Critical currents and vortex states at fractional matching fields in superconductors with periodic pinning

Abstract

We study vortex states and dynamics in two-dimensional ͑2D͒ superconductors with periodic pinning at fractional submatching fields using numerical simulations. For square pinning arrays we show that ordered vortex states form at 1/1,1/2, and 1/4 filling fractions while only partially ordered states form at other filling fractions, such as 1/3 and 1/5, in agreement with recent imaging experiments. For triangular pinning arrays we observe matching effects at filling fractions of 1/1, 6/7, 2/3, 1/3, 1/4, 1/6, and 1/7. For both square and triangular pinning arrays we also find that, for certain submatching fillings, vortex configurations depend on pinning strength. For weak pinning, ordering in which a portion of the vortices are positioned between pinning sites can occur. Depinning of the vortices at the matching fields, where the vortices are ordered, is elastic while at the incommensurate fields the motion is plastic. At the incommensurate fields, as the applied driving force is increased, there can be a transition to elastic flow where the vortices move along the pinning sites in 1D channels and a reordering transition to a triangular or distorted triangular lattice occurs. We also discuss the current-voltage curves and how they relate to the vortex ordering at commensurate and incommensurate fields.

Vortex configurations and critical parameters in superconducting thin films containing antidot arrays: Nonlinear Ginzburg-Landau theory

“…In this regime, the vortices act like charged point particles and their interaction with periodic pinning potential can be described using molecular dynamic simulations. 18,19,20,21 . However, the overlap of vortex cores (with size ∼ ξ), and the exact shape of the inter-vortex interaction (depending on the superconducting material properties reflected through κ), may significantly modify the vortex structures and consequently the critical current when this criteria is no longer satisfied.…”

“…In this respect, arrays of microholes (antidots) 1,2,3,4,5,6,7,8,9,10,11,12 and submicron magnetic dots, 13,14,15 have been studied, as their presence in the SC film strongly modifies the vortex structure compared to the one in non-patterned films. 16,17 Direct imaging experiments, 1 magnetization and transport measurements, 2,3,4,5 and theoretical simulations 18,19,20,21,22 of vortex structures in samples with periodic pinning centers have shown that the vortices form highly ordered configurations at integer H n = nΦ 0 /S and at some fractional H p/q = p q Φ 0 /S (n,p,q being integers) matching fields, where Φ 0 = hc/2e = 2.07 · 10 −7 Gcm 2 is the flux quantum, and S is the area of the primitive cell of the artificial lattice. This remarkable variety of stabilized vortex lattices may even be broadened by multiple possible degeneracies.…”

“…For example, extensive molecular dynamics simulations 18,19,20,21,22 in the London limit have been performed in an attempt to calculate the vortex structure and their dynamics in a periodic pinning potential. Although the general behavior of vortex lattices was accurately described, made approximations are valid only in certain range of parameters.…”

Driving force for commensurate vortex domain formation in periodic pinning arrays

“…7(a) [19]. One might anticipate that a multi-domain state would have lower energy, even exactly at the matching field, since the chain state clearly represents an inefficient way of packing vortices [20]. The multi-domain SHPM image captured at H ¼ ÀH 1 =3 (Fig.…”

Vortex kinks in superconducting films with periodically modulated thickness

“…The typical matching signature is the appearance of minima in the resistivity (or maxima in the critical current) for magnetic fields such that the number of vortices n V is a multiple (or a simple fraction like 1/4, 1/2 and 3/4) of the number of minima n P in potential landscape. For this purpose, films having different types of artificial pinning centers like holes [1,2] magnetic [3,4] or non-magnetic particles [5] in different geometries [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21], have been studied both experimentally and theoretically [22,23,24,25,26,27,28,29,30].…”