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

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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-0833184 NASA HRNNX09AV07A ARO 577969-PH-H Collaborators: Lilia Woods group University of South Florida, Tampa, USA Slide 2 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 Slide 3 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, 12-16 April, 2010 Slide 4 pp pzpz pzpz pp (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 m3q (q=1,2,3,) (m,n) chiral CN: metallic or semi- conducting depending on the radius and chiral angle pp pzpz Calculated energy dependence of the CN axial conductivity I.Bondarev PLMCN10, Cuernavaca, Mexico, 12-16 April, 2010 Slide 5 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 Slide 6 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, 035451; PRB 70, 035407 I.V.Bondarev et al., PRL 89, 115504 The Hamiltonian: Dominant Suppressed in quasi-1D I.Bondarev PLMCN10, Cuernavaca, Mexico, 12-16 April, 2010 Slide 7 Exact Diagonalization via Bogoliubovs 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 Slide 8 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, 085407 (2009) I.Bondarev PLMCN10, Cuernavaca, Mexico, 12-16 April, 2010 Slide 9 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] I.Bondarev PLMCN10, Cuernavaca, Mexico, 12-16 April, 2010 Slide 10 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) Slide 11 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 Slide 12 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, 085407 (2009) Perebeinos at al., PRL94,027402 Spataru at al., PRL95,247402 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, 12-16 April, 2010 Slide 13 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 Slide 14 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, 085407 (2009) I.Bondarev PLMCN10, Cuernavaca, Mexico, 12-16 April, 2010 Slide 15 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, 12-16 April, 2010 Perebeinos at al., PRL94,027402 Pedersen at al., NanoLett.5,291 Slide 16 The strong exciton-surface plasmon coupling effect with Rabi splitting ~0.1-0.3 eV has been demonstrated for individual small diameter (