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

Moir\'e systems have emerged in recent years as a rich platform to study strong correlations. Here, we will discuss a simple, experimentally feasible setup based on periodically strained graphene that reproduces several key aspects of twisted moir\'e heterostructures -- but without introducing a twist. We consider a monolayer graphene sheet subject to a $C_2$-breaking periodic strain-induced psuedomagnetic field (PMF) with period $L_M \gg a$, along with a scalar potential of the same period. This system has {\it almost ideal} flat bands with valley-resolved Chern number $\pm 1$, where the deviation from ideal band geometry is analytically controlled and exponentially small in the dimensionless ratio $(L_M/l_B)^2$ where $l_B$ is the magnetic length corresponding to the maximum value of the PMF. Moreover, the scalar potential can tune the bandwidth far below the Coulomb scale, making this a very promising platform for strongly interacting topological phases. Using a combination of strong-coupling theory and self-consistent Hartree fock, we find quantum anomalous Hall states at integer fillings. At fractional filling, exact diagonaliztion reveals a fractional Chern insulator at parameters in the experimentally feasible range. Overall, we find that this system has larger interaction-induced gaps, smaller quasiparticle dispersion, and enhanced tunability compared to twisted graphene systems, even in their ideal limit.