Flat bands with local Berry curvature in multilayer graphene

TL;DR

This paper shows that multilayer graphene on boron nitride can host nearly flat bands with local Berry curvature, providing a platform to study interaction effects in quantum systems with nontrivial quantum geometry.

Contribution

It demonstrates the emergence of flat bands with local Berry curvature in chiral multilayer graphene on BN, highlighting tunability and potential for exploring many-body physics.

Findings

Nearly flat bands appear at N=7 layers with 3.6 meV bandwidth.

Band crossings become avoided crossings due to intervalley tunneling.

The system exhibits nontrivial quantum geometry without net Chern number.

Abstract

We demonstrate that flat bands with local Berry curvature arise naturally in chiral (ABC) multilayer graphene placed on a boron nitride (BN) substrate. The degree of flatness can be tuned by varying the number of graphene layers N. For N = 7 the bands become nearly flat, with a small bandwidth of 3.6 meV. The two nearly flat bands coming from the K and K' valleys cross along lines in the reduced zone. Weak intervalley tunneling turns the bandcrossing into an avoided crossing, producing two nearly flat bands with global Chern number zero, but with local Berry curvature. The flatness of the bands suggests that many body effects will dominate the physics, while the local Berry curvature of the bands endows the system with a nontrivial quantum geometry. The quantum geometry effects manifest themselves through the quantum distance (Fubini-Study) metric, rather than the more conventional Chern number. Multilayer graphene on BN thus provides a platform for investigating the effect of interactions in a system with a non-trivial quantum distance metric, without the complication of non-zero Chern numbers. We note in passing that flat bands with non-zero Chern number can also be realized by making use of magnetic adatoms, and explicitly breaking time reversal symmetry.