Lattice relaxation, mirror symmetry and magnetic field effects on ultraflat bands in twisted trilayer graphene

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