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

TL;DR

This paper presents a theoretical study of the frequency-dependent ratchet effect in superconducting films with a tilted washboard pinning potential, analyzing vortex dynamics under ac and dc currents using an exact Langevin equation solution.

Contribution

It introduces an exact analytical approach to model vortex ratchet response in superconducting films with a tilted washboard potential at finite temperature.

Findings

Derived formulas for dc voltage and power response as functions of ac amplitude and frequency.

Analyzed adiabatic and high-frequency regimes of vortex ratchet behavior.

Compared theoretical results with recent experimental data on high-frequency ratchet effects.

Abstract

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].