Twisted graphene multilayers exhibit strongly correlated insulating states and superconductivity due to the presence of ultraflat bands near the charge neutral point. In this paper, the response of ultraflat bands to lattice relaxation and a magnetic field in twisted trilayer graphene (tTLG) with different stacking arrangements is investigated by using a full tight-binding model. We show that lattice relaxations are indispensable for understanding the electronic properties of tTLG, in particular, of tTLG in the presence of mirror symmetry. Lattice relaxations renormalize the quasiparticle spectrum near the Fermi energy and change the localization of higher energy flat bands. Furthermore, different from the twisted bilayer graphene, the Hofstadter butterfly spectrum can be realized at laboratory accessible strengths of magnetic field. Our work verifies tTLG as a more tunable platform than the twisted bilayer graphene in strongly correlated phenomena.

扭曲的石墨烯多层膜由于在电荷中性点附近存在超平带，因此表现出高度相关的绝缘状态和超导性。在本文中，通过使用完全紧密结合模型研究了具有不同堆叠排列的扭曲三层石墨烯（tTLG）中超平坦带对晶格弛豫和磁场的响应。我们表明，晶格弛豫对于理解tTLG的电子特性是必不可少的，特别是在存在镜面对称性的情况下tTLG的电子特性。晶格弛豫使费米能量附近的准粒子谱重新规范化，并改变了高能平带的定位。此外，与扭曲的双层石墨烯不同，霍夫施塔特蝴蝶光谱可以在实验室可及的磁场强度下实现。