Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session A28: Focus Session: Carbon Nanotube Optics I 
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Sponsoring Units: DMP Chair: Stephen Doorn, Los Alamos National Laboratory Room: Colorado Convention Center 302 
Monday, March 5, 2007 8:00AM  8:36AM 
A28.00001: Magnetic Brightening of Dark Excitons in Carbon Nanotubes Invited Speaker: Junichiro Kono To gain insight into the internal energy structure and radiative properties of excitons in singlewalled carbon nanotubes (SWNTs), we have studied photoluminescence (PL) from individualized HiPco and CoMoCAT samples as a function of magnetic field ($B$) and temperature ($T$). The PL intensity increased, or ``brightened,'' with $B$ applied along the tube axis and the amount of brightening increased with decreasing $T$. These results are consistent with the existence of a dark state below the first bright state~[1]. In the presence of time reversal symmetry, exchangeinteractioninduced mixing between excitons in two equivalent valleys (the K and K' valleys) is expected to result in a set of exciton states, only one of which is optically active. This predicted bright state, however, is not the lowest in energy. Excitons would be trapped in the dark, lowestenergy state without a radiative recombination path. When a tubethreading $B$ is applied, addition of an AharonovBohm phase modifies the circumferential boundary conditions on the wave functions and lifts time reversal symmetry~[2,3]. This symmetry breaking splits the K and K' valley transitions, lessening the intervalley mixing and causing the recovery of the unmixed direct K and K' excitons, which are both optically active. We have calculated PL spectra through $B$dependent effective masses, populations of finite$k$ states, and acoustic phonon scattering, which quantitatively agree with the observations. These results demonstrate the existence of dark excitons, their influence on the PL quantum yield, and their elimination through symmetry manipulation by a $B$. This work was performed in collaboration with J.~Shaver, S.~Zaric, O.~Portugall, V.~Krstic, G.~L.~J.~A.~Rikken, X.~Wei, S.~A.~Crooker, Y.~Miyauchi, S.~Maruyama, and V.~Perebeinos and supported by the Robert A.~Welch Foundation, the NSF, and EuroMagNET. \newline \newline [1]~V.~Perebeinos {\it et al}., Phys.~Rev.~Lett.~{\bf 92}, 257402 (2004); H.~Zhao and S.~Mazumdar, Phys.~Rev.~Lett.~{\bf 93}, 157402 (2004); V.~Perebeinos {\it et al}., Nano Lett.~{\bf 5}, 2495 (2005); C.~D.~Spataru {\it et al}., Phys.~Rev.~Lett.~{\bf 95}, 247402 (2005). \newline [2]~T.~Ando, J.~Phys.~Soc.~Jpn.~{\bf 75}, 024707 (2006). \newline [3]~S.~Zaric {\it et al}., Science {\bf 304}, 1129 (2004); Phys.~Rev.~Lett.~{\bf 96}, 016406 (2006). [Preview Abstract] 
Monday, March 5, 2007 8:36AM  8:48AM 
A28.00002: Magnetic field effects on the excitonic absorption spectra of semiconducting singlewalled carbon nanotubes Hongbo Zhao, Zhendong Wang, Sumit Mazumdar We have investigated the magnetic field effects on the electronic structure and absorption spectra of semiconducting singlewalled carbon nanotubes (SSWCNTs) within a Coulomb correlated $\pi$electron model. \footnote{H. Zhao and S. Mazumdar, Phys. Rev. Lett. {\bf 93}, 157402(2004).} \footnote{Z. Wang, H. Zhao, and S. Mazumdar, Phys. Rev. B {\bf 74}, 195406 (2006).} We consider magnetic field parallel to the nanotube axis, which introduces the AharonovBohm phase in the wavefunction. Recent experiments claim to have observed the energy shift and splitting due to the magnetic fields \footnote{S. Zaric {\it et al.,} Phys. Rev. Lett. {\bf 96}, 016406 (2006).} Some of our theoretical results are substantively different from existing results. Comparison with recent experiments are made. [Preview Abstract] 
Monday, March 5, 2007 8:48AM  9:00AM 
A28.00003: Activating Dark Excitons on Carbon Nanotubes with Electric Fields J.M. Kinder, D. Zhabinskaya, E.J. Mele The valley degeneracy of the singlet excitons on a semiconducting carbon nanotube is lifted by Coulomb backscattering which produces two intervalley superposition states: a bright optically allowed singlet exciton, and a dark (dipole forbidden) singlet exciton at lower energy. We study theoretically the perturbations to this spectrum due to a longitudinal static electric field. We find the electric field transfers oscillator strength from the bright to the dark singlet states and activates the lower energy state in the fluorescence spectrum for modest values of the field strength. Modelling the K and K' point excitons as a two state system, we find that the field induces a complex phase in the intervalley scattering amplitude, which in turn renders the dark state optically active. We study the dependence of this effect on the chiral angle of the tube and further analyze other field configurations that can coherently manipulate the intervalley superposition states produced in this system. [Preview Abstract] 

