▎ 摘　　要

Graphene is a promising material for designing next-generation electronic and valleytronic devices, which often demand the opening of a bandgap in the otherwise gapless pristine graphene. To date, several conceptually different mechanisms have been extensively exploited to induce., bandgaps in graphene, including spin-orbit coupling and inversion symmetry breaking for monolayer graphene, and quantum confinement for graphene nanoribbons (GNRs). Here, we present a multiscale study of the competing gap opening mechanisms in a graphene overlayer and GNRs proximity-coupled to topological insulators (TIs). We obtain sizable graphene bandgaps even without inversion symmetry breaking and identify the Kekule lattice distortions caused by the TI substrates to be the dominant gap opening mechanism. Furthermore, Kekule distorted armchair GNRs display intriguing non monotonous gap dependence on the nanoribbon width, resulting from the coexistence of quantum confinement, edge passivation, and Kekule distortions. The present study offers viable new approaches for tunable bandgap engineering in graphene and GNRs.