1. Plasmonics in double-layer graphene
Tobias Stauber 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 graphene3

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

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 temperature7

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, (2012).

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

11. Graphene on top of Pt(111):
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, (2012).

12. Near-field amplification12

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, (2012).

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

16. Retardation effects 16

17. Strong light-matter coupling
Plasmon Dispersion:
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, (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. Quasi-localized states between two doped graphene layers
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 bilayer22

23. Atomic structure
For small angles, the formation of periodic Moiré superlattices is seen.
P. Moon and M. Koshino, arXive: (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, (2007).

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

26. 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 30

31. Thanks for your attention!
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!