AC-driven Vortices and the Hall Effect in a Superconductor with a Tilted Washboard Pinning Potential

TL;DR

This paper provides an exact analytical solution for vortex motion in a superconductor with a tilted washboard pinning potential under ac and dc drives, revealing detailed effects on resistivity, impedance, and power absorption.

Contribution

It introduces a novel exact solution to the nonlinear vortex dynamics in a 2D tilted washboard potential considering Hall effects and ac influences.

Findings

Analytical formulas for temperature-dependent impedance tensor Zl are derived.

The influence of Hall effect and anisotropy on vortex power absorption is analyzed.

The shape and position of Shapiro-like steps depend on ac amplitude and frequency.

Abstract

The Langevin equation for a two-dimensional (2D) nonlinear guided vortex motion in a tilted cosine pinning potential in the presence of an ac is exactly solved in terms of a matrix continued fraction at arbitrary value of the Hall effect. The influence of an ac of arbitrary amplitude and frequency on the dc and ac magnetoresistivity tensors is analyzed. The ac density and frequency dependence of the overall shape and the number and position of the Shapiro-like steps on the anisotropic current-voltage characteristics are considered. The influence of a subcritical or overcritical dc on the time-dependent stationary ac longitudinal and transverse resistive vortex responses (on the frequency of an ac drive W) in terms of the nonlinear impedance tensor Z and the nonlinear ac response at W-harmonics are studied. Analytical formulas for 2D temperature-dependent linear impedance tensor Zl in the presence of a dc which depend on the angle a between the current-density vector and the guiding direction of the washboard planar pinning potential are derived and analyzed. Influence of a-anisotropy and the Hall effect on the nonlinear power absorption by vortices is discussed.