Engineering Fractional Chern Insulators through Periodic Strain in Monolayer Graphene and Transition Metal Dichalcogenides

TL;DR

This paper demonstrates that periodically strained monolayer graphene and TMDs can host various fractional Chern insulators, including novel high-C states, through extensive many-body simulations, revealing new topological phases and challenging existing theories.

Contribution

It introduces a method to realize and analyze fractional Chern insulators with tunable topological orders in strained 2D materials, including high-C states, using exact diagonalization.

Findings

Evidence for Laughlin and Halperin states in strained monolayer materials.

Discovery of Laughlin-like topological order in high-C (|C|=2) bands.

Insights into the relationship between band geometry, filling, and spin polarization.

Abstract

We propose the realization of interaction-driven insulators in periodically strained monolayer graphene and transition metal dichalcogenides (TMDs). Through extensive many-body exact diagonalization, we provide compelling evidence for various fractional Chern insulators (FCIs) in both strained monolayer graphene and TMDs, including the Laughlin states, Halperin states, and FCIs with tunable topological orders in Chern number |C| = 2 bands. We also discuss the relationship among band geometry, band filling and spin polarization. Notably, by examining both the entanglement spectrum and many-body Chern number, we reveal a state with Laughlin-like topological order emerging in the |C| = 2 band, which challenges the existing theoretical understanding of high Chern number (high-C) FCIs. These findings suggest that periodically strained monolayer graphene and TMDs provide promising platforms for engineering fractional Chern insulators and underscore the need for further investigation into high-C FCIs.