Topological flat bands in twisted trilayer graphene

Twisted trilayer graphene (TLG) may be the simplest realistic system so far, which has flat bands with nontrivial topology. Here, we give a comprehensive calculation about its band structures and the band topology, i.e., valley Chern number of the nearly flat bands, with the continuum model. With realistic parameters, the magic angle of twisted TLG is about 1.12 degrees, at which two nearly flat bands appears. Unlike the twisted bilayer graphene, a small twist angle can induce a tiny gap at all the Dirac points, which can be enlarged further by a perpendicular electric field. The valley Chern numbers of the two nearly flat bands in the twisted TLG depends on the twist angle theta and the perpendicular electric field E-perpendicular to. Considering its topological flat bands, the twisted TLG should be an ideal experimental platform to study the strongly correlated physics in topologically nontrivial flat band systems. And, due to its reduced symmetry, the correlated states in twisted TLG should be quite different from that in twisted bilayer graphene and twisted double bilayer graphene. (C) 2020 Science China Press. Published by Elsevier B.V. and Science China Press. All rights reserved.

Automated summary

Twisted trilayer graphene is a simple realistic system with flat bands and nontrivial topology, making it an ideal platform for studying strongly correlated physics. The band structures of twisted TLG are influenced by the twist angle and perpendicular electric field, resulting in unique correlated states compared to other graphene structures.