A theory of dissipative nonlinear conductivity, ${\sigma }_1(\omega ,H)$, of $s$-wave superconductors under strong electromagnetic fields at low temperatures 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 a low-frequency ($\hslash \omega \ll k_{B}T$) 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.

• Received 23 December 2013

DOI:https://doi.org/10.1103/PhysRevLett.113.087001