Diapositiva 1

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Plasmonics in double-layer graphene
Tobias Stauber and Guillermo Gómez-Santos

Graphene Nanophotonics Benasque, 5th March 2013
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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
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Plasmons in double-layer graphene
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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. Ponomarenko et. 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 Nano 2011
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Double-layer graphene
Linear response in matrix form
Define loss function
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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.

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Results for the loss function at finite
temperature
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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).
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Plasmons at zero doping
There are plasmons at zero doping at T300K
TS and G. Gómez-Santos, New J. Phys. 14, 105018
(2012).
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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).
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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).
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Near-field amplification
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Near-field amplification
Exponential amplification for R0.
Analogy to Pendrys perfect lens
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Numerical results
Longitudinal polarization
Transverse polarization
See also Poster 20 by A. Gutiérrez
TS and G. Gómez-Santos, Phys. Rev. B 85, 075410
(2012).
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Numerical results
For different densities order of layers
determines amplification
n1gtn2
n1ltn2
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Retardation effects
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Strong light-matter coupling
The presence of doped graphene at the interfaces
leads strong light-matter coupling for ?lta?F

• Quenched Fabry-Pérot resonances
• Extraordinary transmission in tunnel region

G. Gómez-Santos and TS, Europhys. Lett. 99, 27006
(2012).
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Fabry-Pérot resonances
Quenched Fabry-Pérot resonances
Response shows Fano lineshape Particle-in-a-box
states leak out and interact with continuum.
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Quantum-Dot model
Quasi-localized states between two doped graphene
layers
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Extraordinary transmission
Extraordinary transmission in tunnel region
Transmission between light cones
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Finite relaxation time
Non-linear absorption sets in for angles beyond
total reflections
Different layer distances
Different relaxation times
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Optical properties of Twisted bilayer
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Atomic structure
For small angles, the formation of periodic Moiré
superlattices is seen.
P. Moon and M. Koshino, arXive1302.5218 (2013).
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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).
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Optical conductivity
The optical conductivity is characterized by a
van Hove singularity independent of the angle.
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Drude weight
Drude weight follows the shell structure of the
DOS.
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Drude weight
For small angles, a substructure appears in the
Drude weight not present in the DOS
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Plasmonic excitations
For small chemical potential Interband plasmons
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Plasmonic excitations
For large chemical potential Intraband plasmons
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Summary
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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!