Order metrics of amorphous solids: structures, hyperuniformity, and implications for ultra-stable glasses.

Due to the lack of long-range order, it remains challenging to characterize the structure of disordered solids and understand the nature of the glass transition. Here we propose a new structural order parameter by taking into account multiple rotational symmetries. By studying the statistics for two-dimensional disordered packings of hard particles along the jamming transition line, we observe the evolution from disordered-particle-rich states to ordered-particle-rich states with the increase in packing fraction, together with the unusual non-monotonic change in the degree of hyperuniformity. At the high packing fraction end of the jamming transition line, the packings are mostly composed of ordered particles and have the smallest long-wavelength density fluctuations. Our work links the local order fluctuations to the thermodynamic stability and density fluctuations of disordered solids. Taking advantage of the order parameter, we propose the structural characteristic of ultra-stable glasses: although globally disordered when evaluated by any single symmetry, they are rich in ordered particles and effectively 'globally ordered' with crystal-like long-wavelength density fluctuations.