The Fluctuating Bond Model, a Glue for Cuprate Superconductivity?

Twenty years of research have yet to produce a consensus on the origin of high temperature superconductivity (HTS). The mechanism of HTS - which originates in the CuO$_{2}$ plane, common to all HTS families - can be constrained by some key experimental facts regarding superconducting and pseudogap behaviors. Superconductivity, involving a $T_{c}$ of order $100 $K, exhibits an unusual $d$-wave superconducting gap, with Fermi liquid nodal excitations, and an anomalous doping- dependent oxygen isotope shift. A ``pseudogap,'' also with $d$-symmetry, leads to a dip in the density of states below a characteristic temperature scale $T^{\ast }$, which has a \textit{negative} isotope shift; we associate the pseudogap with the recently observed spatially inhomogeneous (nanometer- scale) C$_{4}$ symmetry breaking. The isotope shifts and other evidence imply a key role for oxygen vibrations, but conventional BCS single-phonon coupling is essentially forbidden by symmetry and by the on-site Coulomb interaction $U$. In a novel approach, we introduce a model based on a strong, local, nonlinear interaction between electrons within the Cu-O-Cu bond in the CuO$_{2}$ plane, and the oxygen vibrational degrees of freedom, termed the Fluctuating Bond Model (FBM) [D.M. Newns and C.C. Tsuei, Nature Physics \textbf {3}, 184 (2007)]. In mean field the model predicts a phase manifesting broken C$_{4}$ symmetry, with a $d$-type pseudogap, and an upper phase boundary in temperature, with a negative isotope shift, which we identify with $T^{\ast }$. An intrinsic $d$-wave pairing tendency is found, leading to a transition temperature dome and an anomalous isotope shift similar to that found experimentally. The softening in the oxygen vibrational frequency below $T_{c}$, seen in Raman and neutron spectra, has a natural explanation in the FBM. Recent \textit{ab initio} calculations have been implemented which provide microscopic support for the model.