Linear ac dynamics of vortices in a periodic pinning array

Abstract

The vortex-dominated ac response of a superconducting film with a periodic array of pinning centers is studied in the linear regime for vortex densities greater than the saturation number. A simple model is introduced to describe small oscillations of the vortex lattice, which is considered to be composed of two distinct lattices formed by trapped vortices and interstitial vortices. The frequency-dependent complex resistivity is calculated as a function of frequency and magnetic induction for vortex densities between the first and the second matching fields. It is shown that the absorption spectra has two peaks corresponding to two characteristic pinning frequencies: one due to the periodic pinning array and another due to vortex-cage pinning. The range of validity of the model is determined from direct numerical simulations.

Observation of commensurability effects in a patterned thin superconducting Pb film using microwave reflection spectrometry

“…Finally, the vortex dynamics can be described by a phenomenological balance equation of the local forces [72,73], η∂u/∂t = F vp + F vv , where η is the vortex viscosity, u is the vortex velocity, F vp is the pinning force due to the trapping of the vortex by an antidot, and F vv is the vortex-vortex repulsive interaction. In this equation, we have not considered the inertial term, since the mass per unit length of the vortex is negligible [74]; the thermal noise force, since high stability of the system temperature is guaranteed by the experimental equipment; and the Lorentz force related to the gradient of the magnetic induction, due to the constant profile described in the multiterrace critical state [24,75].…”

2. Probing vortex dynamics on a single vortex level by scanning ac-susceptibility microscopy

“…However, in these artificial pinning arrays for a zero-field-cooling condition or for a small detuning from the matching field a coexistence of different types of vortices, each experiencing a different ⟨α L ⟩, will take place. For example, pinned vortices by an antidot lattice will experience a completely different restoring force than interstitial vortices caged by the pinned ones [24]. In the linear response regime, the steady state solution of this, simplified, equation of motion is given by:…”

Maximal persistent current in a type-II superconductor with an artificial pinning array at the matching magnetic field

“…6 Recently there has been an advance in the fabrication method of the periodic arrays of pinning sites. 7 The arrays with triangular, square, and rectangular geometries have been fabricated using either microholes or blind holes, 3 magnetic dots, 4 and columnar defects. 5 Theoretically these systems were studied, using mostly numerical methods, within a model of interacting twodimensional ͑2D͒ points representing vortices subject to pinning potential.…”