Generalized Peierls substitution for the tight-binding model of twisted graphene systems in a magnetic field

This work addresses an important advanced methodology for twisted layered graphene in the presence of applied magnetic field by combining the Bloch-basis tight-binding model (TBM) and the generalized Peierls substitution. We investigate extensively the band structures, Landau levels (LLs), and quantum Hall conductivity (QHC) of twisted bilayer graphene and twisted double-bilayer graphene at large angles and the magic angles. Our theoretical model opens up an opportunity for comprehension of the interplay between an applied magnetic field and the twisting effect associated with layered graphene. The proposed method is expected to be applicable for the calculation of magnetic quantization problems of other complex systems.