  Disordered hyperuniformity is a state of matter which has isotropic liquid
like properties while simultaneously having crystalline like properties such as
little variation in the density fluctuations over long distances. Such states
arise for the packing of photoreceptor cells in chicken eyes, jammed particle
assemblies, and in nonequilibrium systems. An open question is what possible
applications could utilize properties of hyperuniformity. One of the major
issues for applications of type-II superconductors is how to achieve high
critical currents by preventing the motion or depinning of vortices, so there
is great interest in understanding which pinning site geometries will lead to
the optimal pinning of vortices. Here, using large scale computational
simulations, we show that vortices in a type-II superconductor with a
hyperuniform pinning arrangement exhibit enhanced pinning compared to an equal
number of pinning sites with a purely random arrangement, and that the
enhancement is robust over a wide range of parameters. The stronger pinning
arises in the hyperuniform arrays due to the suppression of pinning density
fluctuations, permitting higher pin occupancy and the reduction of weak links
that lead to easy flow channeling. We also show that in general, in amorphous
vortex states in the presence of either random or hyperuniform pinning arrays,
the vortices themselves exhibit disordered hyperuniformity due to the repulsive
nature of the vortex-vortex interactions.
