Advertisement

Surface Plasmon Retardation in Graphene Bilayer

  • Konstantin Batrakov
  • Vasil Saroka
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 146)

Abstract

Surface plasmons can be used for generation of radiation by \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\text{C}} \)erenkov mechanism in carbon nanotubes. However, slowing down of the plasmon phase speed is not enough for the synchronization with a nonrelativistic electron beam. Using the density-matrix formalism and the tight-binding approximation, we developed the method of obtaining the dispersion equation for plasmons in n-layer graphene systems. It was found that a graphene single layer can reduce the surface plasmon phase speed by 3–6 times. Reduction up to the Fermi velocity of p-electrons is achieved in spatially separated graphene bilayer. Thus, graphene bilayer seems to be suitable material for realization of the \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\text{C}} \)erenkov-type emitters in nanoscale.

References

  1. 1.
    Barnes WL, Ebbesen TW (2003) Surface plasmon subwavelength optics. Nature 424:824–830ADSCrossRefGoogle Scholar
  2. 2.
    Anker JN, Ebbesen TW (2008) Biosensing with plasmonic nanosensors. Nat Matter 7:442–453CrossRefGoogle Scholar
  3. 3.
    Liu Y, Bartal G, Genov DA, Zhang X (2007) Subwavelength discrete solitons in nonlinear metamaterials. Phys Rev Lett 99:153901ADSCrossRefGoogle Scholar
  4. 4.
    Stockman MI (2004) Nanofocusing of optical energy in tapered palsmonic waveguides. Phys Rev Lett 93:137404ADSCrossRefGoogle Scholar
  5. 5.
    Ren-Min M, Oulton RF, Sorger VJ, Guy B, Zhang X (2011) Room-temperature sub-diffraction-limited plasmon laser by total internal reflection. Nat Mater 10:110–113ADSCrossRefGoogle Scholar
  6. 6.
    Batrakov KG, Kuzhir PP, Maksimenko SA (2006) Radiative instability of electron beam in carbon nanotubes. Proc SPIE 6328:63280ZADSCrossRefGoogle Scholar
  7. 7.
    Batrakov KG, Maksimenko SA, Kuzhir PP, Thomsem C (2009) Carbon nanotube as a Cherenkov-type light emitter and free electron laser. Phys Rev B 70:125408–125420ADSCrossRefGoogle Scholar
  8. 8.
    Batrakov KG, Kuzhir PP, Maksimenko SA (2008) Toward the nano-FEL: undulator and Cherenkov mechanisms of light emission in carbon nanotubes. Physica E 40:1065–1068ADSCrossRefGoogle Scholar
  9. 9.
    Batrakov KG, Kuzhir PP, Maksimenko SA (2008) Stimulated emission of electron beam in nanotube bundles. Physica E 40:2370–2374ADSCrossRefGoogle Scholar
  10. 10.
    Slepyan GY, Maksimenko SA, Lakhtakia A, Yevtushenko O, Gusakov AV (1999) Electrodynamics of carbon nanotubes: dynamic conductivity, impedance boundary conditions and surface wave propagation. Phys Rev B 60:17136–17149Google Scholar
  11. 11.
    Frank S, Poncharal P, Wang ZL, de Heer WA (1998) Carbon nanotube quantum resistors. Science 280:1744ADSCrossRefGoogle Scholar
  12. 12.
    Berger C, Yi Y, Wang ZL, de Heer WA (2002) Multiwalled carbon nanotubes are ballistic conductors at room temperature. Appl Phys A 74:363–365ADSCrossRefGoogle Scholar
  13. 13.
    Wei BQ, Vajtai R, Ajayan PM (2001) Reliability and current carrying capacity of carbon nanotubes. Appl Phys Lett 79:1172ADSCrossRefGoogle Scholar
  14. 14.
    Batrakov KG, Kuzhir PP, Maksimenko SA (2010) Cherenkov synchronism: non-relativistic electron beam in multi-walled carbon nanotube and multi-layer graphene. Phys B: Phys Condens Matter 405:3050–3053ADSCrossRefGoogle Scholar
  15. 15.
    Partoens B, Peeters FM (2006) From graphene to graphite: electronic structure around the K points. Phys Rev B 74:075404ADSCrossRefGoogle Scholar
  16. 16.
    Saito R, Dresselhaus G, Dresselhaus M (1998) Physical properties of carbon nanotubes. Imperial College Press, LondonCrossRefGoogle Scholar
  17. 17.
    Zhang Y, Tang T, Girit C, Hao Z, Martin MC, Zettl A, Crommie MF, Shen YR, Wang F (2009) Direct observation of a widely tunable bandgap in bilayer graphene. Nature 459:820ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institute for Nuclear ProblemsBelarusian State UniversityMinskBelarus

Personalised recommendations