Fluctuating Cu-O-Cu bond model of high-temperature superconductivity

Twenty years of research have yet to produce a consensus on the origin of high-temperature superconductivity (HTS). However, several generic characteristics of the copper oxide superconductors have emerged as the essential ingredients of and/or constraints on any viable microscopic model of HTS. Besides a critical temperature T-c of the order of 100 K, they include a d-wave superconducting gap with Fermi liquid nodal excitations, a pseudogap with d-symmetry and the characteristic temperature scale T*, an anomalous doping-dependent oxygen isotope shift, nanometre-scale gap inhomogeneity and so on. The isotope shift implies a key role for oxygen vibrations, but conventional Bardeen - Cooper - Schrieffer single-phonon coupling is essentially forbidden by symmetry and by the on-site Coulomb interaction U. Here we invoke the nonlinear modulation of the Cu - Cu bond by planar oxygen vibrations. The Fermi liquid nature of the d-wave superconducting ground state supports a weak-coupling treatment of this modulation. The dominant fluctuations are manifested in a pattern of oxygen vibrational square amplitudes with quadrupolar symmetry around a given Cu site. On the basis of such bond fluctuations, both dynamic and static, we can understand the salient features of HTS.