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 $\left|\mathcal{C}\right|=2$ 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 $\left|\mathcal{C}\right|=2$ band, which challenges the existing theoretical understanding of high Chern number (high-$\mathcal{C}$) 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-$\mathcal{C}$ FCIs.

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• Chern insulators
• Fractional quantum Hall effect
• Graphene
• Transition metal dichalcogenides
• Exact diagonalization