DYNAMIC SUSCEPTIBILITY AND PHONON ANOMALIES IN THE BILAYER T-J

We consider a bilayer version of the extended t-J model, with a view t o computing the form of certain experimentally observable properties. Using the slave-boson decomposition, we show at the mean-field level t hat in the bilayer system the existence of in-plane d-wave singlet pai ring excludes any interplane singlet order for reasonable values of th e interplane superexchange parameter. Restricting the analysis to the regime of no interplane singlet pairing, we deduce parameter sets repr oducing the Fermi surfaces of YBCO- and BSCCO-like bilayer systems. Fr om these we calculate the form of the dynamic susceptibility X(q, omeg a) in both systems, and of the anomalies in frequency and linewidth of selected phonon modes in YBCO. We compare the results with experiment , and discuss the features which differ from the single-layer case.