Tunable topological narrow bands in twisted bilayer-trilayer graphene

RESUMO

We investigate the low-energy band structure and topology of twisted bilayer--trilayer graphene with four stacking configurations: AB--ABC, BA--ABC, AB--ABA, and BA--ABA. Using both tight-binding and continuum models, we first establish that the two approaches show good agreement in the band structure in low-energy regime. We then study the evolution of the flat bands and their valley Chern numbers as functions of twist angle, perpendicular electric field, and the self-consistent Hartree potential. At relatively large twist angles and under electric field, we find a topological transition between the narrow bands, with the total Chern number of the flat bands following the Chern number sum rules derived from the chiral-limit description. We also observe another type of topological transition when the flat bands hybridize with adjacent remote bands, where gap closing and reopening processes lead to Chern number and charge density transfer. By constructing topological phase diagrams in the space of twist angle and electric field, we show that the perpendicular electric field provides an efficient tuning knob for controlling the stability and transitions of the Chern bands. Finally, we find that the Hartree potential mainly induce weak band shifts and reshaping in the narrow bands. However, with a combination of Hartree potential and the electric fields, the narrow bands show rich topological phase diagram. Our results clarify the interplay between the stacking, twist angle and electric field in manipulating the narrow bands and their topology in twisted bilayer--trilayer graphene, and provide guidance for engineering topological narrow bands with tunable Chern numbers in realistic twisted multilayer graphene systems.