Finite-size effects in hyperuniform vortex matter

Novel hyperuniform materials are emerging as an active field of applied and basic research since they can be designed to have exceptional physical properties. This ubiquitous state of matter presents a hidden order that is characterized by the density of constituents of the system being uniform at large scales, as in a perfect crystal, although they can be isotropic and disordered like a liquid. In the quest for synthesizing hyperuniform materials in experimental conditions, the impact of finite-size effects remains as an open question to be addressed. We use vortex matter in type-II superconductors as a toy model system to study this issue. We previously reported that vortex matter nucleated in samples with point disorder is effectively hyperuniform and thus presents the interesting physical properties inherent to hyperuniform systems. In this work we present 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.