Exciton-phonon sidebands in metallic carbon nanotubes studied using semiconductor Bloch equations

Bobkin, Evgeny; Knorr, Andreas; Malić, Ermin

doi:10.1103/physrevb.85.033409

Cited by 5 publications

(3 citation statements)

References 45 publications

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“…The weaker, higherenergy feature alongside each excitonic transition has been attributed to a phonon sideband arising from the longitudinal optical phonon. This is supported by recent theoretical work by Bobkin et al 134 and earlier less denitive experimental claims. 82,110 Finally, with these facts in hand, the true armchair absorption spectrum line shape can be investigated.…”

Section: Optical Absorption and Colors Of Armchair Carbon Nanotubessupporting

confidence: 75%

Fundamental optical processes in armchair carbon nanotubes

Hároz

Duque

et al. 2013

Nanoscale

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Single-wall carbon nanotubes provide ideal model 1-D condensed matter systems in which to address fundamental questions in many-body physics, while, at the same time, they are leading candidates for building blocks in nanoscale optoelectronic circuits. Much attention has been recently paid to their optical properties, arising from 1-D excitons and phonons, which have been revealed via photoluminescence, Raman scattering, and ultrafast optical spectroscopy of semiconducting carbon nanotubes. On the contrary, dynamical properties of metallic nanotubes have been poorly explored, although they are expected to provide a novel setting for the study of electron-hole pairs in the presence of degenerate 1-D electrons. In particular, (n,n)-chirality, or armchair, metallic nanotubes are truly gapless with massless carriers, ideally suited for dynamical studies of Tomonaga-Luttinger liquids. Unfortunately, progress towards such studies has been slowed by the inherent problem of nanotube synthesis whereby both semiconducting and metallic nanotubes are produced. Here, we use post-synthesis separation methods based on density gradient ultracentrifugation and DNAbased ion-exchange chromatography to produce aqueous suspensions strongly enriched in armchair nanotubes. Through resonant Raman spectroscopy of the radial breathing mode phonons, we provide macroscopic and unambiguous evidence that density gradient ultracentrifugation can enrich armchair nanotubes. Furthermore, using conventional, optical absorption spectroscopy in the nearinfrared and visible range, we show that interband absorption in armchair nanotubes is strongly excitonic. Lastly, by examining the G-band mode in Raman spectra, we determine that observation of the broad, lower frequency (G − ) feature is a result of resonance with non-armchair "metallic" nanotubes. These findings regarding the fundamental optical absorption and scattering processes in metallic carbon nanotubes lay the foundation for further spectroscopic studies to probe many-body physical phenomena in one dimension.

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Section: Optical Absorption and Colors Of Armchair Carbon Nanotubessupporting

confidence: 75%

Fundamental optical processes in armchair carbon nanotubes

Hároz

Duque

et al. 2013

Nanoscale

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“…While further refinements will be important, as presented our fifth-order model addresses the shortcomings of the molecular approach and that of Moura et al by accounting for excitons as discrete states and in providing a physical origin for the observed asymmetries that may be applied generally for both metallic and semiconducting SWCNTs. Such generality further supports the assignment of the absorption sideband in armchair SWCNTs as a K-momentum phonon sideband 20,38,39,46 . This picture provides predictive capability for understanding relative differences in REP asymmetries that may be found for different phonons (RBM, TO, LO), which is the subject of ongoing work.…”

Section: Fifth-order Raman Processesmentioning

confidence: 54%

Asymmetric excitation profiles in the resonance Raman response of armchair carbon nanotubes

et al. 2015

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We performed tunable resonance Raman spectroscopy on samples highly enriched in the (5,5), (6,6), (7,7), and (8,8) armchair structures of metallic single-wall carbon nanotubes. We present Raman excitation profiles (REPs) for both the radial breathing mode and G-band phonons of these species. G-band excitation profiles are shown to resolve the expected incoming and outgoing resonances of the scattering process. Notably, the profiles are highly asymmetric, with the higherenergy outgoing resonance weaker than the incoming resonance. These results are comparable to the asymmetric excitation profiles observed previously in semiconducting nanotubes, introduce a new electronic type, and broaden the structural range over which the asymmetry is found to exist. Modeling of the behavior with a third-order quantum model that accounts for the k -dependence in energies and matrix elements, without including excitonic effects, is found to be insufficient for reproducing the observed asymmetry. We introduce an alternative fifth-order model in which the REP asymmetry arises from quantum interference introduced by phonon-mediated state-mixing between the E M 11 and K-momentum excitons. Such state-mixing effectively introduces a nuclear coordinate dependence in the transition dipole moment and thus may be viewed as a non-Condon effect from a molecular perspective. This result unifies a molecular-like picture of nanotube transitions (introduced by their excitonic nature) with a condensed matter approach for describing their behavior.

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“…The phonon population n α q follows the Bose-Einstein statistics. We solve the coupled system of differential equations (B1)-(B3) by Fourier transformation considering non-Markovian processes 40 . Inserting the phonon-assisted polarizations in Eq.…”

Section: Appendix B: Computation Of the Inhomogeneous Broadened Spectrummentioning

confidence: 99%

Phonon Sidebands in Monolayer Transition Metal Dichalcogenides

et al. 2017

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Excitons dominate the optical properties of monolayer transition metal dichalcogenides (TMDs). Besides optically accessible bright exciton states, TMDs exhibit also a multitude of optically forbidden dark excitons. Here, we show that efficient exciton-phonon scattering couples bright and dark states and gives rise to an asymmetric excitonic line shape. The observed asymmetry can be traced back to phonon-induced sidebands that are accompanied by a polaron redshift. We present a joint theory-experiment study investigating the microscopic origin of these sidebands in different TMD materials taking into account intra- and intervalley scattering channels opened by optical and acoustic phonons. The gained insights contribute to a better understanding of the optical fingerprint of these technologically promising nanomaterials.

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Exciton-phonon sidebands in metallic carbon nanotubes studied using semiconductor Bloch equations

Cited by 5 publications

References 45 publications

Fundamental optical processes in armchair carbon nanotubes

Fundamental optical processes in armchair carbon nanotubes

Asymmetric excitation profiles in the resonance Raman response of armchair carbon nanotubes

Phonon Sidebands in Monolayer Transition Metal Dichalcogenides

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