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

TL;DR

This paper introduces a generalized Peierls substitution method combined with tight-binding models to analyze magnetic effects and quantum Hall phenomena in twisted multilayer graphene, covering various twist angles and their impact on electronic properties.

Contribution

It develops a unified theoretical framework for studying magnetic quantization in twisted multilayer graphene, including large and small twist angles, and elucidates the role of twisting in electronic behavior.

Findings

Band structures and Landau levels depend on twist angle.

Unique inter-Landau level transition rules identified.

Quantum Hall conductivity exhibits twist-dependent features.

Abstract

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 (LLs), and quantum Hall conductivity (QHC) of twisted bilayer graphene and twisted double bilayer graphene, as well as their dependence on the twist angle. Comparison between these crucial properties of monolayer graphene, Bernal bilayer graphene, and the twisted systems is carefully made to highlight the roles played by twisting. The unique selection rules of inter-LL transition, which is crucial for achieving a deep understanding of the step structures of QHC, are identified through the properties of LL wave functions. 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.