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

TL;DR

This paper introduces ideal noncrystals, a new class of two-dimensional ordered matter lacking traditional symmetry but exhibiting crystal-like properties such as phononic modes and hyperuniformity, expanding the understanding of ordered states.

Contribution

It presents the discovery and characterization of ideal noncrystals, a novel form of matter that combines disorder with crystal-like properties, without apparent symmetry breaking.

Findings

Exhibit high steric order despite lack of Bragg peaks

Show phononic vibrational modes following Debye law

Possess hyperuniformity and fully affine elastic responses

Abstract

Order and disorder constitute two fundamental and opposite themes in condensed matter physics and materials science. Crystals are considered the epitome of order, characterised by long-range translational order. The discovery of quasicrystals, which exhibit rotational symmetries forbidden in crystals and lack periodicity, led to a paradigm shift in solid-state physics. Moving one step forward, it is intriguing to ask whether ordered matter can exist without apparent symmetry breaking. The same question arises considering how ordered amorphous (noncrystalline) solids can be structured. Here, we present the discovery of ideal noncrystals in two dimensions, which are disordered in the conventional sense, lacking Bragg peaks, but exhibit high orderliness based on the steric order, i.e., they are ideally packed. A path-integral-like scheme reveals the underlying long-range structural correlation. We find that these ideal noncrystals are characterised by phononic vibrational modes following the Debye law, fully affine elastic responses, and suppressed density fluctuations at longer wavelengths, reminiscent of hyperuniformity -- all characteristics typically associated with crystals. Therefore, ideal noncrystals represent a peculiar form of matter with a mixed nature -- noncrystalline yet possessing crystal-like properties. Notably, these states are found to be thermodynamically favourable, indicating them as a possible new class of ordered matter without apparent symmetry breaking. Our findings significantly broaden the conceptualization of ordered states of matter and may contribute to a deeper understanding of entropy-driven ordering, particularly in generic amorphous materials.