| In recent years Angle-resolved Photoemission Spectroscopy (ARPES) has uncovered ubiquitous evidence of electron-boson coupling in the cuprate family of high-temperature superconductors. This evidence comes in the form of dispersion anomalies, or "kinks", which are found to be anisotropic in strength throughout the first Brillouin zone. More recently, Scanning Tunneling Microscopy (STM) studies have found further signatures of coupling to a bosonic mode in the local density of states of Bi2Sr2CaCu2O 8+delta. Furthermore, in both types of experiment, an appreciable and unusual isotope effect has been observed which suggests that the responsible mode is related to a lattice vibration. As a result, debate has been reopened over the exact role of the electron-phonon interaction in the cuprates. This thesis sets out to examine the signatures of anisotropic electron-phonon coupling in the cuprates in a effort to better understand how this interaction is manifested in both ARPES and STM experiments. The theoretical framework for this study is existing Migdal-Eliashberg theory built upon microscopic models for electron-phonon coupling. With the presented model, ARPES and STM spectra are calculated for the specific cases of Bi2Sr2Ca2Cu3O 10+delta and Bi2Sr2CaCu2O8+delta respectively using a weak coupling limit of the Migdal-Eliashberg formalism. In the latter case, the interplay between electron-phonon coupling and local inhomogeneity and damping effects are also considered in a phenomenological way. The results are compared directly to experimental data and found to be in good agreement. Higher order processes are also considered by summing the so-called "rainbow" diagrams to infinite order using a self-consistent numerical method. In this way, renormalizations deep in the band-structure due to multi-phonon processes are examined. Finally, the material dependence of electron-phonon coupling is also considered and the implications of such dependencies on the superconducting transition temperature and electron-phonon coupling are discussed. |
