Inspired by the studies on the influence of transition metal impurities in high Tc superconductors and what is already known about nonmagnetic suppression of T c in unconventional superconductors, we set out to investigate the behavior of the nonmagnetic disordered elastic scattering for a realistic 2D anisotropic high T c superconductor with line nodes and a Fermi surface in the tight-binding approximation. For this purpose, we performed a detailed self-consistent 2D numerical study of the disordered averaged scattering matrix with nonmagnetic impurities and a singlet line nodes order parameter, varying the concentration and the strength of the impurities potential in the Born, intermediate and unitary limits. In a high T c anisotropic superconductor with a tight binding dispersion law averaging over the Fermi surface, including hopping parameters and an order parameter in agreement with experimental data, the tight-binding approximation reflects the anisotropic effects. In this study, we also included a detailed visualization of the behavior of the scattering matrix with different sets of physical parameters involved in the nonmagnetic disorder, which allowed us to model the dressed scattering behavior in different regimes for very low and high energies. With this study, we demonstrate that the scattering elastic matrix is affected by the non-magnetic disorder, as well as the importance of an order parameter and a Fermi surface in agreement with experiments when studying this effect in unconventional superconductors.

Inspired by the physics of the Miyake - Narikiyo model (MN) for superconductivity in the γ sheet of Sr2RuO4, we set out to investigate numerically the behavior caused by a non-magnetic disorder in the imaginary part of the elastic scattering matrix for an anisotropic tight-binding model. We perform simulations by going from the Unitary to the Born scattering limit, varying the parameter c which is inverse to the strength of the impurity potential. It is found that the unitary and intermedia limits persist for different orders of magnitude in simulating the disorder concentration. Subsequently and in order to find the MN tiny gap, we perform a numerical study of the unitary limit as a function of disorder concentration, to find the tiny anomalous gap.

We compare the quasiparticle lifetime behavior in the unitary limit of two unconventional superconductors dressed by nonmagnetic impurity scattering to differentiate an anomalous functional behavior in its shape when the disorder concentration is changed in a triplet paired model with respect to the well behave singlet model. For singlet paired superconductors, the functional shape of the lifetime due to elastic scattering around the nodal regions in the reduced elastic scattering space, does not change with the disorder concentration, but for a triplet model with a tiny gap, an anomalous drop in shape is observed only when small values of disordering are added. We use a 2D tight-binding parametrization to study the reduced phase space of the first Brillouin zone, where the low-energy scattering is restricted to the nodal/quasinodal regions for two irreducible representations of the crystal lattice. A new class of Wigner probabilistic distribution functions is discussed for triplet superconductors.

We perform a numerical study of the unitary regime as a function of disorder concentration in the imaginary part of the elastic scattering cross-section for the compound Sr2RuO4 in the flat band non-disperse limit. By using a self-consistent tight binding (TB) method, we find a couple of families of Wigner probabilistic functions that help to explain macroscopically the distribution between Fermion dressed quasiparticles and Cooper pairs, and also the position of nodes in the order parameter for Sr2RuO4. Therefore, we are able to show that a TB model for the FS γ-sheet, numerically shows 4 point nodes in a flat γ sheet limit, or 4 quasi-point nodes for strong dispersion γ sheet limit in the reduced phase scattering space (RPS).

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