Current materials simulation faces computational limitations, prompting a keen interest in large-scale Density Functional Theory (DFT) algorithms. We have developed three distinct methods—ML-TB, charge density patching, and optimized atomic orbital DFT—each capable of computing the electronic structure of materials containing up to 100,000 atoms. Employing these advanced self-consistent calculations, we explored the electronic and optical properties of twisted bilayer systems and the possible applications in devices, without relying on any free parameters. Our investigations revealed artificial-atom states and quantum-dot arrays in twisted PbS, and we extended the computation of twistronics beyond van der Waals (vdW) materials, marking the first instance of a twisted structure non-vdW materials. Leveraging the localized and well-arranged states near the Fermi level in real space, we innovatively designed a new class of scalable qubits. Additionally, we delved into the geometry of 3D moiré superlattices, unveiling potential properties such as a novel nonlinear Hall effect, nontrivial magnetism, and unique optical selection rules (e.g., chiral selection) in various twisted materials.
