EXCITON-PLASMON COUPLING AND BIEXCITONIC NONLINEARITIES IN INDIVIDUAL CARBON NANOTUBES Igor Bondarev Physics Department North Carolina Central University Durham, NC 27707, USA Supported by: US National Science Foundation – HRD NASA – HRNNX09AV07A ARO – 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, April, 2010

BASIC PHYSICAL PROPERTIES OF SINGLE-WALLED CARBON NANOTUBES Classification a1a1 a2a2 ma 1 + na 2 x y 30 0 Graphene single sheet Single-walled CN of (m,n) type I.Bondarev – PLMCN10, Cuernavaca, Mexico, April, 2010

pp pzpz pzpz pp (m,m) – “Armchair”: metallic for all m BASIC PHYSICAL PROPERTIES OF SINGLE-WALLED CNs Brillouin 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 pp pzpz Calculated energy dependence of the CN axial conductivity I.Bondarev – PLMCN10, Cuernavaca, Mexico, 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, April, 2010

EXCITON-PLASMON INTERACTIONS. THE MODEL I.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, ; PRB 70,  I.V.Bondarev et al., PRL 89, The Hamiltonian: Dominant Suppressed in quasi-1D I.Bondarev – PLMCN10, Cuernavaca, Mexico, 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, (2009); Opt. Commun. 282, 661 (2009) I.Bondarev – PLMCN10, Cuernavaca, Mexico, April, 2010

Plasmon DOS EELS response function 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, (2009) I.Bondarev – PLMCN10, Cuernavaca, Mexico, 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, ] I.Bondarev – PLMCN10, Cuernavaca, Mexico, April, 2010

Numerical Results Exciton-Plasmon DOS & Dispersion in (10,0)& (8,0) CNs I.V.Bondarev, K.Tatur, and L.M.Woods, Optics Commun. 282, 661 (2009)

Theory of Optical Absorption Close to a Photonic DOS Resonance I.Bondarev&B.Vlahovic, PRB74, 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, (2009) I.Bondarev – PLMCN10, Cuernavaca, Mexico, April, 2010

Numerical Results Tuning Excitons to Plasmon Resonances in (11,0) & (10,0) CNs I.V.Bondarev, L.M.Woods, and K.Tatur, Phys. Rev. B 80, (2009) Perebeinos at al., PRL94, Spataru at al., PRL95, E pl =1.50 eV E pl =1.39 eV & & Calculated Absorption/Emission Lineshapes Exciton-plasmon Rabi splitting ~ 0.1 eV –> STRONG COUPLING !!! I.Bondarev – PLMCN10, Cuernavaca, Mexico, 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, (2009)F I.Bondarev – PLMCN10, Cuernavaca, Mexico, April, 2010

Exciton absorption when tuned to the plasmon resonance F Longitudinal Coulomb potential with 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, (2009) I.Bondarev – PLMCN10, Cuernavaca, Mexico, April, 2010

3 rd -order Longitudinal Nonlinear Susceptibility (close to a plasmon resonance) S.Mukamel, Principles of Nonlinear Optical Spectroscopy, Oxford, 1995 I.Bondarev – PLMCN10, Cuernavaca, Mexico, April, 2010 Perebeinos at al., PRL94, Pedersen at al., NanoLett.5,291

The strong exciton-surface plasmon coupling effect with Rabi splitting ~ 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, April, 2010

I.V.Bondarev, L.M.Woods, and K.Tatur, Phys. Rev. B 80, (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, April, 2010