  We propose the realization of interaction-driven insulators in periodically
strained monolayer graphene and transition metal dichalcogenides (TMDs). By
analyzing the tunable band structure and band geometry via strain, and
performing extensive many-body exact diagonalization of a realistic model, we
present compelling evidence for realizing various fractional Chern insulators
in both strained monolayer graphene and TMDs. Our thorough analysis across
different strain parameters, accounting for experimental variability, reveals
that a broad spectrum of fractional Chern insulators, including the Laughlin
states, Halperin 112, 332 and 111 states, and Chern number |C| = 2 states, can
be stabilized in distinct regions of the phase diagram. These findings suggest
that periodically strained monolayer graphene and TMDs provide promising
platforms for engineering fractional Chern insulators.
