  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.