A28.00004: ABSTRACT WITHDRAWN 
Monday, March 5, 2007 9:12AM  9:24AM 
A28.00005: Aromatic trends in singlewalled carbon nanotubes: diamagnetic anisotropy for arbitrary chiralities O.N. Torrens, D.E. Milkie, H.Y. Ban, M. Zheng, G.B. Onoa, T.D. Gierke, J.M. Kikkawa The chirality dependence of singlewalled carbon nanotube (SWNT) properties often leads to ``fanout'' diagrams whose departure from the large diameter scaling limit is of fundamental interest. ~Here we present the first experimental indication of fanout behavior for orbital magnetic anisotropy ($\Delta $\textit{$\chi $}), which has long been an important probe of electronic structure in aromatic molecules. ~We will discuss the experimental approach (polarized resonant photoluminescence) that made this backgroundfree measurement possible, and explain how these results can be used to predict $\Delta $\textit{$\chi $} for \textit{arbitrary} SWNT chiralities. ~Taking into account general symmetry considerations, \textit{ab initio} calculations, largediameter tightbinding theory, and our experimental data, we obtain a chiral expansion for $\Delta $\textit{$\chi $} using a single fitting parameter. ~The results show (2n+m) family trends whose asymmetry between ``mod 1'' and ``mod 2'' semiconducting families is reminiscent of those seen in other SWNT optical, phonon, and exciton properties. ~Finally, we discuss the (n,m) dependence of zonefolding tight binding calculations when applied to realistic tube sizes. [Preview Abstract] 
Monday, March 5, 2007 9:24AM  9:36AM 
A28.00006: Electronelectron interaction effects on crosspolarized optical absorption in semiconducting singlewalled carbon nanotubes (SSWCNTs) Zhendong Wang, Sumit Mazumdar Within the tight binding theory of SSWCNTs optical transitions polarized transverse to the nanotube axis, E$_{12}$ and E$_{21}$, are degenerate, and occur at (E$_{11}$ + E$_{22}$)/2, where E$_{11}$ and E$_{22}$ are the optical transitions polarized along the nanotube axis. Electronelectron interactions split the degeneracy of the transverse transitions, giving new eigenstates that are a redshifted optically forbidden odd superposition and a blueshifted (by several tenths of 1 eV) optically allowed even superposition of the oneelectron excitations \footnote{H. Zhao and S. Mazumdar, Phys. Rev. Lett. {\bf 93}, 157402 (2004)}. Recent experiments \footnote{Y. Miyauchi, M. Oba and S. Maruyama, Phys. Rev. B, accepted (2006)} have confirmed our qualitative prediction. Here we report quantitative calculations of the longitudinal versus transverse optical absorptions in the four SSWCNTs studied by Miyauchi {\it et al.}, within a $\pi$electron Hamiltonian with long range Coulomb interactions \footnote{Z. Wang, H. Zhao and S. Mazumdar, Phys. Rev. B {\bf 74}, 195406 (2006)}. We make detailed comparisons between experiments and theory. We also comment on the role of electron hoppings beyond nearest neighbor and the binding energy of the transverse exciton. [Preview Abstract] 
Monday, March 5, 2007 9:36AM  9:48AM 
A28.00007: Dielectric response of aligned semiconducting singlewall nanotubes B.J. Landi, J.A. Fagan, J.R. Simpson, L.J. Richter, I. Mandelbaum, D.L. Ho, R. Raffaelle, A.R. Hight Walker, B.J. Bauer, E.K. Hobbie We report measurements of the full intrinsic optical anisotropy of isolated singlewall carbon nanotubes (SWNTs). By combining absorption spectroscopy with transmission ellipsometry and polarizationdependent resonant Raman scattering, we obtain the real and imaginary parts of the intrinsic SWNT permittivity from aligned semiconducting carbon nanotubes dispersed in stretched polymer films. Our results are in agreement with theoretical predictions, highlighting the limited polarizability of excitons in a quasi1D system. We discuss the dependence of the measured optical response on nanotube length. [Preview Abstract] 
Monday, March 5, 2007 9:48AM  10:00AM 
A28.00008: Electronic Structure Effects in Single Wall Carbon Nanotubes Dielectric Response. Kevin Tatur, Lilia Woods The electronic structure of various single wall carbon nanotubes is considered within the $sp^3$ tightbinding model. Parameters for this model are taken from the SlaterKoster model. The $sp^3$ approach is applied in order to take into account the hybridization of the carbon $\sigma \pi $ orbitals due to curvature of the cylindrical surface of the nanotubes. The curvature dependence of the hopping integrals is also taken into account. Only nearest neighbor interaction is used. The obtained electronic states and energies are then used to calculate the dielectric response of the carbon nanotubes within random phase approximation methods. The real and imaginary parts of the dielectric response function are calculated and the curvature and geometry effects of the different nanotubes are discussed. [Preview Abstract] 
Monday, March 5, 2007 10:00AM  10:12AM 
