First-principles Study of Nearly Flat Bands in Monolayer Graphene Induced by Periodic Strains

Flat bands in condensed matter systems are of profound interest due to their potential for hosting exotic correlated and topological states. While their theoretical foundations are well-established in select lattice geometries (e.g., Lieb and Kagome lattices) and moir'e systems like twisted bilayer graphene, experimental realizations remain challenging. Recent advances propose a simpler, strain-based approach: nearly flat bands in periodically strained monolayer graphene were predicted using tight-binding models, offering a promising experimental pathway. In this work, we perform first-principles calculations to systematically investigate the emergence of nearly flat bands in monolayer graphene under periodic strains. Our results demonstrate that even considering lattice relaxation, these flat bands arise robustly across a well-defined range of strain amplitudes for multiple modulation periods. Furthermore, through a strained Kagome lattice model based on first-principles calculation results, we compute the topological properties of the nearly flat bands in monolayer graphene under periodic strain, revealing nonzero valley Chern numbers.