Quantum graph spectra of a graphyne structure
Nanoscale Systems: Mathematical Modeling, Theory and Applications (2013)
- Volume: 2, page 107-123
- ISSN: 2299-3290
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topNgoc T. Do, and Peter Kuchment. "Quantum graph spectra of a graphyne structure." Nanoscale Systems: Mathematical Modeling, Theory and Applications 2 (2013): 107-123. <http://eudml.org/doc/267301>.
@article{NgocT2013,
abstract = {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.},
author = {Ngoc T. Do, Peter Kuchment},
journal = {Nanoscale Systems: Mathematical Modeling, Theory and Applications},
keywords = {graphyne; graphene; spectrum; Floquet-Bloch theory; dispersion relation; Dirac point; Hill operator},
language = {eng},
pages = {107-123},
title = {Quantum graph spectra of a graphyne structure},
url = {http://eudml.org/doc/267301},
volume = {2},
year = {2013},
}
TY - JOUR
AU - Ngoc T. Do
AU - Peter Kuchment
TI - Quantum graph spectra of a graphyne structure
JO - Nanoscale Systems: Mathematical Modeling, Theory and Applications
PY - 2013
VL - 2
SP - 107
EP - 123
AB - 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.
LA - eng
KW - graphyne; graphene; spectrum; Floquet-Bloch theory; dispersion relation; Dirac point; Hill operator
UR - http://eudml.org/doc/267301
ER -
References
top- 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] Zbl1052.81689
- 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) Zbl1317.81127
- G. Borg, Eine Umkehrung der Sturm-Liouvillischen Eigenwertaufgabe, Acta Math. 78, 1–96(1946) Zbl0063.00523
- 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) Zbl0287.34016
- 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] Zbl1316.35214
- 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) Zbl05207472
- 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) Zbl1063.81058
- P. Kuchment, Quantum graphs II. Some spectral properties of quantum and combinatorial graphs J. Phys. A 38(22), 4887–4900 (2005) Zbl1070.81062
- P. Kuchment, Floquet Theory for Partial Differential Equations Birkhauser Verlag, Basel (1993) Zbl0789.35002
- P. Kuchment, L. Kunyansky, Spectral properties of high-contrast band-gap materials and operators on graphs., Experimental Mathematics 8, 1–28 (1999) [Crossref] Zbl0930.35112
- P. Kuchment, O. Post, On the Spectra of Carbon Nano-Structures. Commun. Math. Phys. 275, 805–826 (2007) [WoS] Zbl1145.81032
- 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] Zbl1113.81056
- M. Reed, B. Simon, Methods of Modern Mathematical Physics: Functional analysis Academic Press, Vol. 4 (1972) Zbl0242.46001
- B. Simon. On the genericity of nonvanishing instability intervals in Hills equation Ann. Inst. Henri Poincaré XXIV(1), 91–93 (1976) Zbl0346.34015
- 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)
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