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Lorentzian line, which is reversible up to 15 mW of power, with a frequency downshift depending nonlinearly on the laser power. Since this effect is observed above T0i, where the molecules are rotating rapidly, and since the dependence on laser intensity is quite different from that shown in Fig. 11.21 [11.107], the physical origin of the phenomena at higher temperature may be different.

11.6. Vibrational Modes in Doped Fullerene Solids

Since the discovery of moderately high-temperature superconductivity in the alkali metal (M)-doped C60 solids MjQq (M = K, Rb), considerable activity has been expended to document the doping-induced changes in the vibrational modes of these materials and to investigate whether or not the superconducting pairing interaction is mediated by vibrational modes and, if so, by which modes. The contributions of the four distinct mode types (acoustic, librational, optic, molecular) to a vibration-mediated pairing mechanism for superconductivity have been considered both theoretically and experimentally. Insulating compositions of M^C^, such as M6C60, have also been studied for comparison to the behavior of C60 itself. Furthermore, the x ~ 1 solid solution system, which is found to be stable at elevated temperatures (T > 200°C) and has been reported to polymerize, has also been studied in Raman scattering experiments [11.19].

The availability of a variable range of alkali metal doping (0 < x < 6) presents the opportunity to consider whether or not the dopant may be treated as simply a perturbing influence on the C60-derived modes (via charge transfer between the M^ and C60 sublattices). For example, many of the Raman- and IR-active molecular modes for the stoichiometrics x ~ 1, and x ~ 6 remain reasonably sharp and are found experimentally to be related simply to the parent (x = 0) solid spectrum [11.19], The mode frequencies of these M^Qq compounds, although shifted from those in the parent C60 material, are, for fixed x, largely independent of the dopant species, dopant mass or the crystal structure [11.19], This suggests that the principal effect of alkali metal doping is to produce Qo anions (C^, where n — 1,3,4,6), which are weakly coupled to one another and also weakly coupled to the cation M+ sublattice [11.110,111],

The introduction of alkali metal dopants into the lattice also gives rise to low-frequency vibrational modes, whereby the alkali metal ions vibrate relative to the large fullerene molecules. Such modes should be accessible for investigation by Raman and infrared spectroscopy, as well as other techniques. The presence of alkali metal ions in the lattice also influences the characteristics of the intermolecular modes of C60, as discussed in §11.6.4.

11.6.1. Doping Dependence of Raman-Active Modes

This section summarizes observed doping-induced shifts in frequency of the Ag and Hg modes and use of these frequency shifts for sample characterization regarding the doping concentration.

The addition of alkali metal dopants to form the superconducting M3C60 (M = K, Rb) compounds and the alkali metal-saturated compounds M6Qo (M = Na, K, Rb, Cs) perturbs the Raman spectra only slightly relative to the solution molecular spectra and to the spectra in the undoped solid C60, as presented in Fig. 11.22, where the Raman spectra for solid C60 are shown in comparison to various MjQo and M6C60 spectra [11.3,15]. One can, in fact, identify each of the features in the M^Qq spectra with those of pristine C60, and very little change is found from one alkali metal dopant to another [11.82], The small magnitude of the perturbation of the Raman spectrum by alkali metal doping and the insensitivity of the M6C60 spectra to the specific alkali metal species indicate a very weak coupling between the C60 molecules and the M+ ions.

The Raman spectra for the M3C60 phase (M = K, Rb) in Fig. 11.22 are of particular interest. Here again, the spectra are quite similar to that of C60, except for the greater sharpness of the Ag modes in the M3C60 phases, the apparent absence in the M3C60 spectra of several of the Raman lines derived from the Hg modes in C60, and the broadening of other Hg lines. This is particularly true in the spectrum of Rb3C60, for which the same sample was shown resistively to exhibit a superconducting transition temperature of Tc ~ 28 K [11.75]. For the case of K3Q0 (see Fig. 11.23) [11.3,114] and 60 [11.88], the coupling between the phonons and a low-energy continuum strongly broadens the Hg-derived modes [11.3,76,115] and gives rise to Breit-Wigner-Fano modifications in the Raman lineshape [see Fig. 11.23 for this effect on the Hg( 1) Raman feature], which is Lorentzian for undoped Qq [11.114], As discussed in §12.7.3, the electronic structure for K3C60 and R^C^ is described in terms of a band model, while that for the 60 compounds is best described by levels for a molecular solid. Furthermore, the molecular ions in the M3C60 compounds are expected to experience a Jahn-Teller distortion while the M6C60 compounds do not (see §14.2.2 and §14.2.4). The symmetry lowering that results from the JahnTeller distortion may be a possible cause for the broadening (or splitting) of some of the degenerate vibrational modes in the M3C60 spectra. The splitting of the Hg( 1) modes for M6C60 in Fig. 11.23 is attributed to crystal field effects, which are expected to be more pronounced in MgCgo compared to CM itself because of the polarization effects of the alkali metal atoms in the M6C60 lattice. The splitting of Hg(\) into a doublet with cubic symmetries Eg+Tg for both polarization geometries HH(||, ||) and HV(||, _L) is consistent with §7.1.3.

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