Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session G18: Focus Session: Carbon Nanotubes: Electronic and Optical Properties I |
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Sponsoring Units: DMP Chair: Tobias Hertel, Vanderbilt University Room: Baltimore Convention Center 315 |
Tuesday, March 14, 2006 8:00AM - 8:36AM |
G18.00001: Excitons in the optical properties of nanotubes Invited Speaker: We present {\it ab initio} calculation of self-energy and electron-hole interaction (excitonic) effects on the optical spectra of single-walled carbon and BN nanotubes. We employed a many-electron Green's function approach that determines both the quasiparticle and optical excitations from first principles. We found important many-electron effects that explain many of the puzzling experimental findings in the optical spectrum of these quasi-one dimensional systems, and the calculated spectra are in excellent quantitative agreement with measurements. In carbon nanotubes, excitons can bind by as much as one eV in semiconducting nanotubes$^{a)}$. We discovered that bound excitons also exist in metallic carbon nanotubes with binding energy of many tens of meVs$^{a)}$. Excitonic effects are shown to be even more inportant in BN nanotubes than in carbon nanotubes. Unlike the carbon nanotubes, theory predicts that excitons in some BN nanotubes are comprised of coherent superposition of transitions from several different subband pairs$^{b)}$. We have also calculated the radiative lifetime of excitons in semiconducting carbon nanotubes. Assuming a thermal occupation of bright and dark exciton bands, we find an effective radiative lifetime of the order of 10 ns at room temperature, in good accord with recent experiments$^{c)}$. \\ {\bf a)} C.D. Spataru, S. Ismail-Beigi, L.X. Benedict and S.G. Louie, Phys. Rev. Lett. {\bf 92}, 077402 (2004). \\ {\bf b)} C.-H. Park, C.D. Spataru and S.G. Louie, to be published. \\ {\bf c)} C.D. Spataru, S. Ismail-Beigi, R.B. Capaz and S.G. Louie, in press Phys. Rev. Lett. [Preview Abstract] |
Tuesday, March 14, 2006 8:36AM - 8:48AM |
G18.00002: Exciton radiative lifetime in carbon nanotubes Vasili Perebeinos, Jerry Tersoff, Phaedon Avouris The optical properties of carbon nanotubes are dominated by excitons, and the exciton radiative lifetime determines the optical efficiency. We calculate the exciton radiative lifetime as a function of tube diameter and chirality, finding an unusual nonmonotonic temperature dependence [1]. This reflects the crucial role of exciton bands that are optically inactive, due to spin or parity, below the optically active exciton. We determine the scaling with diameter of the singlet-triplet and parity forbidden exciton splittings. We also calculate the exciton dispersion, finding a non-parabolic behavior of the optically active band. Excitons that thermalize into low-energy optically inactive bands cannot contribute to light emission, unless they are thermally excited into the active band, resulting in reduced emission yield at low temperature. However, in real systems there is typically some symmetry breaking, which mixes optically allowed and forbidden bands; and as a result, some emission is still possible from the nominally forbidden bands. This may account for the multiple emission peaks and complex temperature dependence seen in some experiments. [1] NanoLett. 5 DOI: nl051828s (2005). [Preview Abstract] |
Tuesday, March 14, 2006 8:48AM - 9:00AM |
G18.00003: Magnetic brightening of ``dark'' excitons in carbon nanotubes S. Zaric, J. Kono, X. Wei, R. H. Hauge, R. E. Smalley We have measured polarized-excitation photoluminescence (PL) on micelle-suspended single-walled carbon nanotubes (SWNTs) in aqueous solution in external magnetic fields ($B)$ up to 45 T at room temperature. Each PL peak, corresponding to a specific chirality, splits into two in a $B$ and the amount of splitting increases with $B$. The magnetic field dependence of the relative intensities of the two peaks reveals that the lower-energy peak increases in intensity (or ``brightens'') with increasing $B$. These results can be understood in terms of ``magnetic brightening'' of an excitonic state that is ``dark'' at 0 T. Namely, recent calculations taking into account intervalley Coulomb mixing in semiconducting SWNTs predict the existence of a dark excitonic state at an energy $\Delta _{X}$ below the lowest optically active (bright) excitonic state. On the other hand, magnetic flux \textit{$\phi $} threading a nanotube removes the intervalley degeneracy which is seen in absorption measurements as peak splittings by an amount $\Delta _{AB}$ proportional to \textit{ $\phi $} (when \textit{$\phi $/$\phi $}$_{0} \quad \le $ 1/6, \textit{$\phi $}$_{0}$: magnetic flux quantum). While two equally-bright excitonic peaks are predicted and observed at high fields ($\Delta _{AB} \quad >> \quad \Delta _{X})$,$^{1}$ magnetic brightening is expected at lower fields ($\Delta _{AB} \quad \sim \quad \Delta _{X})$, which is consistent with our observations. $^{1}$ S. Zaric \textit{et al}, Phys. Rev. Lett., to appear (see also cond-mat/0509429) [Preview Abstract] |
