A NONLINEAR MINIMIZATION CALCULATION OF THE RENORMALIZED FREQUENCY w IN DIRTY d-WAVE SUPERCONDUCTORS Page No: 4765-4772

By: Pedro Contreras and Juan Moreno

Keywords: Nonlinear minimization algorithm, fixed-point routine, HTS dirty d-wave superconductors, self-consistent frequency, quasi-particle lifetime, superconducting density of states

Abstract: This work performs a comparative numerical study of the impurity average self-frequency w in an unconventional superconducting alloy with non-magnetic impurities. Two methods are used: the Levenberg-Marquardt algorithm as a nonlinear minimization problem, and a fixed-point iteration procedure. The unconventional superconducting renormalized by impurities w is a self-consistent complex nonlinear equation with two varying parameters: the impurity concentration ?+ and the strength of the impurities c, for which its numerical solution is a computational challenge. This study uses an order parameter that corresponds to the high-temperature superconducting ceramics (HTS) with a wellestablished gap symmetry. The results reveal the computational efficiency of the non-linear minimization technique by improving the calculations of the w computation when using a two-dimensional parameter space (?+, c), particularly in the unitary regime, where the imaginary part of w is a complicated expression of those parameters; this allows to enhance the study of the universal behavior of this particular quantum mechanical state.



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