Hofstadter Butterfly In Twisted Trilayer Graphene

The Morie lattice in twisted trilayer graphene(tTLG) exhibits magic angle flat band phenomena along with superconductivity. In this talk, we will discuss the energy dispersion of tTLG and Hofstadter butterfly patterns at high magnetic field, as a function of the displacement field and twist angle. We show that for zero displacement field tTLG exhibits mirror symmetry, with even parity twisted bilayer graphene Hofstadter bands and odd parity Dirac Landau levels. We calculate the Chern numbers associated with the energy gaps in of tTLG at high magnetic field. We also show that as the displacement field is increased, the Hofstadter bands hybridize with the relativistic Landau levels and identify and characterize topological transition as a function of the displacement field and twist angle.