Tmk

yielding an unreasonably short mean free path i of 1-3 A at room temperature for film samples. A value as small as I = 0.63 A has been quoted for Rb3C60 at 525 K based on thin-film samples with a grain size of ~1 /urn

[14.8]. Such a small I value is less than the nearest-neighbor carbon-carbon distance and much less than the distance between adjacent CM molecules. From the lattice constant of 14.24 A and assuming three electrons per CgQ anion, a carrier density of 4.1xl021/cm3 is obtained, implying kF = (ir2«)1/3 — 3.4 x 107 cm-1 on the basis of a nearly free electron model. More detailed calculations yield even lower estimates for kF (e.g., 1.8 x 107 cm-1

[14.9]). The short mean free path thus yields lkF < 1, which implies a breakdown in the one-electron band picture, and further implies that the carriers are strongly localized. In such a case we should then write the electrical conductivity as o- = crDrude + A a (14.2)

where Act is given by localization theory [14.46]. Some authors have identified the apparent short mean free path with a strong reflection of electron waves at the crystallite boundaries (the intermolecular distance), so that the electrons move freely within a crystallite (e.g., a single molecule) but the transmission probability of an electron to a neighboring crystallite (or molecule) is small. As mentioned above, the physical mechanism for the intermolecular scattering is likely the merohedral disorder discussed above. The short mean free path suggests that the normal state of K3C60 might be highly correlated (for instance, due to strong electron-electron interactions and localization effects), so that use of the Boltzmann theory is invalid. The merohedral disorder mechanism is also consistent with an enhanced role for electron-electron interactions in a highly correlated electronic system. In a disordered system, electron-electron interactions play a more important role due to localization effects. An independent estimate of i can then be obtained by comparing experimental p(T) results with predictions based on localization theory. Through such an analysis, an electron mean free path of 10-20 A is estimated for the conduction electrons in K3C50 [14.16], which is of similar magnitude to that obtained for high-quality single-crystal samples [14.17], consistent with a merohedral disorder mechanism. Near Tc, superconducting fluctuations are observed in K3Cfi0 in both single crystals and thin films, and the results for K3C60 film samples are in good agreement with the fluctuation-induced tunneling model of Sheng [14.47],

14.1.3. Alkaline Earth-Doped C60

The dependence of the resistivity on dopant concentration appears to be more complex in the alkaline earth compounds than for the alkali metal dopants for several reasons: the divalence of the alkaline earth ions, their small physical size, and the variety of crystal structures which they exhibit in the solid state. Thus far, special attention has been given to the depen dence of the transport properties on stoichiometry, and explicit measurements are available for Ca, Sr, and Ba doping. For example, plots similar to those in Fig. 14.2 show that Sr addition to C60 gives rise to resistivity minima at x = 2 and 5, and maxima at x = 3 and 6.5, as shown in Fig. 14.4. Similar transport results were obtained with the other alkaline earths [14.48,49], and results for the stoichiometrics for the minimum and maximum resistivities are given in Table 14.2, together with the corresponding activation energies for Sr^C60, CaxC60, and Ba_,.C60 at the listed resistivity extrema. Referring to Fig. 14.4, two minima in the resistivity are observed in SrxC60 with increasing x, as well as two maxima. The first minimum in p(x) occurs at *min ~ 2 for both Sr^C60 and Ca^Qo, corresponding to the occupation of all the tetrahedral sites with alkaline earth dopants; both the resistivities and activation energies are relatively high at Pmini- Upon further addition of alkaline earth dopant, the tiu bands become filled at x = 3, corresponding to two electrons transferred to the C60 anion per alkaline earth ion. Further addition of Sr and Ca results in occupation of the tlg bands (see Fig. 12.2). At the stoichiometries x — 5, a second minimum in resistivity pmjn2 is observed, corresponding to much lower values of both resistivity and activation energy (see Table 14.2) and implying an approximately half filled tlg band [14.50,51], At higher doping levels, it is believed that somewhat less than two electrons per alka-

Fig. 14.4. The resistivity and the activation energy of the conductivity of an annealed Sr^C^ film 190 A thick at 60°C in ultrahigh vacuum (UHV) as a function of x. The stoichiometry was determined by use of a quartz crystal microbalance and ex situ RBS (Rutherford backscattering) measurements [14.48],

Fig. 14.4. The resistivity and the activation energy of the conductivity of an annealed Sr^C^ film 190 A thick at 60°C in ultrahigh vacuum (UHV) as a function of x. The stoichiometry was determined by use of a quartz crystal microbalance and ex situ RBS (Rutherford backscattering) measurements [14.48],

Table 14.2

Summary of transport data for alkaline earth-doped fullerenes M,Cm [14.48,49],

Table 14.2

Summary of transport data for alkaline earth-doped fullerenes M,Cm [14.48,49],

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