Physical description of crystal

Ishitobi, Takayuki

Conventional descriptions of crystals are based on space groups, whereas physical phenomena are naturally expressed through physical quantities that transform as tensors. This makes it difficult to directly connect symmetry with physical properties. In this study, we propose a new framework that directly represents crystalline and magnetic structures in terms of tensorial quantities. In this approach, a minimal set of tensorial order parameters characterizes the symmetry breaking, and other physical quantities can be derived from their products and derivatives. Furthermore, by matching tensor indices between the order parameters and coupling tensors, a one-to-one correspondence between structure and observable properties is explicitly established. This framework simplifies symmetry analysis and enables a unified treatment of structural analysis, macroscopic properties, local symmetries, and band degeneracies.