▎ 摘　　要

We investigate the band structure of twisted monolayer-bilayer graphene (tMBG) trilayers, or twisted graphene on bilayer graphene, as a function of twist angles and perpendicular electric fields in search of optimal conditions for achieving isolated nearly flat bands. Narrow bandwidths comparable to or smaller than the effective Coulomb energies satisfying U-eff/W greater than or similar to 1 are expected for twist angles in the range of 0.3 degrees-1.5 degrees, more specifically in islands around theta similar to 0.5 degrees, 0.85 degrees, 1.3 degrees for appropriate perpendicular electric field magnitudes and directions. The valley Chern numbers of the electron-hole asymmetric bands depend intrinsically on the details of the hopping terms in the bilayer graphene, and extrinsically on factors like electric fields or average staggered potentials in the graphene layer aligned with the contacting hexagonal boron nitride substrate. This tunability of the band isolation, bandwidth, and valley Chern numbers makes tMBG trilayers a more versatile system than twisted bilayer graphene for finding nearly flat bands prone to strong correlations.