Emergent geometric frustration and flat band in moir\'e bilayer graphene

TL;DR

This paper reveals that large-angle moiré bilayer graphene can exhibit strong interlayer coupling leading to electron localization, geometric frustration, and flat bands, contrary to previous beliefs of weak coupling at such angles.

Contribution

It demonstrates that near commensurate angles, interlayer coupling in moiré bilayer graphene is strong enough to cause electron localization and flat bands, with an exact analytical solution available.

Findings

Interlayer coupling is strong near commensurate angles.

Emergence of flat bands due to geometric frustration.

Exact analytical solution for low-energy physics near commensuration.

Abstract

So far the physics of moir\'e graphene bilayers at large, incommensurate rotation angles has been considered uninteresting. It has been held that the interlayer coupling in such structures is weak and the system can be thought of as a pair of decoupled single graphene sheets to a good approximation. Here, we demonstrate that for large rotation angles near commensurate ones, the interlayer coupling, far from being weak, is able to completely localize electrons to within a large scale, geometrically frustrated network of topologically protected modes. The emergent geometric frustration of the system gives rise to completely flat bands, with strong correlation physics as a result. All of this arises although in the lattice structure no large scale pattern appears to the unguided eye. Sufficiently close to commensuration the low-energy physics of this remarkable system has an exact analytical solution.