plasmonics in double-layer graphene
DESCRIPTION
Plasmonics in double-layer graphene. Tobias Stauber and Guillermo Gómez-Santos. Graphene Nanophotonics Benasque, 5 th March 2013. Overview. Optical properties double-layer graphene. Effect of temperature and inhomogeneous dielectric background on Plasmons Near-field amplification - PowerPoint PPT PresentationTRANSCRIPT
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Plasmonics in double-Plasmonics in double-layer graphene layer graphene
Tobias StauberTobias Stauber and Guillermo Gómez-Santos and Guillermo Gómez-Santos
Graphene Nanophotonics Graphene Nanophotonics
Benasque, 5Benasque, 5thth March 2013 March 2013
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Overview
Optical properties of twisted bilayer graphene
(Work in progress with L. Brey, P. San Jose, E. Prada)
Drude weight
Plasmons excitations
Optical properties double-layer graphene
Effect of temperature and inhomogeneous dielectric background on Plasmons
Near-field amplification
Perfect transmission
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Plasmons in double-Plasmons in double-layer graphenelayer 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)
Johan Christensen et al, ACS Nano 2011
Ming Liu et al., Nano Lett. 12, 1482 (2012).
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Double-layer graphene
Define loss function:
Linear response in matrix form:
ext
ext
A
A
j
j
2
1
2221
1211
2
1
2221
1211Im),(
Trq
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Previous approaches
02
001
0
02
001
0
2221
1211
1
1det),(
vv
vvq
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.
The loss function is given by:),(
1Im),(
Often, the dielectric function is discussed:
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Results for the loss Results for the loss function at finite function at finite
temperaturetemperature
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Plasmons at finite temperature
TS and G. Gómez-Santos, New J. Phys. 14, 105018 (2012).
4/FTT
FTT
The plasmon dispersion is red-shifted for intermediate temperatures and blue-shifted for high temperatures.
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Plasmons at zero doping
eVv
kTk TT 035.02ln2
There are plasmons at zero doping at T=300K:
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:
FFg
a vdk
v2
12
Graphene on top of Pt(111):
Fa vv 15.1
TS and G. Gómez-Santos, New J. Phys. 14, 105018 (2012).
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Near-field Near-field amplificationamplification
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Near-field amplification
Analogy to Pendry´s perfect lens
qdeT 2
2
1
Exponential amplification for
R=0.
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Numerical results
Longitudinal polarization:
Transverse polarization:
TS and G. Gómez-Santos, Phys. Rev. B 85, 075410 (2012).
See also Poster 20 by A. Gutiérrez
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Numerical results
n1>n2 n1<n2
For different densities: order of layers determines amplification:
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Retardation effectsRetardation effects
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21 12 23
Strong light-matter coupling
The presence of doped graphene at the interfaces leads strong light-
matter coupling for ω<αωF:
Plasmon Dispersion:
• Quenched Fabry-Pérot resonances
• Extraordinary transmission in tunnel region
F
r
1
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.
22*
2
)2/()(
)2/(Im
ss
sQ32
/* Q
ds F
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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
Different layer distances Different relaxation times
Non-linear absorption sets in for angles beyond total reflections:
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Optical properties Optical properties of Twisted bilayerof Twisted bilayer
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Atomic structure
P. Moon and M. Koshino, arXive:1302.5218 (2013).
For small angles, the formation of periodic Moiré superlattices is seen.
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Electronic structure
Kv
tvv
FF
91
Renormalization of the Fermi velocity:
J. M. B. Lopes dos Santos et al., Phys. Rev. Lett. 99, 256802 (2007).
The electronic structure changes for small twist angles.
)2/sin(2 KK
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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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SummarySummary
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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 Thanks for your attention!attention!