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2013 | 2 | 107-123
Tytuł artykułu

Quantum graph spectra of a graphyne structure

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the dispersion relations and spectra of invariant Schrödinger operators on a graphyne structure (lithographite). In particular, description of different parts of the spectrum, band-gap structure, and Dirac points are provided.
Twórcy
autor
  • Mathematics Department, Texas A&M University,
    College Station, TX 77843-3365
  • Mathematics Department, Texas A&M University,
    College Station, TX 77843-3365
Bibliografia
  • C. Amovilli, F. Leys, N. March, Electronic Energy Spectrum of Two-Dimensional Solids and a Chain of C Atoms from a Quantum Network Model. J. Math. Chem. 36(2), 93–112 (2004) [Crossref]
  • D. Bardhan, Novel New Material Graphyne Can Be A Serious Competitor To Graphene. http://techiebuzz. com/science/graphyne.html (2012)
  • G. Berkolaiko, P. Kuchment, Introduction to quantum graphs AMS, Providence, RI (2012)
  • G. Borg, Eine Umkehrung der Sturm-Liouvillischen Eigenwertaufgabe, Acta Math. 78, 1–96(1946)
  • M. J. Bucknum, E. A. Castro, The squarographites: A lesson in the chemical topology of tessellations in 2- and 3-dimensions. Solid State Sciences 10, 1245–1251 (2008) [WoS]
  • M.S.P. Eastham, The Spectral Theory of Periodic Differential Equations Edinburgh-London: Scottish Acad. Press Ltd. (1973)
  • A. Enyanshin, A. Ivanovskii, Graphene Alloptropes: Stability, Structural and Electronic Properties from DF-TB Calculations. Phys. Status Solidi (b) 248, 1879–1883 (2011)
  • C.L. Fefferman, M.I. Weinstein, Honeycomb latice potentials and Dirac points J. Amer. Math. Soc. 25, 1169–1220 (2012) [Crossref]
  • C.L. Fefferman, M.I. Weinstein, Waves in Honeycomb Structures http://arxiv.org/pdf/1212.6684.pdf
  • A. Geim, Nobel lecture: Random walk to graphene Rev. Mod. Phys. 83, 851–862 (2011) [WoS]
  • E. Korotyaev, I. Lobanov, Schrödinger operators on zigzag graphs. Ann. Henri Poincaré 8(6), 1151–1176 (2007)
  • E. Korotyaev, I. Lobanov, Zigzag periodic nanotube in magnetic field. http://arxiv.org/list/math.SP/0604007 (2006)
  • P. Kuchment, Quantum graphs I. Some basic structures. Waves in Random media 14, S107–S128 (2004)
  • P. Kuchment, Quantum graphs II. Some spectral properties of quantum and combinatorial graphs J. Phys. A 38(22), 4887–4900 (2005)
  • P. Kuchment, Floquet Theory for Partial Differential Equations Birkhauser Verlag, Basel (1993)
  • P. Kuchment, L. Kunyansky, Spectral properties of high-contrast band-gap materials and operators on graphs., Experimental Mathematics 8, 1–28 (1999) [Crossref]
  • P. Kuchment, O. Post, On the Spectra of Carbon Nano-Structures. Commun. Math. Phys. 275, 805–826 (2007) [WoS]
  • D. Malko, C. Neiss, F. Viñes,A. Görling, Competition for Graphene: Graphynes with Direction-Dependent Dirac Cones. Phys. Rev. Lett. 108, 086804 (2012) [WoS][PubMed][Crossref]
  • K. Novoselov, Nobel lecture: Graphene: Materials in the flatland Rev. Mod.Phys. 83, 837–849 (2011) [WoS]
  • K. Pankrashkin, Spectra of Schrödinger operators on equilateral quantum graphs, Lett. Math. Phys. 77(2), 139–154 (2006) [Crossref]
  • M. Reed, B. Simon, Methods of Modern Mathematical Physics: Functional analysis Academic Press, Vol. 4 (1972)
  • B. Simon. On the genericity of nonvanishing instability intervals in Hills equation Ann. Inst. Henri Poincaré XXIV(1), 91–93 (1976)
  • K. Ruedenberg, C.W. Scherr, Free-electron network model for conjugated systems I. Theory. J. Chem. Phys. 21(9), 1565–1581 (1953) [Crossref]
  • L. E. Thomas. Time dependent approach to scattering from impurities in a crystal. Comm. Math. Phys. 33, 335–343 (1973)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_nsmmt-2013-0007
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