Effect of nonlinearity, magnetic and nonmagnetic impurities, and spin-orbit scattering on the nonlocal microwave response of a d-wave superconductor

Abstract

By using linear response theory the low-temperature microwave response of a nonlocal and nonlinear d-wave superconductor with magnetic and nonmagnetic impurities is calculated. We will show that for the local, linear, and pure sample, penetration depth, ∆λ(T), and conductivity, ∆σ1(T), vary linearly with temperature, consequently the resistance, ∆R(T), would change linearly with temperature in agreement with experimental results and for the nonlocal, nonlinear sample the linear temperature dependences ∆R(T) change to quadratic function. For impure samples the nonlocality and nonlinearity effects are completely hidden by impurities and the temperature dependences ∆λ(T) and ∆σ1(T) are determined by temperature interval namely the ranges of T < T* and T* << T << Tc which T* is determined by nonmagnetic impurity concentration and the strength of impurity scattering. For T < T* , ∆R(T) varies as T2, on the other hand for, T* << T << Tc, ∆R(T) varies linearly with temperature. We will also show that the temperature dependence of surface resistance is unaffected by spin-orbit interaction and magnetic impurities.