Engineering Three Dimensional Moir\'e Flat Bands

TL;DR

This paper extends the concept of moiré flat bands from two-dimensional materials to three dimensions by stacking twisted layers in a specific pattern, enabling new electronic properties and phases.

Contribution

It introduces a method to engineer three-dimensional flat bands in layered van der Waals materials through controlled stacking and twisting patterns.

Findings

Proposes stacking twisted layers to achieve 3D flat bands.

Develops an ab initio tight-binding model for boron nitride.

Suggests potential for 3D correlated quantum phases.

Abstract

We demonstrate that the concept of moir\'e flat bands can be generalized to achieve electronic band engineering in all three spatial dimensions. For many two dimensional van der Waals materials, twisting two adjacent layers with respect to each other leads to flat electronic bands in the two corresponding spatial directions -- a notion sometimes referred to as twistronics as it enables a wealth of physical phenomena. Within this two dimensional plane, large moir\'e patterns of nanometer size form. The basic concept we propose here is to stack multiple twisted layers on top of each other in a predefined pattern. If the pattern is chosen such that with respect to the stacking direction of layers, the large spatial moir\'e features are spatially shifted from one twisted layer to the next, the system exhibits twist angle controlled flat bands in all of the three spatial directions. With this, our proposal extends the use of twistronic to three dimensions. We exemplify the general concept by considering graphitic systems, boron nitride and WSe$_2$ as candidate materials, but the approach is applicable to any two-dimensional van der Waals material. For hexagonal boron nitride we develope 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.