Tuesday, March 14, 2006 9:00AM - 9:12AM |
G18.00004: Diameter and chirality dependence of exciton properties in carbon nanotubes Rodrigo Capaz, Catalin Spataru, Sohrab Ismail-Beigi, Steven Louie We calculate the binding energies and sizes of excitons in carbon nanotubes using a symmetry-based, effective-mass, variational method. This approach provides exciton binding energies in good agreement with available first-principles results and its simplicity allows calculations for a variety of diameters ($d$) and chiralities. The exciton binding energies present an overall decrease with $1/d$, with strong chirality dependence and family behavior. The exciton sizes scale with $d$, also showing family behavior. We also address the important issue of bright-dark exciton splittings, which are found to decrease as $1/d^2$. Dependence of these properties on the dielectric screening will also be addressed, in the light of recent experimental measurements. This work was supported in part by the NSF under Grant No. DMR04-39768, and the U.S. DOE under Contract No. DE-AC03- 76SF00098. [Preview Abstract] |
Tuesday, March 14, 2006 9:12AM - 9:24AM |
G18.00005: Nearly quantitative fitting of exciton energies and exciton binding energies of semiconducting single-walled carbon nanotubes (S-SWCNTs) within a $\pi$-electron model Zhendong Wang, Sumit Mazumdar We use to Pariser-Parr-Pople $\pi$-electron Hamiltonian, which has been widely used to understand the excitonic energy spectra of $\pi$-conjugated polymers, to determine the energy spectra of S-SWCNTs. For the Coulomb interaction parameters, we use the screened Ohno parameters that were successfully used before for the quantitative fitting of the excitonic energy spectrum of poly-(paraphenylenevinylene) \footnote{M. Chandross and S. Mazumdar, Phys. Rev. B {\bf 55}, 1497 (1997)}. In order to take into account of the curvature effects, we use a $\pi$-electron nearest neighbor hopping integral that is substantially smaller than the standard 2.4 eV. With these modified parameters we are able to fit the lowest two exciton energies of a very large number of S-SWCNTs. We make detailed comparisons between the calculated and experimental \footnote{R.B. Weisman and S.M. Bachilo, Nano Lett. {\bf 3}, 1235 (2003)}. We also obtain a binding energy of $\sim$ 0.4 eV for the lowest exciton of S-SWCNTs with diameters $\sim$ 0.8 nm, in agreement with experiments. [Preview Abstract] |
Tuesday, March 14, 2006 9:24AM - 9:36AM |
G18.00006: Determination of the exciton binding energy in single-walled carbon nanotubes Todd Krauss, Zhenjia Wang, Hermenegildo Pedrosa, Lewis Rothberg The optical properties of single-walled carbon nanotubes (SWNTs) are intrinsically important for potential applications in photonics and also provide insight into their structural and electrical properties. Absorption and emission of semiconducting SWNTs are dominated by excitonic effects, but a determination of central features such as exciton binding energies remains elusive. We will present measurements of the exciton binding energy in SWNTs using resonance Raman scattering of isolated SWNTs under an electrochemical bias. The Raman intensity under an applied voltage is sensitive to state filling and enables a determination of the (electronic) gap between the second Van Hove singularities in densities of states for electrons and holes in specific semiconducting SWNTs. On the other hand, Raman scattering preferentially selects sets of SWNTs whose excitonic transitions (optical gap) are resonant with the incident and scattered photon energies. Simultaneous measurement of the electronic gap and exciton resonance allows us to infer binding energies for the exciton of 0.49 and 0.62 eV for tubes with structural (n,m) indices (10, 3) and (7, 5), respectively. Analogous Raman and electrochemical studies in metallic SWNTs imply the absence of a sharp excitonic feature. [Preview Abstract] |
Tuesday, March 14, 2006 9:36AM - 9:48AM |
