Microwave Absorption by Vortices in Superconductors with a Washboard Pinning Potential

Abstract

let us compare the results presented in the chapter with the analogous but more general results obtained by the authors [25] on the basis of a stochastic model for arbitrary temperature T and densities j0 and j1. In that work, the Langevin equation (1), supplemented with a thermofluctuation term, has been exactly solved for γ = 1 interms ofamatrix continued fraction [52] and, depending on the WPP’s tilt caused by the dc current, two substantially differentmodes in the vortexmotion have been predicted. Inmore detail, at low temperatures and relatively high frequencies in a nontilted pinning potential each pinned vortex is confined to its pinning potential well during the ac period. In the case of superimposed strong ac and dc driving currents a running state of the vortex may appear when it can visit several (or many) potential wells during the ac period. As a result, two branches of new findings have been elucidated [25, 27]. First, the influence of an ac current on the usual E0(j0) and ratchet E0(j1) CVCs has been analyzed. Second, the influence of a dc current on the ac nonlinear impedance response and nonlinear power absorption has been investigated. In particular, the appearance of Shapiro-like steps in the usual CVC and the appearance of phase-locking regions in the ratchet CVC has been predicted. At the same time, it has been shown that an anomalous power absorption in the ac response is expected at close-to critical currents j0 jc and relatively low frequencies ω ωp. Figure 8 shows the main predictions of these works. Namely, predicted are (i) an enhanced power absorption at low frequencies, (ii) a temperature- and current-dependent minimum at intermediate frequencies. (iii) At substantially low temperatures, the absorption can acquire negative values which physically corresponds to the generation by vortices. However, a more general and formally precise solution of the problem in terms of a matrix-continued fraction does not allow the main physical results of the problemto be investigated in the formof explicit analytical functions of the main physical quantities (j0, j1, ω, α, T, , and γ) which, we believe, has helped us greatly to elucidate the physics in the problem under consideration.