Magic momenta and three dimensional Landau levels from a three dimensional graphite moir\'e superlattice

TL;DR

This paper introduces a three-dimensional graphite moiré superlattice that exhibits unique flat bands, magic momenta, and three-dimensional Landau levels, potentially enabling robust 3D quantum Hall effects across various twist angles.

Contribution

It theoretically demonstrates the existence of magic momenta, co-existing flat bands, and 3D Landau levels in a novel bulk three-dimensional moiré system, expanding the understanding of moiré physics beyond 2D.

Findings

Existence of magic momenta where Fermi velocities vanish.

Co-existence of topologically distinct flat bands at different wavevectors.

Emergence of dispersionless 3D zeroth Landau level leading to quantum Hall effects.

Abstract

Twisted bilayer graphene (TBG) and other quasi-two-dimensional moir\'e superlattices have attracted significant attention due to the emergence of various correlated and topological states associated with the flat bands in these systems. In this work, we theoretically explore the physical properties of a new type of \textit{three dimensional graphite moir\'e superlattice}, the bulk alternating twisted graphite (ATG) system with homogeneous twist angle, which is grown by in situ chemical vapor decomposition method. Compared to TBG, the bulk ATG system is bestowed with an additional wavevector degrees of freedom due to the extra dimensionality. As a result, we find that when the twist angle of bulk ATG is smaller than twice of the magic angle of TBG, there always exist ``magic momenta" at which the in-plane Fermi velocities of the moir\'e bands vanish. Moreover, topologically distinct flat bands of TBG at different magic angles can even co-exist at different out-of-plane wavevectors in a single bulk ATG system. Most saliently, when the twist angle is relatively large, exactly dispersionless three dimensional zeroth Landau level would emerge in the bulk ATG, which may give rise to robust three dimensional quantum Hall effects over a large range of twist angles.