Title: Ideal noncrystals: A possible new class of ordered matter without apparent broken symmetry

Abstract: Order and disorder constitute two fundamental and opposite themes in condensed matter physics and materials science. Crystals are considered the epitome of order characterized by long-range translational order. The discovery of quasicrystals, with no periodicity but rotational symmetries forbidden for crystals, leads to a paradigm shift in solid-state physics. Moving one step forward, it is intriguing to ask whether ordered matter exists without apparent symmetry breaking. The same question may arise in the pursuit of how ordered amorphous (noncrystalline) solids can be. Here we report the finding of ideal noncrystals in two dimensions, which are disordered in the conventional sense without Bragg peaks but highly ordered according to the steric order. We find that such ideal noncrystals have vibrational modes the same as phonons following the Debye law. The elastic responses are fully affine, which is again characteristic of crystals, and the spatial fluctuations of local volume fractions approach hyperuniformity. Therefore, ideal noncrystals represent an anomalous form of matter with a mixed nature of noncrystalline structure but crystal-like properties. Since such states are found to be thermodynamically favorable, we identify them as a possible new class of ordered matter without apparent broken symmetry. Our results thus extend the scope of the ordered state of matter and may impact the understanding of entropy-driving ordering also in generic amorphous materials.