Fractional Chern mosaic in supermoir\'e graphene

TL;DR

This paper introduces the concept of a fractional Chern mosaic in supermoiré graphene, where spatially varying topological order emerges due to electron correlations on multiple length scales.

Contribution

It proposes a novel state called fractional Chern mosaic enabled by a supermoiré structure in twisted graphene layers, combining topological order with spatial variation.

Findings

Fractional Chern mosaic arises from electron correlations in supermoiré graphene.

Spatial variation of fractionalization pattern occurs at the supermoiré scale.

The structure features both moiré and supermoiré lattices.

Abstract

We propose the realization of a fractional Chern mosaic: a state characterized by a spatially varying topological order. This state is enabled by a separation of length scales that emerges when three graphene sheets are sequentially rotated by a small twist angle. The resulting structure features not only conventional moir\'e lattices, but also a much larger supermoir\'e lattice. We demonstrate that a fractional Chern mosaic arises when electron correlations induce fractionalization locally on the moir\'e scale, while the pattern of fractionalization varies at the supermoir\'e scale.