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

Abstract

The measurement of the complex impedance response and accompanied power absorption P(ω) in the radiofrequency and microwave ranges represents a most popular experimental method to investigate pinning mechanisms and the 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 the increase of 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.