Coexistence of Magnetism, Stripes and Superconductivity in the 2-dim Hubbard-Model

In this study the Hubbard Model is investigated up to a system of 12 x 12 lattice sites. This study shows that antiferromagnetismus, stripes and superconductivity can coexist together in the doped case. The approach is new, a diagrammatic selfconsistent Feynman Approch. In this study the graphs selfconsitent up to second order in irreducible selfenergy, where the symmetry is broken in charge, spin and superconductivity (Nambu Formalism). The self-consistent dynamical Nambu approach reveals a short-range anisotropic pairing state associated with the charge stripes. The anomalous pairing function is predominantly localized within the stripes, with a larger delocalization along the stripe direction than perpendicular to it. Furthermore, the pairing correlations on the two parallel stripes exhibit the same phase, indicating a phase-aligned inter-stripe coupling. The symmetry of the superconducting phase is a mix of s-wave and d-wave. The ratio (d/s)-wave is (1/2). The coherence length parallel to the stripe has nearly the same quantity than vertical to it 8. That means the superconducting phase is as large as the lattice size. The stripes are not independent in superconductivity. In this study the transition temerature can be calculated. So the complete set of correlation functions, single particle density of states are presented. The result is checked on a 4 x 4 Hubbard Cluster, where exact results are possible by Lanczos Diagonalization. With more CPU-power larger clusters are possible to determine, and it is in principle possible to determine the transition temerature in a Emery Model. So one could make a phase diagramm for every U. It is possible to calculate transition temerature depending on the hole concentration.