Spectroscopy of 2D Materials II

The lattice-level description of optical polarization in crystalline materials within a quantum theory has long remained unresolved. Inspired by the electronic band theory, we propose a microscopic optical band theory of solids specifically applicable to optical polarization. This framework reveals propagating waves hidden deep within a crystal lattice. We show that these hidden waves arise from nonlocal optical-indices, a family of functions obeying crystal symmetries, and cannot be described by the conventional concept of refractive index. In contrast to the macroscopic refractive index widely today, this framework shows that hidden optical waves exhibit unique optical polarization texture and crowding. Further, the nonlocal optical-indices serve as symmetry indicators and provide a signature for identifying light-induced topological phases of natural materials. We also present an open-source software package, Purdue-Picomax, for the research community to obtain the deep microscopic optical band structure of a variety of materials, including bulk semiconductors and van der Waal moiré materials. Our work establishes a foundational crystallographic feature to discover deep microscopic optical waves in light-matter interaction.