Determination of coordinate dependence of a pinning potential from a microwave experiment with vortices

Abstract

The measurement of the complex impedance response accompanied by power absorption P(ω) in the radiofrequency and microwave ranges represents a most popular experimental method for the investigation of pinning mechanisms and vortex dynamics in type-II superconductors. In the theory, the pinning potential (PP) well for a vortex must be a priori specified in order to subsequently analyze the measured data. We have theoretically solved the inverse problem at T = 0 K and exemplify how the coordinate dependence of a PP can be determined from a set of experimental curves P(ω|j0) measured at subcritical dc currents 0 < j0 < jc under a small microwave excitation j1 ≪ jc with frequency ω. We furthermore elucidate how and why the depinning frequency ωp, which separates the non-dissipative (quasi-adiabatic) and the dissipative (high-frequency) regimes of small vortex oscillations in the PP, is reduced with increasing j0. The results can be directly applied to a wide range of conventional superconductors with a PP subjected to superimposed dc and small microwave ac currents at T ≪ Tc.