The superconducting instability of the Fermi-liquid state is investigated by considering anisotropic electron-boson couplings. Both electron-electron interactions and anisotropic electron-boson couplings are treated with a renormalization group method that takes into account retardation effects. Considering a noninteracting circular Fermi surface, we find analytical solutions for the flow equations and derive a set of generalized Eliashberg equations. Electron-boson couplings with different momentum dependences are studied and we find superconducting instabilities of the metallic state with competition between order parameters of different symmetries. Numerical solutions for some couplings are given to illustrate the frequency dependence of the vertices at different coupling regimes. © 2009 The American Physical Society.

The electron-electron interactions affect the low-energy excitations of an electronic system and induce deformations of the Fermi surface. These effects are especially important in anisotropic materials with strong correlations, such as copper-oxide superconductors or ruthenates. Here we analyze the deformations produced by electronic correlations in the Fermi surface of anisotropic two-dimensional systems, treating the regular and singular regions of the Fermi surface on the same footing. Simple analytical expressions are obtained for the corrections, based on local features of the Fermi surface. It is shown that, even for weak local interactions, the behavior of the self-energy is nontrivial, showing a momentum dependence and a self-consistent interplay with the Fermi surface topology. Results are compared to experimental observations and to other theoretical results. © 2006 The American Physical Society.

We analyze the deformations of the Fermi surface induced by electron-electron interactions in anisotropic two-dimensional systems. We use perturbation theory to treat, on the same footing, the regular and singular regions of the Fermi surface. It is shown that, even for weak local coupling, the self-energy presents a nontrivial behavior showing momentum dependence and interplay with the Fermi surface shape. Our scheme gives simple analytical expressions based on local features of the Fermi surface. © EDP Sciences.