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Published: 1994

Total Pages: 195

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Interest in solid state physics naturally gravitates towards novel systems such as the copper oxide superconductors or the alkali-doped fullerenes. This paper tackles high temperature superconductivity by extension of the BCS theory for ordinary superconductors, in particular, incorporation of anharmonicity in phonon dynamics and anisotropy in electron-phonon coupling. These refinements can account for many anomalous properties of the cuprates. Phonon anharmonicity is consistent with a small isotope effect at optimal doping and a larger isotope effect in suboptimal systems. Anisotropy in the interaction, a plausible consequence of certain anharmonic models, can circumvent objections to electron-phonon coupling based on transport measurements. Such anisotropy is consistent with gap anisotropy and strong temperature dependence of Hall coefficient. In contrast to cuprates, the doped fullerenes appear understandable within the standard model of single electron band theory and BCS theory. Microscopic parameters derivable from transport and critical field measurements yield a self-consistent picture of a disordered Type-2 BCS superconductor. Isotope effects imply that superconductivity is mediated by carbon phonons opposed to alkali atom vibrations. The novel properties of the fullerenes are generally traceable to their microscopic heterogeneity, being a collection of tightly bound but weakly overlapping molecules. Separation of electronic regimes into weak intermolecular overlap and strong carbon-carbon on-ball bonds yields a superconductor with both a large density of states and a high phonon frequency, properties consistent with a relatively high {Tc}. Disordered nature of intermolecular overlap produces a large residual resistivity and a universal dependence to the Hall coefficient. This disorder is also consistent with the anomalously large carbon isotope effect for heterogeneous isotopic substitution.