Effect of nonlinearity, magnetic and nonmagnetic impurities, and spin-orbit scattering on the nonlocal microwave response of ad-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, Δλ(T), and conductivity, Δσ1(T), vary linearly with temperature, consequently the resistance, ΔR(T), would change linearly with temperature in agreement with experimental results and for the nonlocal, nonlinear sample the linear temperature dependences ΔR(T) change to quadratic function. For impure samples the nonlocality and nonlinearity effects are completely hidden by impurities and the temperature dependences Δλ(T) and Δσ1(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*, ΔR(T) varies as T2, on the other hand for, T* ≪ T ≪ Tc, ΔR(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.