Fast Dynamics of Vortices in Superconductors

The last decade has been marked by great interest in the dynamics of vortices moving at high ($>$10\,km/s) velocities in superconductors. However, the flux-flow instability (FFI) prevents its exploration and sets practical limits for the use of vortices in various applications. Even so, FFI has turned into a valuable tool for studying the quasiparticle energy relaxation in superconductors, with the view of enhancement of the single-photon detection capability of micrometer-wide strips operated at large bias currents. In this context, the failure of ``global'' FFI models for materials with strong intrinsic and edge vortex pinning has urged the elaboration of ``local'' FFI models. This chapter outlines the recent advances in the research on FFI and highlights superconductors with perfect edges and weak volume pinning as prospective materials for studying fast vortex dynamics and nonequilibrium superconductivity. This manuscript is based on the author-prepared version of the review published in Encyclopedia of Condensed Matter Physics, vol. 2 (2024) 735--754.Comment: 18 pages, 6 figure

Microwave Absorption by Vortices in Superconductors with a Washboard Pinning Potential

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

Frequency-dependent ratchet effect in superconducting films with a tilted washboard pinning potential

The influence of an ac current of arbitrary amplitude and frequency on the mixed-state dc-voltage-ac-drive ratchet response of a superconducting film with a dc current-tilted uniaxial cosine pinning potential at finite temperature is theoretically investigated. The results are obtained in the single-vortex approximation, i.e., for non-interacting vortices, within the frame of an exact solution of the appropriate Langevin equation in terms of a matrix continued fraction. Formulas for the dc voltage ratchet response and absorbed power in ac response are discussed as functions of ac current amplitude and frequency as well as dc current induced tilt in a wide range of corresponding dimensionless parameters. Special attention is paid to the physical interpretation of the obtained results in adiabatic and high-frequency ratchet responses taking into account both running and localized states of the (ac+dc)-driven vortex motion in a washboard pinning potential. Our theoretical results are discussed in comparison with recent experimental work on the high-frequency ratchet response in nanostructured superconducting films [B. B. Jin et al., Phys. Rev. B 81 (2010) 174505].Comment: 13 pages, 11 figure