Interference of the Bloch phase in layered materials with stacking shifts

Abstract: In periodic systems, electronic wave functions of the eigenstates exhibit the periodically modulated Bloch phases and are characterized by their wave numbers ${\bf k}$. We theoretically address the effects of the Bloch phase in general layered materials with stacking shift. When the interlayer shift and the Bloch wave vector ${\bf k}$ satisfy certain conditions, interlayer transitions of electrons are prohibited by the interference of the Bloch phase. We specify the manifolds in the ${\bf k}$ space where the hybridization of the Bloch states between the layers is suppressed in accord with the stacking shift. These manifolds, named stacking-adapted interference manifolds (SAIM), are obviously applicable to general layered materials regardless of detailed atomic configuration within the unit cell. We demonstrate the robustness and usefulness of the SAIM with first-principles calculations for layered boron nitride, transition-metal dichalcogenide, graphite, and black phosphorus. We also apply the SAIM to general three-dimensional crystals to derive special ${\bf k}$-point paths for the respective Bravais lattices, along which the Bloch-phase interference strongly suppresses the band dispersion. Our theory provides a general and novel view on the anisotropic electronic kinetics intrinsic to the periodic-lattice structure.