A28.00009: Bilayer Graphene: An Electrically Tunable Semiconductor Hongki Min, Bhagawan Sahu, Sanjay Banerjee, Allan MacDonald Using \textit{ab initio} density functional theory calculations, we verify [1,2] that the energy band structure of bilayer graphene can be tuned by applying an external electric field. As the strength of the external electric field increases, the electronic spectrum of bilayer graphene changes from a that of a zerogap semiconductor to that of a gapped semiconductor. From the \textit{ab initio} calculations the external field dependence of the screened interlayer potential difference and tunneling amplitudes are extracted by fitting to a tightbinding model. We discuss the role of interlayer correlations in determining the size of the gap and the accuracy of local density approximation. [1] Edward McCann and Vladimir I. Fal'ko, Phys. Rev. Lett. {\bf 96}, 086805 (2006). [2] Taisuke Ohta, Aaron Bostwick,, Thomas Seyller, Karsten Horn, and Eli Rotenberg, Science {\bf 313}, 951 (2006). [Preview Abstract] 
Monday, March 5, 2007 10:12AM  10:24AM 
A28.00010: Magnetooptical conductivity in Graphene: signatures of the Dirac quasiparticles Sergei Sharapov, Valery Gusynin, Jules Carbotte Landau level quantization in graphene reflects the Dirac nature of its quasiparticles and has been found to exhibit an unusual integer quantum Hall effect. In particular the lowest Landau level can be thought as shared equally by electrons and holes and this leads to characteristic behavior of the diagonal and Hall magnetooptical conductivity as a function of frequency $\Omega$ for various values of the chemical potential $\mu$. We show that the evolution of the pattern of absorption lines as $\mu$ is varied encodes the information about the presence of the anomalous lowest Landau level. The first absorption line related to the lowest level always appears with full intensity or is entirely missing, while all other lines disappear in two steps. We demonstrate that if a gap develops, the main absorption line splits into two provided that the chemical potential is greater than or equal to the gap.\\ \noindent References: V.P.~Gusynin, S.G.~Sharapov and J.P.~Carbotte, condmat/0607727. [Preview Abstract] 
Monday, March 5, 2007 10:24AM  10:36AM 
A28.00011: Excitations from Filled Landau Levels in Graphene Drew Iyengar, Jianhui Wang, H.A. Fertig, Luis Brey We consider particlehole excitations of graphene over an integer quantum hall state. We first analyze the twobody problemof a single Dirac electron and hole in a magnetic field interactingvia Coulomb forces. We then turn to the manybody problem, where particlehole symmetry and the existence of two valleys lead to a number of effects peculiar to graphene. The appearance of different branches in the exciton spectrum is sensitive to the filling factor. The coupling together of a large number of lowlying excitations leads to strong many body corrections, which could be observed in inelastic light scattering or optical absorption. [Preview Abstract] 
Monday, March 5, 2007 10:36AM  10:48AM 
A28.00012: Magnetoplasmon excitations in graphene. Gerard Martinez, Yuri Bychkov Graphene is a monolayer of graphite with a band structure composed of two cones located at two inequivalent corners of the Brillouin zone at which conduction and valence bands merge. In contrast with conventional two dimensional electron gas, the dispersion relation obeys a Dirac law with an energy linear as a function of momentum which leads to a specific square root dependence of the Landau levels under an applied magnetic field. The magnetooptical transitions are either of cyclotron type or valence to conduction type. We derive in this frame the magnteplasmon picture, for filling factor lower than 2, which should be used to interpret the magnetooptical experiments in this compound. [Preview Abstract] 
Monday, March 5, 2007 10:48AM  11:00AM 
A28.00013: Infrared absorption in graphene Erik Henriksen, Zhigang Jiang, Richard Tung, YongJie Wang, Mollie Schwartz, Melinda Han, Philip Kim, Horst Stormer We present evidence for the cyclotron resonance transition between the lowest lying Landau levels near the Dirac point in a single layer of graphene, in magnetic fields up to 18T. At constant field, we modulated the back gate voltage on large area graphene samples to determine the infrared absorption from 400 to 3000 cm$^{1}$ using a FTIR spectrometer. All data were taken at 4.2K with simultaneous measurement of the graphene carrier densities and mobilities. We find transmission minima having widths of $\approx$500 cm$^{1}$, whose shift in energy is consistent with a square root dependence on the magnetic field as expected for two dimensional Dirac fermions. From this field dependence, the Fermi velocity is estimated at 1.1$\times$10$^6$m/s, in good agreement with literature values. [Preview Abstract] 
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