Phonon-induced dephasing in single-wall carbon nanotubes

Abstract

International audienceWe report on original nonlinear spectral hole-burning experiments in ensembles of single-wall carbon nanotubes. We have measured the temperature dependence of the excitonic homogeneous linewidth from 5 K up to room temperature. We show that the phonon-induced broadening in the weak coupling regime predominantly consists in pure dephasing. We present theoretical calculations of the exciton scattering rate due to phonon absorption within a one-dimensional framework for both excitons and phonons. We obtain a fair agreement with our experimental data and we discuss the specific properties of the exciton-phonon coupling in single-wall carbon nanotubes

Exciton scattering from impurities and acoustic phonons in carbon nanotubes

“…Lines and symbols denote calculated and experimental results, respectively. Chiral indices of the used nanotubes are (9, 8) (solid lines and triangles 26 ), (10, 3) (dashed lines and squares 25 ), and (6, 5) (dotted lines and crosses 24 ) and those for the circles 27 are not assigned where the theoretical results are calculated in the lowest-order effective-mass scheme with the corresponding tube diameters and chiral angles. For the experiments, the originally estimated values of i are chosen as the origins of the energy broadening, which are 2.5 (triangles), 1.4 (squares), 2.45 (crosses), and 6.9 (circles) meV.…”

“…For p i , effects of the impurity scattering on p can be taken into account by introducing the imaginary part of the exciton energy of −i i /2, i.e., by setting l = i in Eq. (27). The observable energy broadening of the exciton peaks corresponds to the energy broadening at the band edges for k c ≈ 0 since the wave vectors of light are negligibly small as compared to the reciprocal lattice vectors.…”

“…4, the temperature dependence of the observable energy broadening of the ground-state exciton due to scattering from the acoustic phonons is shown for calculations with the use of Eq. (27) by setting (a) l = i and (b) l = p . The coupling constants are chosen as g 1 = 25 eV and g 2 = 1,2, and 3 eV.…”

“…The temperature dependencies of the transition rate or energy broadening for excitons near band edges are monotonically increasing functions, which have been attributed to scattering from acoustic phonons around the point and analyzed by using linear functions, sometimes plus the Bose-Einstein distribution with a constant phonon frequency. [24][25][26][27] Recent experiments on the exciton-acousticphonon scattering using nanotubes with an almost unique chirality 24 or single isolated nanotubes 25,26 are suitable to quantitative comparison between experiments and theories.…”

“…So far, many theoretical studies on this subject have been reported which include, for example, excitons trapped by impurity potentials, 15,16 phonon side bands for exciton peaks in optical spectra, 17 the interaction of excitons with acoustic and optical phonons in zigzag nanotubes, 18 and the chirality dependence of the Raman scattering intensity for the breathing-mode phonons. 19,20 Experimentally, transition rates, [21][22][23][24] the linewidth of exciton peaks, [25][26][27] and diffusion constants and diffusion lengths [28][29][30][31][32][33][34][35] have been intensively studied for excitons interacting with disorders and phonons in nanotubes. The results strongly depend on the experiments.…”