G18.00007: Nanotube exciton spectrum: Triangular quantum well model. Slava V. Rotkin, Alexey G. Petrov The analytical solution for the problem of NT-exciton is found using the approximation for the {\bf screened} Coulomb potential between the electron and hole. We derive the screening via calculating a self-consistent dielectric function with {\bf both spatial and time dispersion} taken into account, $\varepsilon(\vec q,\omega)$, which characterizes the response to the $\vec q$ component of the Coulomb potential at the frequency $\omega$. The latter corresponds to the energy of the exciton and is to be sought. We calculated the RPA dielectric function of the SWNT in the orthogonal tight-binding approach. Then, the inverse Fourier transform of the screened Coulomb potential gives the shape of the potential well for the electron-hole pair (direct Coulomb interaction term). We show that this screened potential can be approximated by a triangular quantum well, which model allows ananlytical solutions for the exciton wavefunction and the binding energy. The exchange term is short-ranged and can be added as the delta-function barrier in the middle of the well. The exciton binding energy is calculated to be a universal function of $E_g$, the one-particle band gap, $R$, the NT radius and $\lambda$, the electric length in the triangular quantum well potential. The effective Bohr radius is also a universal function of $R$ and $\lambda$. The analytical expression for the oscillator strength of the optical transition is presented. [Preview Abstract] |
Tuesday, March 14, 2006 9:48AM - 10:00AM |
G18.00008: Theory of electroabsorption in semiconducting single-walled carbon nanotubes Hongbo Zhao, Sumit Mazumdar Eletroabsorption (EA) is a standard nonlinear optical technique to probe the excitonic characteristics of semiconductors. \footnote{L.~Sebastian and G.~Weiser, Phys. Rev. Lett. {\bf 46}, 1156 (1981); D.~Guo {\it et al.}, Phys. Rev. B {\bf 48}, 1433 (1993).} In the context of single-walled carbon nanotubes (SWCNTs) the advantage of EA is that it can directly probe the excitons associated with higher bands, which lie in the continuum region of the lowest band, and cannot be probed by other nonlinear optical techniques like photoinduced absorption or two-photon absorption. Although currently it is still difficult to carry out EA experiments, because it requires separation of semiconducting SWCNTs from metallic ones, theoretical calculations can provide a benchmark results for future study. We have calculated EA for several S-SWCNTs with both zigzag and chiral tubes.~\footnote{ J. W. Kennedy, Z. V. Vardeny, S. Collins, R. H. Baughman, H. Zhao, and S. Mazumdar, cond-mat/0505071.} For the lowest exciton we find the usual Stark shift, the emergence of absorption due to two-photon states and continuum band. We also find unusual and interesting behavior of the higher energy excitons from second band. [Preview Abstract] |
Tuesday, March 14, 2006 10:00AM - 10:12AM |
G18.00009: Interactions between individual carbon nanotubes studied by Rayleigh scattering spectroscopy Tony Heinz, Feng Wang, Matthew Sfeir, Limin Huang, X.M. Henry Huang, Yang Wu, Jaehee Kim, James Hone, Stephen O'Brien, Louis Brus Single-walled carbon nanotubes (SWNTs), with diameters of nanometers and lengths up to millimeters, represent highly one-dimensional (1D) systems. Because all the carbon atoms of a SWNT lie on its surface, the physical properties of SWNTs depend sensitively on local environment.[1] In particular, the electronic properties of SWNTs are altered by inter-tube coupling whenever nanotube bundles are formed. We examine such inter-tube interactions experimentally at the single nanotube level. This is achieved by applying Rayleigh scattering spectroscopy[2] to probe the optical transitions of individual SWNTs in their isolated and bundled forms. Upon bundling, the transition energies of SWNTs are observed to undergo red shifts of tens of meVs, without any significant line broadening. These inter-tube coupling effects can be understood as arising from the mutual dielectric screening of SWNTs in a bundle. 1. Kong, J., et al., Science, \textbf{287, }622 (2000). 2. Sfeir, M.Y., et al., Science, \textbf{306,} 1540 (2004). [Preview Abstract] |
Tuesday, March 14, 2006 10:12AM - 10:24AM |
