Molecular-orbital basis for superconductivity in high- and low-dimensional metals

Abstract A real-space molecular-orbital description of electronic wave functions which are postulated to be the precursors of the superconducting state in high- and low-dimensional metals is presented, based on self-consistent X-alpha scattered-wave (SCF-Xα-SW) molecular-orbital calculations for clusters representing the local molecular environments in these materials. It is shown that there is a persistent correlation between the occurrence of superconductivity in a material and the existence of spatially delocalized molecular orbitals at the Fermi energy which are bonding within and anti-bonding between “layers” or “tubes” of overlapping atomic orbitals that span many atoms, forming a type of “electron network” at the Fermi energy, as exemplified by pπ “layered” molecular-orbital topologies in Al and (TMTSF)2PF6, and by dδ “tubular” molecular-orbital topologies in Nb and Nb3Sn. This description of the precursor superconducting state is consistent with the original conjectures of London that the superconducting-state wave function is “molecular” in nature, “rigid” in character, and of wide spatial extent, from which observed physical properties (e.g., diamagnetism and nondissipative electrical currents) of the superconducting state logically follow. The molecular-orbital model is further shown to be consistent with Cooper's concept of electron pairing in the superconducting state through a net attractive electron-electron interaction but differs from the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity in attributing the pairing to “valence-bond-like” electron occupation of the layered or tubular molecular orbitals at the Fermi energy, coupled with lattice ion displacements through a dynamic Jahn-Teller effect, rather than to the absorption and emission of virtual phonons. However, recent simple physical arguments presented by Weisskopf for the formation of Cooper pairs suggest that the two points of view are not incompatible. Approximate formulae for calculating the electron pair binding energy and superconducting transition temperature, analogous to the BCS formulae but expressed entirely in terms of two simple molecular-orbital parameters, are derived and applied to various superconductors. Moreover, through an elementary phase-space argument, the molecular-orbital description of Cooper pairs is shown to be qualitatively consistent with Schafroth's description of electron pairs as “quasi-molecules” undergoing Bose-Einstein-like condensation to the superconducting state. The above molecular-orbital criteria for superconductivity are diametrical to those for the occurrence of local magnetic moments and ferromagnetism, namely, the existence of spatially localized, exclusively antibonding (e.g., d σ ∗ , d π ∗ , or d δ ∗ ) molecuar orbitals at the Fermi energy. Furthermore, in contrast to the ordering of electron spins on atomic sublattices in conventional antiferromagnetism, the valence-bond-like correlation of Cooper-Schafroth electron pairs at the Fermi energy in composite bonding-antibonding layered or tubular molecular-orbital components, spatially delocalized between the atoms, corresponds to a type of conduction-electron “antiferromagnetism” or spin-density wave, thus offering an explanation for the occurrence of such antiferromagnetism in superconductors such as (TMTSF)2PF6 and Nb3Sn. These molecular-orbital criteria therefore provide a conceptual basis for understanding the generally mutually exclusive incidence of superconductivity and magnetism among the elements of the Periodic Table, although they can also be used to explain the occasional coexistence of superconductivity and ferromagnetism or antiferromagnetism in some materials. The molecular-orbital model for superconductivity complements BCS theory in that it permits the prediction of which materials are likely to be superconductors and which are not, entirely on the basis of the molecular-orbital topology at the Fermi energy. It offers an explanation of the vanishing isotope effect in certain superconductors. It contributes to the clarification of the issue of non-phonon mechanisms of superconductivity. It provides insight into the correlations of superconductivity with other physical properties, such as lattice instabilities. It is readily applicable to superconductors lacking long-range crystalline order, such as amorphous alloys and small particles. Finally, the molecular-orbital approach can be used to explain in simple terms why some materials (e.g., Cu, Ag, and Au) are neither superconducting nor magnetic, why certain quasi-one-dimensional organic solids, such as TTF-TCNQ, are not superconductors while others, such as (TMTSF)2PF6, are superconductors, and to assess critically the likelihood of superconductivity in certain other types of substances (e.g., other types of organic solids; metallic hydrogen at attainable high pressures), and to suggest ways of systematically improving existing classes or synthesizing novel classes of superconducting materials.