Spatiotemporal dynamics and plastic flow of vortices in superconductors with periodic arrays of pinning sites

Abstract

We present simulations of flux-gradient-driven superconducting rigid vortices interacting with square and triangular arrays of columnar pinning sites in an increasing external magnetic field. These simulations allow us to quantitatively relate spatio-temporal microscopic information of the vortex lattice with typically measured macroscopic quantities, such as the magnetization M (H). The flux lattice does not become completely commensurate with the pinning sites throughout the sample at the magnetization matching peaks, but forms a commensurate lattice in a region close to the edge of the sample. Matching fields related to unstable vortex configurations do not produce peaks in M (H). We observe a variety of evolving complex flux profiles, including flat terraces or plateaus separated by winding current-carrying strings and, near the peaks in M (H), plateaus only in certain regions, which move through the sample as the field increases.

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.…”

Dynamic regimes for driven colloidal particles on a periodic substrate at commensurate and incommensurate fillings

“…The type of particle motion that occurs at depinning strongly depends on the filling fraction and on whether the configuration is commensurate or incommensurate. Specific examples of systems that exhibit commensurate-incommensurate depinning transitions include vortices in type-II superconductors interacting with nanostructured periodic pinning arrays [5][6][7][8][9][10], vortices in Bose-Einstein condensates with a co-rotating periodic optical trap array [11], sliding charge density wave systems [12], colloidal particles interacting with periodic substrates [13][14][15][16][17][18][19][20][21][22], and charged metallic balls on patterned surfaces [23]. There are also many models of frictional systems in which a monolayer of atoms is driven over a pinned periodic monolayer of atoms, producing behavior that depends on whether the driven monolayer is commensurate or incommensurate with the underlying pinned layer [24][25][26][27][28][29][30][31].…”

Driving force for commensurate vortex domain formation in periodic pinning arrays

“…Much weaker effects are, however, also seen at fields corresponding to rational fractional filling. Simulations originally indicated that these correspond to simple ordered vortex structures which are commensurate with the underlying pinning array but where the occupation of each pinning site was not necessarily the same [8]. There have been several high-resolution studies of commensurate structures in these systems using Lorentz [9] and scanning Hall probe (SHPM) [10,11] microscopies.…”