Quantum mechanical picture of the coupling between interlayer electronic   excitations and infrared active phonons in bilayer cuprate superconductors
  The formula frequently used to describe the c-axis infrared response of the coupled electron-phonon system of bilayer cuprate superconductors and providing important insights into the physics of these materials has been originally obtained at the level of the phenomenological multilayer model. Here we derive it using diagrammatic perturbation theory. 
Jiri Vasatko and Dominik Munzar
cond-mat.supr-con