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$°$, 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 $E_{\perp }$. 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.

扭曲三层石墨烯 (TLG) 可能是迄今为止最简单的现实系统，它具有非平凡拓扑结构的平带。在这里，我们使用连续介质模型对其能带结构和能带拓扑结构，即近平带的谷陈数进行了综合计算。现实参数下，扭曲TLG的魔角约为1.12$°$，出现两个几乎平坦的带。与扭曲的双层石墨烯不同，小的扭曲角可以在所有狄拉克点处产生微小的间隙，垂直电场可以进一步扩大间隙。扭曲的 TLG 中两个近乎平坦的带的谷陈数取决于扭曲角$\theta$和垂直电场${乙}_{\perp }$. 考虑到其拓扑平带，扭曲的 TLG 应该是研究拓扑非平凡平带系统中强相关物理的理想实验平台。而且，由于其对称性降低，扭曲 TLG 中的相关态应该与扭曲双层石墨烯和扭曲双双层石墨烯中的相关态完全不同。