Chiral magic-angle twisted bilayer graphene in a magnetic field: Landau level correspondence, exact wave functions, and fractional Chern insulators

We show that the flat bands in the chiral model of magic-angle twisted bilayer graphene remain exactly flat in the presence of a perpendicular magnetic field. This is shown by an exact mapping between the model and the lowest Landau level wave functions at an effective magnetic field, in which the external field is either augmented or reduced by one flux quantum per unit cell. When the external field reaches one flux quantum per unit cell, the model exhibits a topological phase transition. These findings allow us to analyze a Jain series of fractional Chern insulators states in the exactly flat band, and to point out an unconventional dependence of the energy gap on the magnetic field.

Automated summary

In the chiral model of magic-angle twisted bilayer graphene, the flat bands remain exactly flat in the presence of a perpendicular magnetic field, with an exact mapping to the lowest Landau level wave functions under an effective magnetic field. A topological phase transition occurs when the external field reaches a specific value, allowing for analysis of fractional Chern insulators states. Unconventional dependence of the energy gap on the magnetic field is also observed.