Abstract
We investigate the recently reported analogies between pinned vortices in nano-structured superconductors or colloids in optical traps, and spin ice materials. It has been found experimentally and numerically that both colloids and vortices exhibit ice or quasi-ice manifolds. However, the frustration of colloids and vortices differs essentially from spin ice at the vertex level. We show that the effective vertex energetics of the colloidal/vortex systems is made identical to that of spin ice materials by the contribution of an emergent field associated to the topological charge of the vertex. The similarity extends to the local low-energy dynamics of the ice manifold, where the effect of geometric hard constraints can be subsumed into the spatial modulation of the emergent field, which mediates an entropic interaction between topological charges. There, as in spin ice materials, genuine ice manifolds enter a Coulomb phase, whereas quasi-ice manifolds posses a well defined screening length, provided by a plasma of embedded topological charges. We also show that such similarities break down in lattices of mixed coordination because of topological charge transfer between sub-latices. This opens interesting perspective for extensions beyond physics, to social and economical networks.
Highlights
We investigate the recently reported analogies between pinned vortices in nano-structured superconductors or colloids in optical traps, and spin ice materials
We investigate spatial modulations, and we show that the equivalence extends to the low-energy physics above the ice manifold, where the emergent field mediates an entropic interaction between topological charges
We have shown that the frustration in trapped colloids is of the emergent kind and differs essentially from that of spin ice materials, their behavior can be seen as controlled, at least in a mean field treatment, by a similar, effective energetics, which adds to the actual energetic the contribution of an emergent field φ associated to the topological charge
Summary
The ice rule is so named because in water ice each oxygen atom sits at the center of a proton sharing tetrahedron. In the experiment of Latimer et al, where holes are nano patterned in a MoGe thin film, at half matching field, only half of the holes are pinning a vortices This introduces an algebraic constraint on the total number of pinned vortices. With respect of this experimental reality, the systems typically studied by Libal, Olson, Reichhardt and collaborators exhibit geometric hard constraints: each vertex of the lattice is connected by links, and each link contains only one colloid/vortex, which can occupy only the extremities. In the experimental arrangement e.g. it is not impossible for two neighboring vertices to both harbor z colloids [47] (z being the coordination of the lattice), but the same is impossible in the numerical models considered by Libal and collaborators. Algebraic constraint, whereas later we will show that the hard constraint implied by links is responsible for emergent interactions between topological charges
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