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Measurement of the isotope shift of the superconducting transition temperature, T sub c , was one of the classic experiments (1) that established the essential role of the electron-phonon interaction in those simple metallic superconductors that are well described by the theory of Bardeen, Cooper, and Schrieffer (BCS). In this report, we wish to examine this effect in a new light-that is, in the context of a recently proposed electronic mechanism of the superconductivity of doped fullerenes (2, 3). We demonstrate that such a mechanism can lead to an isotope effect, and the observed magnitudes of delta T sub c are consistent with microscopic estimates we make in the context of the electronic mechanism (4). Moreover, we make further predictions of the pressure and the dopant species dependence of the isotope shift that are susceptible to experimental test.
The isotope effect is conventionally characterized by an exponent x, where T sub c alpha M sup -x , where M is the mass of the isotope. Recent experiments have led to widely differing values of x, ranging from 0.3 to 1.8 in Rb-doped C sub 60 (5, 6). (It is important to note that such a power law dependence, while natural in the context of the conventional BCS theory, is not self-evident. A better characterization is the ratio delta T sub c /T sub c , where delta T sub c is the shift of the transition temperature upon isotopic substitution. For Rb sub 3 C sub 60 with T sub c = = 30 K, values of delta T sub c have been reported by different groups ranging from -0.5 to -1.5 K.) As has been already noted (5), it is difficult to obtain an x > 0.5 in the context of a conventional electron-phonon mechanism. From the discussions given in this report, it follows that on such natural upper bounds exist for the proposed electronic mechanism for the superconductivity of fullerenes.
In the proposed electronic mechanism for superconductivity in doped C sub 60 , we have computed the effective attraction, E sub p , between electrons at an average electron density of three extra (conduction) electrons per molecule. Once the strength of the attraction is determined, T sub c can be estimated in accordance...