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Plasmonics in double-layer graphene

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  1. Plasmonics in double-layer graphene TobiasStauber and Guillermo Gómez-Santos Graphene Nanophotonics Benasque, 5th March 2013

  2. Overview Optical properties double-layer graphene Effect of temperature and inhomogeneous dielectric background on Plasmons Near-field amplification Perfect transmission Optical properties of twisted bilayer graphene (Work in progress with L. Brey, P. San Jose, E. Prada) Drude weight Plasmons excitations

  3. Plasmons in double-layer graphene

  4. Double-layer graphene Coulomb drag, field effect tunneling transistor, and optical modulator. S. Kim, et. al., Phys. Rev. B 83, 161401(R) (2011). L. A. Ponomarenkoet. al., Nature Physics 7, 958 (2011). L. Britnell et. al., Science 335 (6071) 947-950 (2012) Ming Liu et al., Nano Lett. 12, 1482 (2012). Johan Christensen et al, ACS Nano2011

  5. Double-layer graphene Linear response in matrix form: Define loss function:

  6. Previous approaches Often, the dielectric function is discussed: The loss function is given by: • Problems: • This function changes sign, because it is not based on a true response function . • The absolute value gives incorrect weight for Landau damping regime.

  7. Results for the loss function at finite temperature

  8. Plasmons at finite temperature The plasmon dispersion is red-shifted for intermediate temperatures and blue-shifted for high temperatures. TS and G. Gómez-Santos, New J. Phys. 14, 105018 (2012).

  9. Plasmons at zero doping There are plasmons at zero doping at T=300K: TS and G. Gómez-Santos, New J. Phys. 14, 105018 (2012).

  10. Inhomogeneous dielectric medium An inhomogeneous dielectric medium can shift relative weight of in-phase and out-of-phase plasmons. Topological insulators have high-dielectric buffer layer: TS and G. Gómez-Santos, New J. Phys. 14, 105018 (2012).

  11. Acoustic plasmon mode A substrate with large dielectric constant turns plasmonic mode into acoustic mode: Graphene on top of Pt(111): TS and G. Gómez-Santos, New J. Phys. 14, 105018 (2012).

  12. Near-field amplification

  13. Near-field amplification Exponential amplification for R=0. Analogy to Pendry´s perfect lens

  14. Numerical results Longitudinal polarization: Transverse polarization: See also Poster 20 by A. Gutiérrez TS and G. Gómez-Santos, Phys. Rev. B 85, 075410 (2012).

  15. Numerical results For different densities: order of layers determines amplification: n1>n2 n1<n2

  16. Retardation effects

  17. Plasmon Dispersion: Strong light-matter coupling The presence of doped graphene at the interfaces leads strong light-matter coupling for ω<αωF: • Quenched Fabry-Pérot resonances • Extraordinary transmission in tunnel region G. Gómez-Santos and TS, Europhys. Lett.99, 27006 (2012).

  18. Fabry-Pérot resonances Quenched Fabry-Pérot resonances: Response shows Fano lineshape: Particle-in-a-box states leak out and interact with continuum.

  19. Quantum-Dot model Quasi-localized states between two doped graphene layers

  20. Extraordinary transmission Extraordinary transmission in tunnel region: Transmission between light cones:

  21. Finite relaxation time Non-linear absorption sets in for angles beyond total reflections: Different layer distances Different relaxation times

  22. Optical properties of Twisted bilayer

  23. Atomic structure For small angles, the formation of periodic Moiré superlattices is seen. P. Moon and M. Koshino, arXive:1302.5218 (2013).

  24. Electronic structure The electronic structure changes for small twist angles. Renormalization of the Fermi velocity: J. M. B. Lopes dos Santos et al., Phys. Rev. Lett. 99, 256802 (2007).

  25. Optical conductivity The optical conductivity is characterized by a van Hove singularity independent of the angle.

  26. Drude weight Drude weight follows the shell structure of the DOS.

  27. Drude weight For small angles, a substructure appears in the Drude weight not present in the DOS:

  28. Plasmonic excitations For small chemical potential: Interband plasmons

  29. Plasmonic excitations For large chemical potential: Intraband plasmons

  30. Summary

  31. Concluding remarks • There is spectral transfer of in-phase and out-of-phase mode, near-field amplification and perfect transmission in double-layer graphene. • Plasmonic spectrum of twisted bilayer graphene stronly depends on doping. Thanks for your attention!