Theory of the high-temperature superconductors

Abstract

The new high-temperature superconductors are poorly metallic, but close to a Mott metal-insulator transition. This incipient Mott transition shows up as a tendency towards a charge-density-wave instability, with wave vectors appropriate for Fermi-surface nesting. Pure La2CuO4 indeed forms a charge-density wave commensurate with the lattice, and suffers a structural transition to a non-metallic state. In the new superconducting materials, we demonstrate that the incipient instability drastically softens the plasmon modes for wave vectors close to the nesting condition. Such soft plasmons may have been seen in some recent experiments. Although these modes have much lower frequencies than ordinary plasmons, they are still much higher than typical phonon frequencies. They couple strongly to conduction electrons and, like phonons, induce an electron-electron attraction. Moreover, the soft-plasmon wave vectors automatically connect points on the Fermi surface, as required for Cooper pairing. Thus the Debye-energy prefactor in the BCS expression for the transition temperature is replaced by the considerably larger plasmon energy, while the strength of the interaction will ensure that the exponential factor is not too small. Note that this mechanism will yield no isotope effect. We suggest that the Ba or La f-orbitals play an important role in strengthening the electron-plasmon coupling and softening the plasma modes. Hence the presence of Ba or La seems to be favourable for high-temperature superconductivity.