Finite-size effects in hyperuniform vortex matter

Abstract

Novel hyperuniform materials are emerging as an active field of applied and basic research sincethey can be designed to have exceptional physical properties. This ubiquitous state of matterpresents a hidden order that is characterized by the density of constituents of the system beinguniform at large scales, as in a perfect crystal, although they can be isotropic and disordered likea liquid. In the quest for synthesizing hyperuniform materials in experimental conditions, theimpact of finite-size effects remains as an open question to be addressed. We use vortex matterin type-II superconductors as a toy model system to study this issue. We previously reportedthat vortex matter nucleated in samples with point disorder is effectively hyperuniform and thuspresents the interesting physical properties inherent to hyperuniform systems. In this work wepresent experimental evidence that on decreasing the thickness of the vortex system its hyperuniform order is depleted. By means of hydrodynamic arguments we show that the experimentally observed depletion can be associated to two crossovers that we describe within a hydrodynamic approximation. The first crossover length is thickness-dependent and separates a class-II hyperuniform regime at intermediate lengthscales from a regime that can become asymptotically non-hyperuniform for large wavelengths in very thin samples. The second crossover takes place at smaller lengthscales and marks the onset of a faster increase of density fluctuations due to the dispersivity of the elastic constants. Our work points to a novel mechanism of emerging hyperuniformity controlled by the thickness of the host sample, an issue that has to be taken into account when growing hyperuniform structures for technological applications.