Flat bands in chiral multilayer graphene

We study the formation and properties of perfectly flat zero-energy bands in a multilayer graphene system in the chiral limit. Employing the degrees of freedom of the multilayer 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 a multilayer chiral system to weakly coupled bi- and trilayer 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 lowest 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.