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

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.

17 pages, 8 figures

References in corpus (4)

• Properties of resonant activation phenomena
• Role of twin boundaries on the vortex dynamics in YBa${}_2$Cu${}_3$O${}_7$
• Hall Anomaly and Vortex-Lattice Melting in Superconducting Single Crystal YBa2Cu3O7-d
• Non-linear microwave impedance of short and long Josephson Junctions

Cited by in corpus (15)

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• Dual cut-off dc-tunable microwave low-pass filter on superconducting Nb microstrips with asymmetric nanogrooves
• AC-driven microwave loss modulation in a fluxonic metamaterial
• Frequency-dependent ratchet effect in superconducting films with a tilted washboard pinning potential
• Pinning effects on self-heating and flux-flow instability in superconducting films near $T_c$
• Vortex ratchet reversal in an asymmetric washboard pinning potential subject to combined dc and ac stimuli
• Pinning effects on flux flow instability in epitaxial Nb thin films
• Guiding of vortices and ratchet effect in superconducting films with asymmetric pinning potential
• Angular magnetic-field dependence of vortex matching in pinning lattices fabricated by focused or masked helium ion beam irradiation of superconducting YBa${}_2$Cu${}_3$O${}_{7-\delta }$ thin films
• Fast Dynamics of Vortices in Superconductors
• ${}^4$He sample probe for combined microwave and dc transport measurements
• Analysis of the measurements of anisotropic a.c. vortex resistivity in tilted magnetic fields
• Pinning effects on hot-electron vortex flow instability in superconducting films
• Zero-bias Shapiro steps in asymmetric pinning nanolandscapes
• Current and Magnetic Field Dependences of a Superconducting Coplanar Waveguide Resonator