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

Po-Hsin Shih^2*, Thi-Nga Do¹, Godfrey Gumbs², Danhong Huang³

¹Department of Physics, National Cheng Kung University, Tainan, Taiwan
²Department of Physics and Astronomy, City University of New York, New York, USA
³US Air Force Research Laboratory, Kirtland Air Force Base, Albuquerque, New Mexico, USA

* Presenter:Po-Hsin Shih, email:phshih@phys.ncku.edu.tw

We propose a generalized Peierls substitution method in conjunction with the tight-binding model to explore the magnetic quantization and quantum Hall effect in twisted multilayer graphene under a magnetic field. The Bloch-basis tight-binding Hamiltonian is constructed for large twist angle while a simplified tight-binding model is employed for the magic angle. We investigate extensively the band structures, Landau levels, and quantum Hall conductivity of twisted bilayer graphene and twisted double bilayer graphene, as well as their dependence on the twist angle. Our theoretical model opens up an opportunity for comprehension of the interplay between an applied magnetic field and the twisting effect associated with multilayer graphene.

Keywords: Peierls substitution, Twisted multilayer graphene, Landau levels, quantum Hall effect, tight-binding model