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