Hyperuniform Aperiodic Materials
Pioneering Functions through Control of
Vast Potential Structural Degrees of Freedom

In this group, we generate various aperiodic structures through computer simulations and classify them based on the hyperuniformity framework. For this purpose, we develop algorithms that automatically generate such structures and train neural networks to classify them efficiently.

We also investigate how electrons and spins are distributed in these aperiodic structures. Using a generalized framework of hyperuniformity, we aim to discover novel electron and spin states. 

The neural network that we develop will be used to analyze experimental data obtained by other project groups (A02–A04). Through computer simulations, we will collaborate closely with other groups, serving as a bridge between theory and experiment.

We reexamine the properties of various types of solids—including crystals, quasicrystals, and amorphous materials—from the hyperuniform perspective. We will use the hyperuniformity to explore the relationship between a material’s structure and its physical properties through both theoretical and experimental methods in the vast field of condensed matter physics.

Recently, quasicrystals have drawn attention for exhibiting exotic properties, such as superconductivity and ferromagnetism, in the absence of structural periodicity. Building on these intriguing properties, our research focuses on three main goals:

1. Understanding how materials respond to external fields,

2. Revealing the mechanisms of phase transitions, and

3. Discovering entirely new types of physical phenomena not found in conventional materials.

In this project group, we focus on artificially designed materials with a mesoscale (i.e., intermediate scale between macro and nano) aperiodicity. Our goal is to design and fabricate two types of such materials: two-dimensional photonic materials that control the flow of light, and three-dimensional soft materials that are flexible and deformable.

We build upon the concept of hyperuniformity (HU)—originally proposed and further developed in a broader context by Salvatore Torquato et al. [Phys. Rev. E 68, 041113 (2003) and Phys. Rev. E 94, 022122 (2016)]— to physical properties, we aim to design structures that optimize light propagation and mechanical strength. This approach could lead to the development of novel materials.

We collaborate closely with other project groups working on structural design (Group A01) and physical properties (Groups A02 and A04), playing a leading role in revealing the connections between structure, physical properties, and functionality.

"Isotropic disordered hyperuniform materials [...] are exotic ideal states of matter that lie between a crystal and liquid: they are like perfect crystals in the way they suppress large-scale density fluctuations, [...] and yet are like liquids or glasses in that they are statistically isotropic with no Bragg peaks and hence lack any conventional long-range order."

[S. Torquato, Hyperuniform states of matter, Physics Reports 745 (2018) 1-95]

Our project aims to apply the concept of hyperuniformity to Materials Science, and investigate materials approaching this exotic state. We plan to examine the atomic structures 3D-(nearly)-hyperuniform materials and to explore the subtle structural changes that become apparent in the long-wavelength limit, such as amorphous-to-amorphous phase transitions. 

Our goal is to establish a new framework for evaluating amorphous materials, which will help us discover new materials with tailored properties that suit specific needs. By integrating experiments, theory, and simulations, this interdisciplinary project represents a significant step toward applying the concept of hyperuniformity to real-world materials development.

This research project consists of an administrative group and 4 planned research groups.

• A01 Group (Computer Simulation) focuses on simulating structures and electronic behavior using computers, as well as developing algorithms and programs required for these simulations. It also supports the analysis of data obtained by other groups.

• A02 Group (Physical Properties) investigates the physical properties of materials, including those developed by Groups A03 and A04, and develops theoretical models based on their findings.

• A03 Group (Structure Design and Synthesis) works closely with Groups A01 and A02 to create materials with specially designed structures and functions. These materials include polymer-based substances and photonic materials that can manipulate light.

• A04 Group (Amorphous Materials) focuses on synthesizing materials with disordered, amorphous structures - specifically, hyperuniform amorphous materials. This Group analyzes their structures in detail and explores their unique properties.

The administrative group oversees the entire project and facilitates the collaboration between the planned research groups.