Strongly Enhanced Pinning of Magnetic Vortices in Type-II Superconductors by Conformal Crystal Arrays

Abstract

Conformal crystals are non-uniform structures created by a conformal transformation of regular two-dimensional lattices. We show that gradient-driven vortices interacting with a conformal pinning array exhibit substantially stronger pinning effects over a much larger range of field than found for random or periodic pinning arrangements. The pinning enhancement is partially due to matching of the critical flux gradient with the pinning gradient, but the preservation of the sixfold ordering in the conformally transformed hexagonal lattice plays a crucial role. Our results can be generalized to a wide class of gradient-driven interacting particle systems such as colloids on optical trap arrays.PACS numbers: 74.25. Wx,74.25.Uv One of the most important problems for applications of type-II superconductors is how to create high critical currents or strong vortex pinning over a wide range of applied magnetic fields 1 . For over sixty years, it has been understood that the ground state vortex structure is a hexagonal lattice 2 , so many methods have been developed to increase the critical current using uniform pinning arrays that incorporate periodicity to match the vortex structure 3-13 . The pinning is enhanced at commensurate fields when the number of vortices equals an integer multiple of the number of pinning sites, but away from these specific matching fields, the enhancement of the critical current is lost 14 . Efforts to enhance the pinning at incommensurate fields have included the use of quasicrystalline substrates 15 or diluted periodic arrays [16][17][18][19][20] , where studies show that new types of non-integer commensurate states can arise in addition to the integer matching configurations. Hyperbolic tessellation arrays were also recently considered 21 .Part of the problem is the fact that under an applied current, the vortex structure does not remain uniform but instead develops a Bean-like flux gradient 22 : the vortex density is highest at the edges of the sample when the magnetic field is increased, and highest in the center of the sample when the magnetic field is removed and only trapped flux remains inside the sample. As a consequence, uniform pinning arrays generally have a portion of the pinning sites that are not fully occupied, suggesting that a more optimal pinning arrangement should include some type of density gradient to match the critical flux gradient. Here we show that a novel type of pinning structure, created using a conformal transformation of a uniform hexagonal lattice, produces a much higher critical current over a much wider range of magnetic fields than any pinning geometry considered up until now. Conformal crystals not only have a density gradient, but also preserve aspects of the hexagonal ordering naturally adopted by the vortex lattice. The pinning enhancement we find is substantial and will be very important for a wide range of superconductor applications and flux control. Our results can also be important for stabilizing novel self-assembled structures created using de...

Bound vortex dipoles generated at pinning centres by Meissner current

“…Our experiments have been carried out on a 200-nm-thick superconducting Pb film with randomly distributed pinning centres. There exist several methods to introduce pinning centres in superconductors, such as lithographically made well-controlled pinning sites 25,26 , ionirradiation-introduced point defects 27 , grain boundaries 28 , thickness variations 29 and so on. Most of these methods lead to the suppression of the superconducting order parameter at the pinning sites that makes them energetically favourable for vortices to localize on 30 .…”

Mapping degenerate vortex states in a kagome lattice of elongated antidots via scanning Hall probe microscopy

“…The appeal and advantage of superconducting systems is that the size and number of the particles can be tuned by changing the temperature and the magnetic field, respectively. In addition, the flexibility in the design and fabrication of artificial vortex traps in superconducting films has stimulated, during the past decade, an in-depth investigation of the interplay between pinning landscape and vortex pattern symmetry [16], influence of the pinning center's size and period [17][18][19][20], vortex rectification on a kagome-like array [21], competition between ordered and disordered defects [22][23][24], or pinning energy dispersion [25,26], to name a few.…”

Pinning, flux diodes and ratchets for vortices interacting with conformal pinning arrays

“…There are conditions where the conformal array is not as optimal as uniform triangular arrays, such as at integer matching fields where the gradient in the conformal arrays can prevent formation of a completely commensurate state. Initial simulations showed that conformal pinning arrays produced enhanced pinning compared to uniform random arrays, random arrays with a gradient, and periodic pinning arrays at non-matching fields, particularly at fields where there are more vortices than pinning sites [23,24]. Experiments indicated that the triangular pinning arrays produced stronger pinning than the conformal arrays below the first matching field, while the conformal pinning array generated stronger pinning at higher fields [28].…”