EXCITON-PLASMON COUPLING AND BIEXCITONIC NONLINEARITIES IN INDIVIDUAL CARBON NANOTUBES Igor Bondarev Physics Department North Carolina Central University

EXCITON-PLASMON COUPLINGAND BIEXCITONIC NONLINEARITIES IN INDIVIDUAL

CARBON NANOTUBES

Igor BondarevPhysics Department

North Carolina Central UniversityDurham, NC 27707, USA

Supported by:US National Science Foundation – HRD-0833184NASA – HRNNX09AV07AARO – 577969-PH-H

Collaborators: Lilia Woods’ group University of South Florida, Tampa, USA

OUTLINE

Introduction. Transverse Quantization and Interband Plasmons in CNs

Exciton-Plasmon Interactions in CNs. Brief Description of the Model

The Quantum Confined Stark Effect. Results of the Calculations

Conclusions

I.Bondarev – PLMCN10, Cuernavaca, Mexico, 12-16 April, 2010

BASIC PHYSICAL PROPERTIES OF SINGLE-WALLED CARBON NANOTUBES

Classification

a1

a2

ma1 + na2

x

y

300

Graphene single sheet Single-walled CN of (m,n) type


00

, 2.7 eV2

x

pf

pz pz

pf

(m,m) – “Armchair”: metallic for all m

, 1,2, ,cn

sp s m

R

BASIC PHYSICAL PROPERTIES OF SINGLE-WALLED CNsBrillouin zone structure

(m,0) – “Zigzag”: metallic for m=3q,semiconducting for m≠3q (q=1,2,3,…)

(m,n) – chiral CN: metallic or semi-conducting depending on the radius and chiral angle

pf

pz

Calculated energy dependence

of the CN axial conductivity


Experimental Electron Energy Loss Spectroscopy (EELS) Spectra of Single-Walled Carbon Nanotubes

T.Pichler, M.Knupher, M.Golden, J.Fink, A.Rinzler, and R.Smalley, PRL 80, 4729 (1998)


EXCITON-PLASMON INTERACTIONS. THE MODELI.V.Bondarev, L.M.Woods, and K.Tatur, PRB80,085407; Optics Commun.282,661(2009)

I.V.Bondarev and H.Qasmi, Physica E 40, 2365 (2008)

FORMALISM: I.V.Bondarev & Ph.Lambin, Trends in Nanotubes Research,

Nova Science, NY, 2006 I.V.Bondarev & Ph.Lambin, PRB 72, 035451; PRB 70, 035407 I.V.Bondarev et al., PRL 89, 115504

e-h

The Hamiltonian:

Dominant

Suppressed in quasi-1D


Exact Diagonalization via Bogoliubov’s Canonical Transformation

Dispersion Equation

THE MODEL (Continued)I.V.Bondarev, L.M.Woods, and K.Tatur,

Phys. Rev. B 80, 085407 (2009); Opt. Commun. 282, 661 (2009)


Plasmon DOS

EELS response function

0.224 0.24 0.26 0.28 0.300

20

40

60

80

100

Pla

smo

n D

OS

Dimensionless Energy

(11,0)

-1

0

1

2

3

4

Dim

en

sio

nle

ss C

on

du

ctiv

ity Re[zz

];

Im[zz

]

EXAMPLE:

(11,0) CN by non-orthogonal tight-binding simulations

Approximate Solution of the Dispersion Equation(the plasmon DOS)

I.V.Bondarev, L.M.Woods, and K.Tatur, Phys. Rev. B 80, 085407 (2009)


Approximate Solution of the Dispersion Equation(obtained by the exact diagonalization of the Hamiltonian)

I.V.Bondarev, K.Tatur, and L.M.Woods, Optics Commun. 282, 661 (2009)

EXAMPLE:

(11,0) CN with the lowest bright exciton parameters from the Bethe-Salpeter eqn [from Spataru et al, PRL 95, 247402]

0.00 0.05 0.10 0.15 0.200.20

0.22

0.24

0.26

0.28

0.30

0.32

Dim

ensi

onle

ss E

nerg

y

(11,0)

Dimensionless Quasimomentum


Theory of Optical Absorption Close to a Photonic DOS Resonance

I.Bondarev&B.Vlahovic, PRB74,073401

Exciton-phonon relaxation

Exciton Absorption/Emission Lineshape(close to a plasmon resonance)



Numerical ResultsTuning Excitons to Plasmon Resonances in (11,0) & (10,0) CNs


0.26 0.27 0.28 0.29 0.30

Lin

esh

ap

e (

arb

. un

its)

(11,0)

Dimensionless energy0.20 0.22 0.24 0.26 0.28 0.30

Dimensionless energy

Lin

esh

ap

e (

arb

. un

its)

(10,0)

Perebeinos at al., PRL94,027402

Spataru at al., PRL95,247402

Epl =1.50 eV Epl =1.39 eV

&&

Calculated Absorption/Emission Lineshapes

<×5.4 eV>

Exciton-plasmon Rabi splitting ~0.1 eV –> STRONG COUPLING !!!


How to tune ? Quantum Confined Stark Effect in Perpendicular Electric Field


F


Exciton absorption

when tuned to the plasmon

resonance

e-h

FLongitudinal Coulomb potentialwith field rise

Exciton-Plasmon parameters with field rise

How to tune ? Quantum Confined Stark Effect in a Perpendicular Electric Field



3rd-order Longitudinal Nonlinear Susceptibility(close to a plasmon resonance)

S.Mukamel, Principles of Nonlinear Optical Spectroscopy, Oxford, 1995


Perebeinos at al., PRL94,027402

Pedersen at al., NanoLett.5,291

The strong exciton-surface plasmon coupling effect with Rabi splitting ~0.1-0.3 eV has been demonstrated for individual small diameter (<~1 nm) semiconducting CNs

Quantum confined Stark effect with an external electro-

static field applied perpendicular to the CN axis, can be used to tune the exciton energy to a plasmon resonance

Predicted tunable strong exciton-plasmon coupling effect may be used to control exciton photoluminescence in CN based optoelectronic device applications in areas such as nanophotonics, nanoplasmonics, and cavity QED

CONCLUSIONS



I.V.Bondarev, K.Tatur, and L.M.Woods, Optics Commun. 282, 661 (2009)

I.V.Bondarev, K.Tatur, and L.M.Woods, Optics & Spectroscopy 108, 376 (2010)


Documents

EXCITON-PLASMON COUPLING AND BIEXCITONIC NONLINEARITIES IN INDIVIDUAL CARBON NANOTUBES Igor Bondarev Physics Department North Carolina Central University