Flat Bands in Slightly Twisted Bilayer Graphene

TL;DR

This paper reports the discovery of flat electronic bands near the Fermi energy in slightly twisted bilayer graphene at around 1.5 degrees, indicating a transition from bilayer to monolayer-like behavior due to layer decoupling.

Contribution

It introduces a detailed tight binding model based on ab-initio calculations to explain the emergence of flat bands in twisted bilayer graphene.

Findings

Flat bands appear near the Fermi energy at ~1.5° twist angle.

Transition from parabolic to linear dispersion occurs at this angle.

Layer decoupling is associated with the flat band formation.

Abstract

The bands of graphite are extremely sensitive to topological defects which modify the electronic structure. In this paper we found non-dispersive flat bands no farther than 10 meV of the Fermi energy in slightly twisted bilayer graphene as a signature of a transition from a parabolic dispersion of bilayer graphene to the characteristic linear dispersion of graphene. This transition occurs for relative rotation angles of layers around $1.5^o$ and is related to a process of layer decoupling. We have performed ab-initio calculations to develop a tight binding model with an interaction Hamiltonian between layers that includes the $\pi$ orbitals of all atoms and takes into account interactions up to third nearest-neighbors within a layer.