Tight-binding approach to penta-graphene

  1. Stauber, T.
  2. Beltrán, J. I. 12
  3. Schliemann, J.
  1. 1 Instituto de Ciencia de Materiales de Madrid, CSIC
  2. 2 2GFMC and Instituto Pluridisciplinar, Departamento de Física Aplicada III, Universidad Complutense de Madrid
Journal:
Scientific Reports

ISSN: 2045-2322

Year of publication: 2016

Volume: 6

Pages: 22672-1-22672-8

Type: Article

DOI: 10.1038/SREP22672 GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Scientific Reports

Sustainable development goals

Abstract

We introduce an effective tight-binding model to discuss penta-graphene and present an analytical solution. This model only involves the π-orbitals of the sp2-hybridized carbon atoms and reproduces the two highest valence bands. By introducing energy-dependent hopping elements, originating from the elimination of the sp3-hybridized carbon atoms, also the two lowest conduction bands can be well approximated - but only after the inclusion of a Hubbard onsite interaction as well as of assisted hopping terms. The eigenfunctions can be approximated analytically for the effective model without energy-dependent hopping elements and the optical absorption is discussed. We find large isotropic absorption ranging from 7.5% up to 24% for transitions at the Γ-point.

Bibliographic References

  • Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).
  • Novoselov, K. S. et al. Two-dimensional atomic crystals. Proc. Natl. Acad. Sci. USA 102, 10451–10453 (2005).
  • Kroto, H. W., Heath, J. R., O’Brien, S. C., Curl, R. F. & Smalley, R. E. C60: Buckminsterfullerene. Nature 318, 162–163 (1985).
  • Iijima, S. Helical microtubules of graphitic carbon. Nature 354, 56–58 (1991).
  • Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009).
  • Zhang, S. et al. Penta-graphene: A new carbon allotrope. Proc. Natl. Acad. Sci. USA 112, 2372–2377 (2015).
  • Yagmurcukardes, M. et al. Pentagonal monolayer crystals of carbon, boron nitride, and silver azide. J. App. Phys. 118 (2015).
  • Wallace, P. R. The band theory of graphite. Phys. Rev. 71, 622–634 (1947).
  • McClure, J. W. Diamagnetism of graphite. Phys. Rev. 104, 666–671 (1956).
  • Slonczewski, J. C. & Weiss, P. R. Band structure of graphite. Phys. Rev. 109, 272–279 (1958).
  • Jorio, A. et al. Structural (n, m) determination of isolated single-wall carbon nanotubes by resonant raman scattering. Phys. Rev. Lett. 86, 1118–1121 (2001).
  • Reich, S., Maultzsch, J., Thomsen, C. & Ordejón, P. Tight-binding description of graphene. Phys. Rev. B 66, 035412 (2002).
  • Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558–561 (1993).
  • Kresse, G. & Hafner, J. Ab initio molecular-dynamics simulation of the liquid-metal amorphous-semiconductor transition in germanium. Phys. Rev. B 49, 14251–14269 (1994).
  • Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).
  • Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
  • Monkhorst, H. J. & Pack, J. D. Special points for brillouin-zone integrations. Phys. Rev. B 13, 5188–5192 (1976).
  • Slater, J. C. & Koster, G. F. Simplified lcao method for the periodic potential problem. Phys. Rev. 94, 1498–1524 (1954).
  • Yuan, S., Rösner, M., Schulz, A., Wehling, T. O. & Katsnelson, M. I. Electronic structures and optical properties of partially and fully fluorinated graphene. Phys. Rev. Lett. 114, 047403 (2015).
  • Hirsch, J. E. & Marsiglio, F. Hole superconductivity in oxides: A two-band model. Phys. Rev. B 43, 424–434 (1991).
  • Hirsch, J. E. Electron- and hole-hopping amplitudes in a diatomic molecule. Phys. Rev. B 48, 3327–3339 (1993).
  • Guinea, F. Effect of assisted hopping on the formation of local moments in magnetic impurities and quantum dots. Phys. Rev. B 67, 195104 (2003).
  • Stauber, T. & Guinea, F. Assisted hopping in the anderson impurity model: A flow equation study. Phys. Rev. B 69, 035301 (2004).
  • Paul, I. & Kotliar, G. Thermal transport for many-body tight-binding models. Phys. Rev. B 67, 115131 (2003).
  • Nair, R. R. et al. Fine structure constant defines visual transparency of graphene. Science 320, 1308–1308 (2008).
  • Mak, K. F. et al. Measurement of the optical conductivity of graphene. Phys. Rev. Lett. 101, 196405 (2008).
  • Fang, H. et al. Quantum of optical absorption in two-dimensional semiconductors 110, 11688–11691 (2013).
  • Stauber, T., Noriega-Pérez, D. & Schliemann, J. Universal absorption of two-dimensional systems. Phys. Rev. B 91, 115407 (2015).
  • García de Abajo, F. J. Colloquium: Light scattering by particle and hole arrays. Rev. Mod. Phys. 79, 1267–1290 (2007).
  • Weaire, D. & Thorpe, M. F. Electronic properties of an amorphous solid. i. a simple tight-binding theory. Phys. Rev. B 4, 2508–2520 (1971).
  • Hatsugai, Y., Shiraishi, K. & Aoki, H. Flat bands in the weaire-thorpe model and silicene. New J. Phys. 17, 025009 (2015).
  • Mielke, A. & Tasaki, H. Ferromagnetism in the hubbard model. examples from models with degenerate single-electron ground states. Comm. Math. Phys. 158, 341–371 (1993).