EXCITON-PLASMON COUPLING AND BIEXCITONIC NONLINEARITIES IN INDIVIDUAL CARBON NANOTUBES Igor Bondarev...

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

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

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

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

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)

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

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

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

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)

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

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)

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

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

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

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)

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

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

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

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

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 !!!

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

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

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

F

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

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

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

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

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

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

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

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

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

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)

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