Angle-dependent electron confinement in graphene moir\'e superlattices

TL;DR

This paper investigates how the electronic band structure in graphene moiré superlattices varies with interlayer rotation angle, revealing new interaction effects and discrete states that could influence electron-phonon interactions.

Contribution

It introduces a detailed analysis of angle-dependent band structure evolution using DFT and band unfolding, uncovering novel interaction regions and discrete states in small-angle regimes.

Findings

Interactions at unexplored regions identified

Discrete energy states emerge at small angles

Energy differences comparable to graphene phonons

Abstract

In graphene moir\'e superlattices, electronic interactions between layers are mostly hidden as band structures get crowded because of folding, making their interpretation cumbersome. Here, the evolution of the electronic band structure as a function of the interlayer rotation angle is studied using Density Functional Theory followed by unfolding bands and then comparing them to their corresponding individual components. We observe interactions at regions not theoretically elucidated so far, where for small interlayer angles, gaps turn into discrete-like states that are evenly spaced in energy. We find that $V_{pp\sigma}$ attractive interactions between out-of-plane orbitals from different layers are responsible for the discretization. Furthermore, when the interlayer angle becomes small, these discrete evenly-spaced states have energy differences comparable to graphene phonons. Thus, they might be relevant to explain electron-phonon-assisted effects, which have been experimentally observed in graphene moir\'e superlattices.