Noise-Assisted Microwave Up-conversion by Vortices in Thin-Film Superconductors with a dc-Biased Washboard Pinning Potential

Abstract

So far the main theoretical basis for understanding and optimization of the microwave properties of vortices in type II superconductors has been relying upon the Coffey–Clem (CC) approach for the linear impedance at nonzero temperature. However, the CC model does not account for the non-linear response and the possibility to control it by changing the value of the dc transport current in a superconducting sample. For this reason, we have exactly solved the Langevin equation for the two-dimensional nonlinear vortex dynamics in a dc bias-tilted cosine pinning potential in the presence of an ac current of arbitrary amplitude and frequency ω and have, thereby, substantially generalized the CC results. In this work we analyze the behavior of the non-linear response on kω-frequency in a wide range of dc and ac current densities, ω, and temperature. The kω- response is found to depend strongly on all these parameters, as exemplified for the third-harmonic (k = 3) transformation coefficient Z3. The parametric window for the most enhanced up-conversion is presented. The predicted effects can be experimentally verified in thin-film superconductors with some pinning potential of the washboard type.