Theory for the excitation spectrum of High-T$_c superconductors : quasiparticle dispersion and shadows of the Fermi surface

Abstract

Using a new method for the solution of the FLEX-equations, which allows the determination of the self energy $Σ_{\bf k}(ω)$ of the $2D$ Hubbard model on the real frequency axis, we calculate the doping dependence of the quasi-particle excitations of High-T$_c$ superconductors. We obtain new results for the shadows of the Fermi surface, their dependence on the deformation of the quasi particle dispersion, an anomalous $ω$-dependence of ${\rm Im}Σ_{\bf k}(ω)$ and a related violation of the Luttinger theorem. This sheds new light on the influence of short range magnetic order on the low energy excitations and its significance for photoemission experiments.