G18.00010: Exciton dynamics in DNA suspended SWNT agglomerates: From delocalized to one-dimensionally confined excited states Jared J. Crochet, Michael Arnold, Mark Hersam, Zipeng Zhu, Tobias Hertel Exciton dynamics in chirality enriched, DNA suspended single-wall carbon nanotube agglomerates are studied using linear absorption, spectrofluorimetry, and ultrafast pump-probe spectroscopies. Suspended SWNT ropes with controlled diameter are isolated using isopycnic density gradient fractionation. Photoluminescence quantum yields are found to decrease with increasing rope diameter concomitantly to a broadening and redshift of exciton transitions. Spectrally resolved optical transients reveal that excited state dynamics are characterized by an increase of $E_{11}$ subband exciton decay rates as the rope size increases. These findings are discussed in terms of the roles of intertube coupling and exciton delocalization. [Preview Abstract] |
Tuesday, March 14, 2006 10:24AM - 10:36AM |
G18.00011: Raman characterization of electronic transition energies of metallic single-wall carbon nanotubes Hyungbin Son, Alfonso Reina Cecco, Jing Kong, Mildred Dresselhaus Theoretical studies using extended tight-binding model are shown to reproduce the optical transition energies of single-wall carbon nanotubes (SWNTs) obtained by experimental studies. However, some of the optical transitions for metallic SWNTs predicted by theory are not reported in previous experimental studies. We present that Raman characterization on a large number of individual SWNTs reveals these missing optical transitions. The intensity variations of different optical transitions are attributed to electron-phonon matrix elements. [Preview Abstract] |
Tuesday, March 14, 2006 10:36AM - 10:48AM |
G18.00012: Inelastic X-ray Scattering Studies of Plasmons in Carbon Nanotubes M. H. Upton, D. Casa, T. Gog, J. Misewich, J. P. Hill, D Lowndes, G. Eres We report preliminary inelastic x-ray scattering measurements of the plasmon dispersions in oriented multi- and single- walled carbon nanotubes (M- and S- WCNT) and compare them to the plasmon dispersion in graphite. Two plasmon bands are observed dispersing along the nanotubes' axes: the $\pi $ and $\pi +\sigma $ plasmon bands. The $\pi +\sigma $ plasmon band exhibits an apparent systematic variation in energy. Specifically, it has a lower energy in MWCNT than in graphite, and a still lower energy in SWCNT. The energy of the $\pi +\sigma $ plasmon band is determined by the plasma frequency of the material, which is proportional to the square root of the electron density. We postulate that the energy shift is a result of a surface effect -- the electron wave function extends past the surface, lowering the average electron density in the bulk. The higher surface-to-volume ratio of the mostly SW sample would then lower the plasmon frequency with respect to the MWCNT sample and graphite. Thus, the systematic variation in plasmon frequency may be explained by a lowering of the net electron density by the surfaces in S- and M-WCNT. Work performed at BNL and the Advanced Photon Source was supported by the US DOE under contracts No. DE-AC02-98CH10886 and No. W-31-109-Eng-38 respectively. [Preview Abstract] |
Tuesday, March 14, 2006 10:48AM - 11:00AM |
G18.00013: Atomic Entanglement in Carbon Nanotubes. Igor Bondarev, Branislav Vlahovic The development of materials that may host quantum coherent states is a critical research problem for the nearest future. Recent progress in the growth of centimeter-long small-diameter single-walled carbon nanotubes (CNs)[1] and successful experiments on the encapsulation of single atoms into CNs[2], stimulate the study of dynamical quantum processes in atomically doped CN systems. We have recently shown[3] that atomic states may be strongly coupled to vacuum surface photonic modes in the CN, thus forming quasi-1D cavity polaritons similar to those observed for quantum dots in semiconductor nanocavities[4], which were recently suggested to be a possible way to produce the excitonic qubit entanglement[5]. Here, we show that, being strongly coupled to the (resonator-like) cylindrical nanotube environment, the two atomic quasi-1D polaritons can be easily entangled as well, thus challenging a novel alternative approach towards quantum information transfer over centimeter-long distances. [1]L.X.Zheng et al, Proc. Nanotech 2005 (May 8-12, 2005, Anaheim, CA, USA), vol.3, p.126. [2]G.-H.Jeong et al, Phys. Rev. B68,075410(2003). [3]I.V.Bondarev and Ph.Lambin, in: Trends in Nanotubes Reasearch (NovaScience, NY, 2005); Phys. Rev. B70,035407(2004); Phys. Rev. B72,035451(2005). [4]T.Yoshie et al, Nature 432,200(2004). [5]S.Hughes, Phys. Rev. Lett.94,227402(2005). [Preview Abstract] |
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