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

This work aims at addressing an important advanced methodology for twisted graphene in the presence of applied magnetic field, which is Bloch-basis tight-binding model (TBM) conjunction with generalized Peierls substitution. We investigate extensively band structures, Landau levels (LLs), and quantum Hall conductivity (QHC) bilayer double-bilayer graphene, as well their dependence on twist angle. Comparison between these crucial properties monolayer Bernal systems carefully made to highlight roles played by twisting. The unique selection rules inter-LL transition, achieving a deep understanding step structures QHC, are identified through LL wave functions. effective TBM combined substitution quantization magic Our theoretical opens up opportunity comprehension interplay field twisting effect associated layered graphene. proposed method expected be applicable calculation problems other complex systems.