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Heterogeneous materials consisting of different phases are ideally suited toachieve a broad spectrum of desirable bulk physical properties by combining thebest features of the constituents through the strategic spatial arrangement ofthe different phases. Disordered hyperuniform heterogeneous materials are new,exotic amorphous matter that behave like crystals in the manner in which theysuppress volume-fraction fluctuations at large length scales, and yet areisotropic with no Bragg peaks. In this paper, we formulate for the first time aFourier-space numerical construction procedure to design at will a wide classof disordered hyperuniform two-phase materials with prescribed spectraldensities, which enables one to tune the degree and length scales at which thissuppression occurs. We demonstrate that the anomalous suppression ofvolume-fraction fluctuations in such two-phase materials endow them with noveland often optimal transport and electromagnetic properties. Specifically, weconstruct a family of phase-inversion-symmetric materials with variabletopological connectedness properties that remarkably achieves a well-knownexplicit formula for the effective electrical (thermal) conductivity. Moreover,we design disordered stealthy hyperuniform dispersion that possesses nearlyoptimal effective conductivity while being statistically isotropic.Interestingly, all of our designed materials are transparent to electromagneticradiation for certain wavelengths, which is a common attribute of allhyperuniform materials. Our constructed materials can be readily realized by 3Dprinting and lithographic technologies. We expect that our designs will bepotentially useful for energy-saving materials, batteries and aerospaceapplications.

Designing Disordered Hyperuniform Two-Phase Materials with Novel Physical Properties