Quasicrystalline symmetry enforced density functional theory

A general method for constructing higher-dimensional physical theories for quasicrystals in general and classes of Moire materials is developed, replacing the conventional approximant method, which approximates quasicrystal electronic states with a series of increasingly complex computations. The theoretical framework for a computational model is set forth, enabling the utilization of modern density functional theory implementations. Additionally, existence questions for the resulting partial differential equations are addressed and numerical stability and convergence speed discussed. Finally, we highlight a unique application of our theory to materials with non-negligible site substitution frequencies as an alternative to modern supercell calculations.