Flat bands and extreme pseudomagnetic fields in monolayer graphene by topography strain engineering

Realizing flat bands via strong pseudomagnetic fields has recently inspired new opportunities for studying strong correlations in monolayer graphene, where a feasible idea is to utilize substrate topography to create strained graphene superlattices. Nevertheless, the effect from topography-induced strain relaxation on these isolated flat bands in monolayer graphene is unknown, posing challenges for rational design on flat bands and pseudomagnetic fields by strain engineering. In this work, we reveal analytical displacement fields due to strain relaxation in monolayer graphene conforming to substrate topography, allowing quantum mechanical design on flat band structures and strong pseudomagnetic fields in monolayer graphene with strain energy minimized. We find that the strong pseudomagnetic fields as well as flat band structures in monolayer graphene are highly sensitive to strain relaxation and substrate topography. The tunability of flat bands in monolayer graphene coupled to several topography designs is demonstrated. Our results contribute to the understanding of flat bands and strong pseudomagnetic fields in monolayer graphene enabled by topography strain engineering.