Resonant interaction in chiral, Eshelby-twisted van der Waals atomic layers

TL;DR

This paper investigates the electronic structures of chiral twisted van der Waals layers, revealing the existence of infinitely many resonant states with unique symmetries and optical properties, and deriving their universal characteristics.

Contribution

It introduces a universal framework for understanding resonant states in chiral twisted layers, highlighting their symmetries, energies, and optical selection rules, which is novel in the study of such materials.

Findings

Existence of infinitely many resonant states with screw symmetries.

Resonant states have a universal form independent of twist angle.

Resonant states exhibit specific optical selection rules.

Abstract

We study the electronic structures of chiral, Eshelby-twisted van der Waals atomic layers with a particular focus on a chiral twisted graphite (CTG), a graphene stack with a constant twist angle $\theta$ between successive layers. We show that each CTG can host infinitely many resonant states which arise from the interaction between the degenerate monolayer states of the constituent layers. Each resonant state has a screw rotational symmetry, and may have a smaller reduced Brillouin zone than other non-resonant states in the same structure. And each CTG can have the resonant states with up to four different screw symmetries. We derive the energies and wave functions of the resonant states in a universal form of a one-dimensional chain regardless of $\theta$, and show that these states exhibit a clear optical selection rule for circularly polarized light. Finally, we discuss the uniqueness and existence of the exact center of the lattice and the self-similarity of the wave amplitudes of the resonant states.