Superconductivity in alkali metal doped fullerenes (K 3C 60): a phonon mechanism

Abstract

The nature of pairing mechanism and the superconducting state parameters of alkali metal doped fullerenes was investigated using the strong coupling theory. Doping of alkali metal ( K) in the parent compound introduces free electrons in the unfilled band of C 60. It was shown that these electrons distort the K 3C 60 lattice and yield low energy intermolecular vibrations. The developed approach properly incorporates the experimental observations on bulk modulus as well the lattice parameters. The Coulomb repulsive parameter, μ*, and the effective coupling strength, λ eff, are obtained for the intermolecular phonon frequency ω er. We then evaluated the transition temperature, T c, for the phonon frequency ω er (= 51.42 cm −1) as 6.0 K, which is lower when compared with the published data. By introducing the intramolecular phonons, ω ra, in an ad hoc way, the T c enhances from 6 to 21.1 K. The analytical results on T c allow one to visualise the relative interplay between the strength of inter- and intramolecular phonons. The approach was further applied to estimate the carbon isotope exponent and the energy gap ratio and were found to be consistent with the published data. We found that both the low frequency intermolecular and high frequency intramolecular phonons participate in the phonon mediated electron pairing, T c mainly arises from high frequency intramolecular phonons. In this article, the implications of the aforementioned analysis are discussed.