Family of ideal Chern flat bands with arbitrary Chern number in chiral twisted graphene multilayers

TL;DR

This paper introduces a family of chiral twisted graphene multilayers with arbitrary Chern numbers, exhibiting perfect flatness and ideal quantum geometry at magic angles, enabling exploration of novel topological phases beyond Landau levels.

Contribution

It generalizes the chiral model of twisted bilayer graphene to multilayers with arbitrary Chern numbers, providing explicit wavefunctions and tunable Berry curvature while maintaining ideal quantum geometry.

Findings

Bands are perfectly flat at magic angles with Chern numbers depending on stacking chirality.

Models satisfy the trace condition, indicating ideal quantum geometry.

Berry curvature can be tuned without losing flatness or ideal geometry.

Abstract

We consider a family of twisted graphene multilayers consisting of $n$-untwisted chirally stacked layers, e.g., AB, ABC, etc, with a single twist on top of $m$-untwisted {chirally stacked} layers. Upon neglecting both trigonal warping terms for the untwisted layers and the same sublattice hopping between all layers, the resulting models generalize several remarkable features of the chiral model of twisted bilayer graphene (CTBG). In particular, they exhibit a set of magic angles which are identical to those of CTBG at which a pair of bands (i) are perfectly flat, (ii) have Chern numbers in the sublattice basis given by $\pm (n,-m)$ or $\pm (n + m - 1, -1)$ depending on the stacking chirality, and (iii) satisfy the trace condition, saturating an inequality between the quantum metric and the Berry curvature, and thus realizing ideal quantum geometry. These are the first higher Chern bands that satisfy (iii) beyond fine-tuned models or combinations of Landau levels. We show that ideal quantum geometry is directly related to the construction of fractional quantum Hall model wavefunctions. We provide explicit analytic expressions for the flat band wavefunctions at the magic angle in terms of the CTBG wavefunctions. We also show that the Berry curvature distribution in these models can be continuously tuned while maintaining perfect quantum geometry. Similar to the study of fractional Chern insulators in ideal $C = 1$ bands, these models pave the way for investigating exotic topological phases in higher Chern bands for which no Landau level analog is available.