Duality between atomic configurations and Bloch states in twistronic materials

TL;DR

This paper introduces a classification of electronic structures in twisted 2D materials based on a duality between atomic configurations and Bloch states, aiding the understanding of moiré phenomena.

Contribution

It presents a novel framework linking interlayer configuration and Bloch momentum, with applications to graphene and MoS₂, advancing the understanding of twistronic electronic properties.

Findings

Classifies electronic structures as 'moiré molecules' or 'moiré crystals'

Predicts electronic properties using local electron density diagrams

Applies the framework to graphene and MoS₂, demonstrating its utility

Abstract

The relative orientation (twist) of successive layers of stacked two-dimensional (2D) materials creates variations in the interlayer atomic registry. The variations often form a super lattice, called a moir\'e pattern, which can alter electronic properties. In this work we introduce a classification of the single-particle electronic structures that can occur in twisted stacks of 2D layers by characterizing them as "moir\'e molecules" or "moir\'e crystals". The molecules generate localized electronic states and moir\'e flat bands, while the crystals are sometimes unconventional and produce electronic banding in the configuration basis. The underpinning of this classification is the duality between interlayer configuration and monolayer Bloch momentum in moir\'e Hamiltonians. We apply this understanding to diagrams of local electron density in untwisted geometries to produce intuitive and quantitative predictions of twistronic properties. We provide a conceptual introduction to this framework through a one-dimensional model, and then apply it to 2D twisted bilayers of the semi-metal graphene, and of MoS$_2$, a representative material of the transition metal dichalcogenide (TMDC) family of semiconductors. This level of thorough understanding of twistronic phenomena is vital in the search for new material platforms for localized moir\'e electrons.