Order and disorder are central concepts in condensed-matter physics. Crystals break translational and rotational symmetries, whereas quasicrystals challenge this paradigm with forbidden rotational symmetries and aperiodicity. Here we report a distinct ordered state-ideal non-crystals-characterized by optimal steric order without symmetry breaking. Steric optimization yields ideal non-crystals as a thermodynamically favoured limiting state, accompanied by maximal steric order that may serve as a true order parameter for the glass transition. Despite their apparent disorder, they exhibit long-range orientational correlations, quantified via a specific path-integral-like approach. Ideal non-crystals possess distinct properties, including Debye-like phononic modes, affine elasticity, thermodynamic ultrastability and long-wavelength density uniformity, reminiscent of hyperuniformity. By uncovering a distinct form of entropy-driven ordering in sterically optimized materials, this work expands the landscape of ordered states and provides a framework for designing amorphous materials with crystal-like mechanical and thermal properties free from the anisotropy inherent in crystals.
Topological photonics expands the landscape of artificial electromagnetic materials and provides a variety of responses via robust boundary modes. Three-dimensional photonic topological insulators are predicted to host robust spin-momentum-locked surface states. However, their all-dielectric experimental realization has remained a fundamental challenge. Here we demonstrate a practical realization of a three-dimensional all-dielectric photonic topological insulator. We show a complete photonic topological bandgap as well as gapless topological surface states trapped on open boundaries of topological systems. The coupling of these states to the radiative continuum offers opportunities for controlling the emission of electromagnetic waves. We unveil that open interfaces in three-dimensional photonic topological insulators behave as effective metasurfaces and show that the helical nature of topological surface states supported by the interfaces enables control over far-field emission via the pseudo-spin degree of freedom. Further structuring of the topological interfaces provides further enhancement of such effective metasurfaces by offering control over far-field radiation patterns and directionality of the surface state emission.

