Soft plasmon theory of the new high-temperature superconductors

Abstract

The newly-discovered high-temperature superconductors are close to, but on the metallic side of, a Mott metal — insulator transition. The incipient Mott transition manifests itself as a tendency towards a charge density wave instability, characterized by wave vectors appropriate for Fermi-surface nesting. In La 2 CuO 4 , this charge-density wave is commensurate with the lattice, and leads to a structural transition to a non-metallic state. We show that in the new superconducting materials, this incipient instability causes a drastic softening of the plasmon modes at these wave vectors. Indeed, there is some experimental evidence for such soft plasmons in these materials. Although these modes have a much lower frequency than ordinary plasmons, it is still much higher than the Debye-cut-off phonon frequency. They are strongly coupled to the conduction electrons, and induce an electron - electron attraction in a way analogous to phonons. Moreover, the soft-plasmon wave vectors are automatically those required for Cooper pairing, since they connect points on the Fermi surface. The Debye-energy prefactor in the BCS expression for the transition temperature is replaced by the considerably larger plasmon energy. Furthermore the strength of the interaction will ensure that the exponential factor is not too small. Note that this mechanism will lead to zero isotope effect. We suggest that the Ba or La f-orbitals play an important role in softening these plasma modes and strengthening the electron - plasmon coupling. This would explain why the presence of Ba or La seems to be favourable for high-temperature superconductivity.