Plasmonics in double-layer graphene Tobias Stauber and Guillermo Gómez-Santos Graphene...
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Transcript of Plasmonics in double-layer graphene Tobias Stauber and Guillermo Gómez-Santos Graphene...
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
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
Plasmons in double-Plasmons in double-layer graphenelayer graphene
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).
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
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:
Results for the loss Results for the loss function at finite function at finite
temperaturetemperature
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.
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).
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).
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).
Near-field Near-field amplificationamplification
Near-field amplification
Analogy to Pendry´s perfect lens
qdeT 2
2
1
Exponential amplification for
R=0.
Numerical results
Longitudinal polarization:
Transverse polarization:
TS and G. Gómez-Santos, Phys. Rev. B 85, 075410 (2012).
See also Poster 20 by A. Gutiérrez
Numerical results
n1>n2 n1<n2
For different densities: order of layers determines amplification:
Retardation effectsRetardation effects
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).
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
Quantum-Dot model
Quasi-localized states between two doped graphene layers
Extraordinary transmission
Extraordinary transmission in tunnel region:
Transmission between light cones:
Finite relaxation time
Different layer distances Different relaxation times
Non-linear absorption sets in for angles beyond total reflections:
Optical properties Optical properties of Twisted bilayerof Twisted bilayer
Atomic structure
P. Moon and M. Koshino, arXive:1302.5218 (2013).
For small angles, the formation of periodic Moiré superlattices is seen.
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
Optical conductivity
The optical conductivity is characterized by a van Hove singularity independent of the angle.
Drude weight
Drude weight follows the shell structure of the DOS.
Drude weight
For small angles, a substructure appears in the Drude weight not present in the DOS:
Plasmonic excitations
For small chemical potential:
Interband plasmons
Plasmonic excitations
For large chemical potential:
Intraband plasmons
SummarySummary
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!