  Disorder hyperuniformity (DHU) is a recently discovered exotic state of
many-body systems that possess a hidden order in between that of a perfect
crystal and a completely disordered system. Recently, this novel DHU state has
been observed in a number of quantum materials including amorphous 2D graphene
and silica, which are endowed with unexpected electronic transport properties.
Here, we numerically investigate 1D atomic chain models, including perfect
crystalline, disordered hyperuniform as well as randomly perturbed atom packing
configurations to obtain a quantitative understanding of how the unique DHU
disorder affects the vibrational properties of these low-dimensional materials.
We find that the DHU chains possess lower cohesive energies compared to the
randomly perturbed chains, implying their potential reliability in experiments.
Our inverse partition ratio (IPR) calculations indicate that the DHU chains can
support fully delocalized states just like perfect crystalline chains over a
wide range of frequencies, i.e., $\omega \in (0, 100)$ cm$^{-1}$, suggesting
superior phonon transport behaviors within these frequencies, which was
traditionally considered impossible in disordered systems. Interestingly, we
observe the emergence of a group of highly localized states associated with
$\omega \sim 200$ cm$^{-1}$, which is characterized by a significant peak in
the IPR and a peak in phonon density of states at the corresponding frequency,
and is potentially useful for decoupling electron and phonon degrees of
freedom. These unique properties of DHU chains have implications in the design
and engineering of novel DHU quantum materials for thermal and phononic
applications.
