Reduction of dissipative nonlinear conductivity of superconductors by static and microwave magnetic fields

A theory of dissipative nonlinear conductivity, $\sigma_1(\omega,H)$, of s-wave superconductors under strong electromagnetic fields at low temperatures and frequencies $\hbar\omega\ll k_BT$ is proposed. Closed-form expressions for $\sigma_1(H)$ and the surface resistance $R_s(\omega,H)$ are obtained in the nonequilibrium dirty limit for which $\sigma_1(H)$ has a significant minimum as a function of the amplitude of magnetic field $H$. The calculated microwave suppression of $R_s(H)$ is in good agreement with recent experiments on alloyed Nb resonator cavities. It is shown that superimposed dc and ac fields, $H=H_0+H_a\cos\omega t$, can be used to reduce ac dissipation in thin film nanostructures by tuning $\sigma_1(H_0)$ with the dc field, consistent with experiments performed in the sixties.