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The key to the development of advanced materials is to understand their electronic structure-property relationship. Utilization of this understanding to design new electronic materials with desired properties led to modern epitaxial growth approaches for synthesizing artificial lattices, which for almost half a century have become the mainstay of electronic and photonic technologies. In contrast to previous scalar modulation approaches, we now study synthetic crystal lattices that have a tensor artificial modulation and develop a theory for photons and conduction band states in these lattices in a regime with an unusual departure from the familiar consequences of translational symmetry and Bloch’s theorem. This study reveals that a nonmagnetic crystal lattice modulated by a purely geometrical orientational superlattice potential can lead to localized states or to spiral states for electrons and photons, as well as weakly or strongly localized states that could be used to markedly slow down the propagation of light and for optical energy storage applications.

Ferroelastic modulation and the Bloch formalism