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

Abstract

Using the non-linear Ginzburg-Landau (GL) theory, we obtain the possible vortex configurations in superconducting thin films containing a square lattice of antidots. The equilibrium structural phase diagram is constructed which gives the different ground-state vortex configurations as function of the size and periodicity of the antidots for a given effective GL parameter κ * . Giant-vortex states, combination of giant-and multi-vortex states, as well as symmetry imposed vortex-antivortex states are found to be the ground state for particular geometrical parameters of the sample. The antidot occupation number no is calculated as a function of related parameters and comparison with existing expressions for the saturation number ns and with experimental results is given. For a small radius of antidots a triangular vortex lattice is obtained, where some of the vortices are pinned by the antidots and some of them are located between them. Transition between the square pinned and triangular vortex lattices is given for different values of the applied field. The enhanced critical current at integer and rational matching fields is found, where the level of enhancement at given magnetic field directly depends on the vortex-occupation number of the antidots. For certain parameters of the antidot lattice and/or temperature the critical current is found to be larger for higher magnetic fields. Superconducting/normal H − T phase boundary exhibits different regimes as antidots are made larger, and we transit from a plain superconducting film to a thin-wire superconducting network. Presented results are in good agreement with available experiments and suggest possible new experiments.

Vortex interaction enhanced saturation number and caging effect in a superconducting film with a honeycomb array of nanoscale holes

“…18 for the extension of their work) established that the saturation number is given by n si ∼ = R/2ξ(T ) with ξ(T ) the temperature dependent coherence length. However, this expression can underestimate the saturation number for an array of holes where the interaction between vortices needs to be considered 7,16 . Indeed, careful analysis within the Ginzburg-Landau (GL) theory shows that 19 for an array of dense pinning centers the saturation number for a defect with a radius of the order of ξ becomes n sa ∼ [R/ξ(T )] 2 due to vortex-vortex interactions.…”

“…On the other hand, scanning tunneling microscopy (STM) 22 and Bitter decoration 23 imagings show an increase of the vorticity of the multi-quanta vortices in the hole after interstitial vortices were observed, revealing the effect of vortex-vortex interaction on the saturation number 16,19 . Though the pinning effect of a blind hole which allows the existence of multiple vortices of single flux quantum may be different from that of a normal (through-) hole having only one vortex with multi-quanta, its saturation number seems also to depend on the vortex-vortex interaction: an increase of vortex number in blind holes after the appearance of interstitial vortices was also proposed to understand the re-occurrence of peaks at high integer matching fields observed in critical current versus magnetic field curves for superconducting films with square arrays of blind holes 24 .…”

“…Indeed, careful analysis within the Ginzburg-Landau (GL) theory shows that 19 for an array of dense pinning centers the saturation number for a defect with a radius of the order of ξ becomes n sa ∼ [R/ξ(T )] 2 due to vortex-vortex interactions. Moreover, computer simulations reveal that interstitial vortices exert pressure on the pinning centers 16,20,21 , forcing additional vortices into the holes. Namely, interstitial vortices appear at lower magnetic fields, but as the vortex-vortex interaction increases at higher fields, vortices with more flux quanta start to form at the pinning sites 16,20,21 .…”

“…It has been found that a periodic pinning landscape 1-11 leads to strong commensurability effects which appear when the number of vortices equals an integer (n) multiple of the number of pinning sites (i.e., at fields H = nH 0 with H 0 the first matching field where the number of vortices equals the number of pins), resulting in peaks in, e.g., the critical current as a function of applied magnetic field. However, at larger magnetic fields the pinning centers become repulsive potentials for the incoming vortices, resulting in excess vortices, located preferentially at the interstitial sites between the pinning centers, forming different type of ordered vortex configurations [12][13][14][15][16] . The interstitial vortices can be highly mobile and lead to strong reduction of the critical parameters of the system.…”

Microfluidic manipulation of magnetic flux domains in type-I superconductors: droplet formation, fusion and fission

“…For that reason, much attention has been given in the past to hampering vortex motion by introducing arrays of artificial pinning centers in superconductors, nanoengineered in size and geometry for optimal vortex pinning and enhancement of maximal sustainable magnetic field and electric current in the superconducting state [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] . Pinning is also of importance in type-I superconductors, for example in defining the structure of the intermediate state (IS) 18,19 , which is a very rich study object and has received a revival of interest in recent years [20][21][22][23][24][25][26][27][28][29][30][31][32] .…”