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I present results from an approach that extends the Eliashberg theory by systematic expansion in the vertex function; an essential extension at large phonon frequencies, even for weak coupling. In order to deal with computationally expensive double sums over momenta, a dynamical cluster approximation (DCA) approach is used to incorporate momentum dependence into the Eliashberg equations. First, I consider the effects of introducing partial momentum dependence on the standard Eliashberg theory using a quasi-local approximation; which I use to demonstrate that it is essential to include corrections beyond the standard theory when investigating d-wave states. Using the extended theory with vertex corrections, I compute electron and phonon spectral functions. A kink in the electronic dispersion is found in the normal state along the major symmetry directions, similar to that found in photo-emission from cuprates. The phonon spectral function shows that for weak coupling $Wlambda < omega_0$, the dispersion for phonons has weak momentum dependence, with consequences for the theory of optical phonon mediated d-wave superconductivity, which is shown to be 2nd order in $lambda$. In particular, examination of the order parameter vs. filling shows that vertex corrections lead to d-wave superconductivity mediated via simple optical phonons. I map out the order parameters in detail, showing that there is significant induced anisotropy in the superconducting pairing in quasi-2D systems.
We review the intermediate coupling model for treating electronic correlations in the cuprates. Spectral signatures of the intermediate coupling scenario are identified and used to adduce that the cuprates fall in the intermediate rather than the wea
We present a combined density-functional-perturbation-theory and inelastic neutron scattering study of the lattice dynamical properties of YNi2B2C. In general, very good agreement was found between theory and experiment for both phonon energies and l
We demonstrate that many features ascribed to strong correlation effects in various spectroscopies of the cuprates are captured by a calculation of the self-energy incorporating effects of spin and charge fluctuations. The self energy is calculated o
We apply the new-generation ARPES methodology to the most widely studied cuprate superconductor YBCO. Considering the nodal direction, we found noticeable renormalization effects known as kinks both in the quasiparticle dispersion and scattering rate
We have determined the electron-coupling spectrum of superconducting Bi2Sr2CaCu2O8+d from high-resolution angle-resolved photoemission spectra by two deconvolution-free robust methods. As hole concentration decreases, the coupling spectral weight at