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Moir\'e systems have emerged in recent years as a rich platform to studystrong correlations. Here, we will discuss a simple, experimentally feasiblesetup based on periodically strained graphene that reproduces several keyaspects of twisted moir\'e heterostructures -- but without introducing a twist.We consider a monolayer graphene sheet subject to a $C_2$-breaking periodicstrain-induced psuedomagnetic field (PMF) with period $L_M \gg a$, along with ascalar potential of the same period. This system has {\it almost ideal} flatbands with valley-resolved Chern number $\pm 1$, where the deviation from idealband geometry is analytically controlled and exponentially small in thedimensionless ratio $(L_M/l_B)^2$ where $l_B$ is the magnetic lengthcorresponding to the maximum value of the PMF. Moreover, the scalar potentialcan tune the bandwidth far below the Coulomb scale, making this a verypromising platform for strongly interacting topological phases. Using acombination of strong-coupling theory and self-consistent Hartree fock, we findquantum anomalous Hall states at integer fillings. At fractional filling, exactdiagonaliztion reveals a fractional Chern insulator at parameters in theexperimentally feasible range. Overall, we find that this system has largerinteraction-induced gaps, smaller quasiparticle dispersion, and enhancedtunability compared to twisted graphene systems, even in their ideal limit.

Untwisting moir\'e physics: Almost ideal bands and fractional Chern insulators in periodically strained monolayer graphene