Direct Observation of Born−Oppenheimer Approximation Breakdown in Carbon Nanotubes

Bushmaker, Adam; Deshpande, Vikram V.; Hsieh, Scott; Bockrath, Marc; Cronin, Stephen B.

doi:10.1021/nl802854x

Cited by 43 publications

(57 citation statements)

References 34 publications

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“…Figure 4͑e͒ shows that a zigzag SWNT has only the G − peak and thus only the LO phonon softening appears by changing E F , experimentally. Brown et al 22 and others 23,24 pointed out that asymmetric line-shape appears in the G − -band Raman spectrum for metallic tubes, which is related to the Fano resonance ͑Breit-Wigner-Fano͒ lines. However it should be pointed out that the present calculation does not consider the interaction of the phonon with the continuum state, which will be studied in a future work.…”

Section: ͑1͒mentioning

confidence: 95%

Fermi energy dependence of theG-band resonance Raman spectra of single-wall carbon nanotubes

et al. 2009

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The Fermi energy dependence of the G-band resonance Raman spectra of single-wall carbon nanotubes ͑SWNTs͒ is calculated, including the Kohn anomaly effect for metallic tubes. The gate voltage dependence of the G-band Raman spectra for SWNTs shows chirality-dependent G + / G − spectra, reflecting their dependence on the eigenvector direction of the optical ͑LO and TO͒ phonon modes and the nanotube chirality. The G-band Raman spectra of single-wall carbon nanotubes ͑SWNTs͒ arise from the first-order, one-phonon, and intravalley G-band Raman-scattering processes, 1,2 which have been widely utilized for characterizing SWNTs and graphene. The G-band spectra of a SWNT consist of a higher-frequency peak ͑G + ͒ near 1580ϳ 1590 cm −1 and a lower-frequency peak ͑G − ͒ in the range 1550ϳ 1570 cm −1 . For semiconducting tubes ͑S-SWNT͒, the G + and G − peaks can be assigned to longitudinal-optical ͑LO͒ and transverseoptical ͑TO͒ phonon modes, respectively, while the G + and G − peaks of metallic tubes ͑M-SWNTs͒ are assigned to TO and LO phonon modes, respectively, because of the Kohn anomaly ͑KA͒ effect for phonons at the ⌫ point. [3][4][5][6][7][8] For the KA effect, the self-energy correction to the LO and TO phonon modes by the virtual excitation of an electron-hole pair causes a softening and a hardening of the LO and TO phonon frequencies, respectively. [7][8][9] Recently Nguyen et al. 7 and Farhat et al. 8 observed the Fermi energy ͑E F ͒ dependence of the phonon-softening effect of SWNTs by using an electrochemical gate, and their results clearly show that the LO phonon mode softens as a function of E F . Thus the E F -dependent Raman spectra measurement is important for SWNT field effect transistor operation. However, the observed G-band Raman spectra of an individual SWNT show an anomalous behavior depending on the chirality ͑n , m͒ of a SWNT, 10 caused in part by the dependence of the relative intensity of the Raman G + to G − -band features ͑I G + / I G −͒ on the chirality and diameter. 11 For S-SWNTs, the G + peak is dominant at the zigzag chiral angle ͑ =0°͒, while both the G + and G − peaks appear at other chiral angles ͑0°Ͻ Ͻ 30°͒. It has been known that the k-dependent electron-phonon ͑el-ph͒ interaction gives rise to the chirality dependence of both the G-band ͑Refs. 9 and 12͒ and radial breathing mode ͑RBM͒ ͑Ref. 12͒ Raman intensities. Thus the G-band spectral analysis is still not well understood, even though the G band has been studied for many years. In this Rapid Communication, resonance Raman spectra of SWNTs as a function of E F are calculated in order to understand and interpret the chirality and E F -dependent G-band spectra. We show here that the k-dependent el-ph interaction affects both the I G + / I G − relative Raman intensity and their spectral widths.The self-energy corrections to the G-band phonon frequencies due to the KA affect not only the LO mode but also the TO mode, and both the LO and TO phonon frequencies depend on the chiral angle . The G-band Raman intensity I is calculated as a f...

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Section: ͑1͒mentioning

confidence: 95%

Fermi energy dependence of theG-band resonance Raman spectra of single-wall carbon nanotubes

et al. 2009

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“…Recently, the ability to fabricate ultra-clean, nearly defect-free, suspended single wall carbon nanotubes (SWNTs) has been developed [1][2][3] . This has allowed scientists to study many interesting physical phenomena such as negative differential conductance (NDC) 4 , breakdown of the BornOppenheimer approximation 5 , Wigner crystallization 6 , Raman intensity modulation 7 , and Mott insulator behavior 2,7 . Because of their one-dimensional nature, pristine, defect-free SWNTs provide an excellent experimental platform to study the exotic physical phenomena of onedimensional systems.…”

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confidence: 99%

“…Time dependent density functional theory (DFT) calculations predict a breakdown of the Born-Oppenheimer approximation 15,16 , which leads to the non-adiabatic Kohn anomaly 17 . In the non-adiabatic KA regime, the gate voltage (V g ) dependence of the G -phonon frequency follows a W shape profile 15 , which provides a signature of the non-adiabatic behavior 17,18 . This phenomenon has been investigated previously, both in carbon nanotubes and graphene, using…”

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confidence: 99%

“…Raman spectroscopy 13,[18][19][20] . It is not surprising that the Born-Oppenheimer approximation breaks down in carbon nanotubes, given the fast vibrational motion of their tightly bound carbon atoms (0.02ps) and long electron lifetimes (0.2-3.0ps) 21 .…”

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confidence: 99%

“…In these previous studies, the nanotubes were lying on a substrate and had undergone lithographic processing, which may induce defects and surface contaminants. In fact, clear non-adiabatic effects have only been observed in ultra-clean, nearly-defect free, suspended carbon nanotubes 5 . This is a testament to the acute sensitivity of this one-dimensional system to perturbations from substrate interactions and surface contaminants.…”

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confidence: 99%

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