Abstract
Twisting two adjacent layers of van der Waals materials with respect to each other can lead to flat two-dimensional electronic bands which enables a wealth of physical phenomena. Here, we generalize this concept of so-called moiré flat bands to engineer flat bands in all three spatial dimensions controlled by the twist angle. The basic concept is to stack the material such that the large spatial moiré interference patterns are spatially shifted from one twisted layer to the next. We exemplify the general concept by considering graphitic systems, boron nitride, and WSe2, but the approach is applicable to any two-dimensional van der Waals material. For hexagonal boron nitride, we develop an ab initio fitted tight binding model that captures the corresponding three-dimensional low-energy electronic structure. We outline that interesting three-dimensional correlated phases of matter can be induced and controlled following this route, including quantum magnets and unconventional superconducting states.
Highlights
In the past few years, twisting adjacent layers of van der Waals materials has emerged as a versatile route to control the ratio between kinetic, potential, and vibrational energy of twodimensional systems
We stress that the idea we present here is general and allows three-dimensional flat band engineering in other materials even beyond the ones discussed explicitly above
Letter twisted hBN: the interlayer hopping t3 is nearly independent of the twist angle, whereas the in-plane hopping t2 and the mixed inter/intralayer term t1 decrease continuously
Summary
In the past few years, twisting adjacent layers of van der Waals materials has emerged as a versatile route to control the ratio between kinetic, potential, and vibrational energy of twodimensional systems. Our idea works generically and relies mainly on basic geometric arguments It is achievable within recent experimental advances to fabricate bulklike artificial twisted materials− and can be applied to any of the many van der Waals materials, which we will exemplify here for three important materials: graphitic systems, WSe2, and hexagonal boron nitride. The last of these will be examined in more details and we provide a full ab initio characterization for its three-dimensional twistdependent band structures. We consider the effects of correlations on the low-energy bands and find three-dimensional magnetic and superconducting states which can be realized as a function of twist angle
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