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Non-magnetic tight binding disorder effects in the $γ$ sheet of $Sr_2RuO_4$

Inspired by the physics of the Miyake - Narikiyo model (MN) for superconductivity in the γ sheet of $Sr_2RuO_4$ 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.