Crossover between macroscopic and mesoscopic regimes of vortex interactions in type-II superconductors

Abstract

In the present work we report the existence of a crossover between the macroscopic and mesoscopic regimes of vortex interactions in type-II superconductors. Our findings rely on a systematic procedure to determine this crossover, which is based on the influence of the surface on the vortex structure of small superconductors. An adjacent result that we have found is that near this regime transformation, the vortex lattice develops a progressive change of symmetry, from square to hexagonal, which is intimately related to the meso-to-macro crossover. Our numerical simulations have been done for a long superconducting cylinder of square cross section for a wide range of length scales and temperatures.

Study of the threshold line between macroscopic and bulk behaviors for homogeneous type II superconductors

“…When we achieve a determined length L/ξ(0) for which these two values of the applied field are equal, within a certain precision, we approach the meso-to-macro crossover. In [26] we explain in more details the physical basis of the criterion. We then repeat the procedure for several temperatures and obtain an L c (T )/ξ(0) diagram.…”

“…In this work we solved the TDGL equations for very long cylinders of square cross section and with several lateral sizes, expressed by L/ξ(0), as described in references [26,31]. Those equations were discretized following the link variables method as developed by Gropp and coworkers [52].…”

“…In addition, in the mixed state, the magnetization is not a smooth function of the applied field; it has a series of jumps which indicate the nucleation of one or more vortices. Second, according to references [26,31], as the size of the sample is increased, there is a length scale above which deep inside the superconductor, the vortex lattice is not perturbed by the surface effects, although they are still present. In this regime, which we denote by macroscopic, the vortices are arranged nearly as a triangular lattice, except near the surface where there are some distortions.…”

“…With the same purpose, the authors of the Ref. [26] proposed the existence of a threshold line between mesoscopic and macroscopic superconducting behaviors. For the mesoscopic-like behavior, the confinement effects are strong enough to induce a crossover of the the vortex lattice and the vortices arrangement follows the symmetry of the sample.…”

“…As a consequence, multi and giant vortex states takes place [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] as well as the coexistence of vortex and antivortex pairs. [6] Such systems also present others exotic behaviors as non-quantized vortex penetration [21] and the arrangement of the vortex lattice in several geometries which follow the symmetry of the samples [1,4,8,[22][23][24][25][26][27][28][29][30][31].…”