Flat bands in chiral multilayer graphene

TL;DR

This paper investigates the formation of perfectly-flat zero energy bands in chiral multilayer graphene, revealing their topological properties, how they can be characterized by Chern numbers, and their behavior under magnetic fields.

Contribution

It introduces a parameter space framework for analyzing flat bands in multilayer graphene and links their Chern numbers to effective Landau levels and flux quantization.

Findings

Flat bands can be characterized by Chern numbers and effective Landau levels.

Flat bands do not disperse under perpendicular magnetic fields.

The gap closes when external flux cancels the effective flux in the flat bands.

Abstract

We study the formation and properties of perfectly-flat zero energy bands in a multi-layer graphene systems in the chiral limit. Employing the degrees of freedoms of the multi-layer system, such as relative twist-angle and relative shifts, in a way that preserves a set of symmetries, we define a two-dimensional parameter plane that hosts lines of two and four flat bands. This plane enables adiabatic continuation of multi-layer chiral systems to weakly coupled bi- and tri-layer systems, and through that mapping provides tools for calculating the Chern numbers of the flat bands. We show that a flat band of Chern number $C$ can be spanned by $C$ effective Landau levels, all experiencing an effective flux of $1/C$ flux quantum per unit cell, and each carrying its own intra-unit-cell wave function. The flat bands do not disperse under the effect of a perpendicular magnetic field, and the gap to the dispersive bands closes when the externally applied flux cancels the $1/C$ effective flux.