Phase Fluctuations and the Role of Electron Phonon Coupling in High-T c Superconductors

Two issues, which play a key role in the present discussion of the microscopic mechanism of the pairing in high-T c superconductors are investigated, employing large-scale computing. In the first part of this paper, the single-particle density of states and the tunneling conductance are studied for a two-dimensional BCS-like Hamiltonian with a d x2-y2-gap and phase fluctuations. The latter are treated by a classical Monte Carlo simulation of an XY model. Comparison of our results with recent scanning tunneling spectra of Bi-based high-T c cuprates supports the idea that the pseudogap behavior observed in these experiments can be understood as arising from phase fluctuations of a d x2-y2 pairing gap whose amplitude forms on an energy scale set by T C MF , well above the actual superconducting transition. We then apply this phase fluctuation model to recent reflectivity measurements, which have shown a violation of the in-plane optical integral in underdoped Bi2212 up to frequencies much higher than those expected by standard BCS theory [28,30]. The sum rule violation can be related to a loss of in-plane kinetic energy. We show that the above BCS-like Hamiltonian with a d-wave gap and phase fluctuations can explain this change of in-plane kinetic energy at T c . Our model is also applicable for other superconductors where phase fluctuations should play a dominant role, i. e. with small charge carrier density like the organic superconductors. In the second part of this paper, we investigate numerically the effects of electronic correlations on the electron-phonon vertex function in the one-band Hubbard model. Our simulations are based on a new numerically exact technique to extract the vertex, which is especially important for the case of interest, i. e. strong correlations, which cannot be controlled perturbatively. The simulations are performed both on one-dimensional and two-dimensional lattices. We find that the on-site Coulomb interaction suppresses the electron-phonon coupling effectively. In particular, the backward scattering with large phonon momentum is suppressed much more than the forward scattering with small phonon momentum. With decreasing the doping density, the electron-phonon coupling is reduced at all phonon momenta. In the weak-coupling regime, our numerical simulations are in good agreement with the Feynman diagram expansions.