Fractional topological states in rhombohedral multilayer graphene modulated by kagome superlattice

TL;DR

This paper proposes using rhombohedral multilayer graphene with a kagome superlattice to realize various fractional topological phases, supported by theoretical analysis and potential experimental tunability.

Contribution

It introduces a new platform combining multilayer graphene and kagome superlattice to achieve fractional topological states, with detailed theoretical characterization.

Findings

Identification of nearly ideal topological flat bands in the system

Prediction of fractional Chern insulators at specific fillings

Demonstration of tunability via electrostatic potential and superlattice parameters

Abstract

Fractional quantum anomalous Hall effects realized in twisted bilayer MoTe$_2$ and multilayer-graphene-based moir\'e heterostructures have captured a tremendous growth of interest. In this work, we propose that rhombohedral multilayer graphene coupled with an artificial kagome superlattice potential is a new platform to realize various fractional topological phases. Taking Bernal bilayer graphene as the simplest example, when it is placed on top of a prepatterned SiO$_2$ substrate with periodic arrays of holes arranged into kagome lattice, the system would be subject to a tunable kagome superlattice potential once an electrostatic voltage drop between the top and bottom gates is applied. Then, we theoretically study the electronic band structures, topological properties, and quantum geometric properties of the Bloch states of Bernal bilayer graphene coupled with a realistic kagome superlattice potential, which is well benchmarked by transport measurements in the weak superlattice-potential regime. We find that the system may exhibit nearly ideal topological flat bands in a substantial region of the parameter space spanned by superlattice constant and electrostatic potential strength. When these topological flat bands are fractionally filled, exact diagonalization calculations suggest that the system would exhibit rich fractional topological phases at 1/3, 2/3, 2/5, 3/5 and 1/2 fillings including both fractional Chern insulators and anomalous composite Fermi liquids under zero magnetic field.