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),(

qq

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:

qq

• 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.

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