic Susceptibilities. Oxford, 1932.
  • Adamo C, Barone V, Bencini A, Broer R, Filatov M, Harrison NM, Illas F, Malrieu JP, Moreira I.de PR. Comment on “About the calculation of exchange coupling constants using density-functional theory: The role of the self-interaction error”. [J. Chem. Phys., 2005, 123:164110]. Journ. Chem. Phys., 2006, 124:107101.
  • Noodleman L. Valence bond description of antiferromagnetic coupling in transition metal dimmers. J. Chem. Phys., 1981, 74:5737-5742.
  • Kahn O. Molecular Magnetism. VCH, New York, 1993.
  • Zayets VA. CLUSTER-Z1: Quantum-Chemical Software for Calculations in the s,p-Basis. Kiev, Institute of Surface Chemistry Nat Ac Sci of Ukraine, 1990.
  • Gao X, Zhou Z, Zhao Y, Nagase S, Zhang SB, Chen ZJ. Comparative study of carbon and BN nanographenes: Ground electronic states and energy gap engineering. Phys. Chem. A, 2008, 112:12677.
  • Enoki T, Kobayashi Y. Magnetic nanographite: an approach to molecular magnetism. J. Mat. Chem., 2005, 15:3999.
  • Sheka EF, Zayets VA, Ginzburg IYa. Nanostructural magnetism of polymeric fullerene crystals. J. Exp. Theor. Phys., 2006, 103:728-739.
  • Nai CT, Xu H, Tan SJR, Loh KP. Analyzing Dirac cone and phonon dispersion in highly oriented nanocrystalline graphene. ACS Nano, 2016, 10:1681-1689.
  • Liu Q, Liu C-X, Xu C, Qi X-L, Zhang S-C. Magnetic impurities on the surface of a topological insulator. Phys. Rev. Lett., 2009, 102:156603.
  • Checkelsky JG, Ye J, Onose Y, Iwasa Y, Tokura Y. Dirac-fermion-mediated ferromagnetism in a topological insulator. Nature Phys., 2012, 8:729-733.
  • Dreiser J, Pacchioni GE, Donati F, Gragnaniello L, Cavallin A, Pedersen KS, Bendix J, Delley B, Pivetta M, Rusponi S, Brune H. Out-of-plane alignment of Er(trensal) easy magnetization axes using graphene. ACS Nano, 2016, 10:2887-2892.
  • Katmis F, Lauter V, Nogueira FS, Assaf BA, Jamer ME, Wei P, Satpati B, Freeland JW, Eremin I, Heiman D, Jarillo-Herrero P, Moodera JS. A high-temperature ferromagnetic topological insulating phase by proximity coupling. Nature, 2016, 533:513–516.
  • Sheka EF. Chemical susceptibility of fullerenes in view of Hartree-Fock approach. Int. J. Quant. Chem., 2007, 107:2803-2816.
  • Sheka EF. Chemical portrait of fullerenes. J. Struct. Chem., 2006, 47:593-599.
  • van der Lit J, Boneschanscher MP, Vanmaekelbergh D, Ijäs M, Uppstu A, Ervasti M, Harju A, Liljeroth P, Swart I. Suppression of electron–vibron coupling in graphene nanoribbons contacted via a single atom. Nat. Commn., 2013, 4:2023.
  • Warner JH, Lin Y-C, He K, Koshino M, Suenaga K. Atomic level spatial variations of energy states along graphene edges. Nano Lett., 2014, 14:6155-6159.
  • Nakada K, Fujita M. Edge state in graphene ribbons: Nanometer size effect and edge shape dependence. Phys. Rev. B, 1996, 54:17954-17961.
  • Barnard AS, Snook IK. Modelling the role of size, edge structure and terminations on the electronic properties of graphene nano-flakes. Modelling Simul. Mater. Sci. Eng., 2011, 19:054001.
  • Acik M, Chabal YJ. Nature of graphene edges: A review. Jpn. J. Appl. Phys., 2011, 50:070101.
  • Mishra PC, Yadav A. Polycyclic aromatic hydrocarbons as finite size models of graphene and graphene nanoribbons: Enhanced electron density edge effect. Chem. Phys., 2012, 402:56-68.
  • Ang LS, Sulaiman S, Mohamed-Ibrahim MI. Effects of size on the structure and the electronic properties of graphene nanoribbons. Monatsh. Chem., 2013, 144:1271–1280.
  • Hoffmann R. Small but strong lessons from chemistry for nanoscience. Ang. Chem. Int. Ed., 2013, 52:93-103.
  • Mayer I. On bond orders and valences in the ab initio quantum chemical theory. Int. J. Quant. Chem., 1986, 29:73-84.
  • Sheka EF, Popova NA. Odd-electron molecular theory of the graphene hydrogenation. J. Mol. Model., 2012, 18:3751-3768.
  • Sheka E, Popova N. Molecular theory of graphene oxide. Phys. Chem. Chem. Phys., 2013, 15:13304-13332.
  • Lu G, Yu K, Wen Z, Chen J. Semiconducting graphene: converting graphene from semimetal to semiconductor. Nanoscale, 2013, 5:1353-1367.
  • Chernozatonski LA, Sorokin PB, Belova EE, Brüning J. Superlattices consisting of ‘lines‘ of adsorbed hydrogen atom pairs on graphene, JEPT Lett., 2007, 85:77-81.
  • Lu N, Huang Y, Li H-b, Li Z, Yang J. First principles nuclear magnetic resonance signatures of graphene oxide. J. Chem. Phys., 2010, 133:034502.
  • Pan S, Aksay IA. Factors controlling the size of graphene oxide sheets produced via the graphite oxide route. ACS Nano, 2011, 5:4073-4083.
  • Nebogatikova NA, Antonova IV, Prinz VYa, Kurkina II, Vdovin VI, Aleksandrov GN, Timofeev VB, Smagulova SA, Zakirova ER, Kesler VG. Fluorinated graphene dielectric films obtained from functionalized graphene suspension: preparation and properties. Phys. Chem. Chem. Phys., 2015, 17:13257-13266.
  • Wang X, Bai H, Shi G. Size fractionation of graphene oxide sheets by pH-assisted selective sedimentation. J. Am. Chem. Soc., 2011, 133:6338-6342.
  • Kang JH, Kim T, Choi J, Park J, Kim YS, Chang MS, Jung H, Park K, Yang SJ, Park CR. The hidden second oxidation step of Hummers method. Chem. Mat., 2016, 28:756-764.
  • Elias DC, Nair RR, Mohiuddin TMG, Morozov SV, Blake P, Halsall MP, Ferrari AC, Boukhvalov DW, Katsnelson MI, Geim AK, Novoselov KS. Control of graphene’s properties by reversible hydrogenation: evidence of graphane. Science, 2009, 323:610-613.
  • Balog R, Jorgensen B, Nilsson L, Andersen M, Rienks E, Bianchi M, Fanetti M, Lægsgaard E, Baraldi A, Lizzit S, Sljivancanin Z, Besenbacher F, Hammer B, Pedersen TG, Hofmann P, Hornekær L. Bandgap opening in graphene induced by patterned hydrogen adsorption. Nature Mat., 2010, 9:315-319.


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