Fractional Chern insulator with higher Chern number in optical lattice

TL;DR

This paper proposes a method to create higher Chern number flat bands in optical lattices, enabling the realization of fractional Chern insulators with enhanced topological properties and potential for exploring exotic quantum phases.

Contribution

It introduces an interlayer coupling scheme to generate higher Chern numbers in flat bands, demonstrated through exact diagonalization and a proposed cold atom experimental setup.

Findings

Engineered a flat band with C=2 from two C=1 bands in a bilayer lattice.

Observed fractional Chern insulator states with C=2/3 and 2/5.

Proposed an experimental realization using cold alkaline-earth-like atoms.

Abstract

Fractional Chern insulators arise in topologically nontrivial flat bands, characterized by an integer Chern number C that corresponds to the number of dissipationless edge states in the non-interacting regime. Higher Chern numbers can replicate the physics of higher Landau levels and often confer enhanced topological robustness. However, realizing correlated fractional phases with higher Chern numbers in such flat band systems remains challenging. Here, we propose an interlayer coupling scheme to generate higher Chern numbers in a flat-band system, where the interlayer coupling transforms two C = 1 bands in a bilayer checkerboard lattice into a single flat band with C = 2 by lifting their degeneracy and merging their topological indices. Exact diagonalization calculation reveals that this engineered band hosts two fractional Chern insulator states with C = 2/3 and 2/5, respectively. An experimental setup is proposed to simulate these states using cold alkaline-earth-like atoms in an effective bilayer optical lattice. Our work provides a general and widely applicable strategy for constructing higher Chern number flat bands, opening a pathway to explore exotic fractional quantum phases.