Universal non-resonant absorption in carbon nanotubes

Abstract : Photoluminescence excitation measurements in semi-conducting carbon nanotubes show a systematic non-resonant contribution between the well known excitonic resonances. Using a global analysis method, we were able to delineate the contribution of each chiral species including its tiny non-resonant component. By comparison with the recently reported excitonic absorption cross-section on the S22 resonance, we found a universal non-resonant absorbance which turns out to be of the order of one half of that of an equivalent graphene sheet. This value as well as the absorption line-shape in the non-resonant window is in excellent agreement with microscopic calculations based on the density matrix formalism. This non-resonant absorption of semi-conducting nanotubes is essentially frequency independent over 0.5 eV wide windows and reaches approximately the same value betweeen the S11 and S22 resonances or between the S22 and S33 resonances. In addition, the non-resonant absorption cross-section turns out to be the same for all the chiral species we measured in this study. From a practical point of view, this study puts firm basis on the sample content analysis based on photoluminescence studies by targeting specific excitation wavelengths that lead to almost uniform excitation of all the chiral species of a sample within a given diameter range. In contrast to graphene, single-wall carbon nanotubes (SWNTs) show marked resonances in their optical spectrum that primarily reflect the one-dimensional quantum confinement of carriers. These resonances that combine one-dimensional and excitonic characteristics have been extensively investigated and are widely used as finger prints of the (n, m) species [1]. However, spectroscopic studies reveal that the absorption of nanotubes does not vanish between resonances and consists of a wealth of tiny structures, such as phonon side-bands, crossed exci-tons (S ij), or higher excitonic states [2–5]. In ensemble measurements, the non-resonant absorption is even more congested due to the contribution of residual catalyst or amorphous carbon and due to light scattering [6]. In total , a relatively smooth background showing an overall increase with photon energy is observed, from which it is challenging to extract any quantitative information. In this study, we show that thorough photolumines-cence excitation (PLE) measurements yield a much finer insight into the non-resonant absorption of carbon nan-otubes, that reveals the universal features of light-matter interaction in carbon nano-structures [7]. In particular, we show that the non-resonant absorption of SWNTs per unit area well above the S 11 or S 22 resonances reaches an universal value of 0.013±0.003 in good agreement with the value α √ 3 (where α is the fine structure constant) predicted by a simple band-to-band theory. Our study of non-resonant absorption is based on the global analysis of PLE maps of ensembles of carbon nan-otubes that allows us to deconvolute the contribution of each (n, m) species while keeping a high signal to noise
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Physical Review B : Condensed matter and materials physics, American Physical Society, 2014, 90 (15), pp.155401. 〈10.1103/PhysRevB.90.155401〉
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Fabien Vialla, Ermin Malic, Benjamin Langlois, Yannick Chassagneux, Carole Diederichs, et al.. Universal non-resonant absorption in carbon nanotubes. Physical Review B : Condensed matter and materials physics, American Physical Society, 2014, 90 (15), pp.155401. 〈10.1103/PhysRevB.90.155401〉. 〈hal-01144986〉



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