Magnetic quantization in multilayer graphenes

TL;DR

This paper explores how the stacking order and number of layers in multilayer graphene influence its Landau levels, revealing diverse electronic, optical, and transport properties with theoretical predictions aligning with experimental data.

Contribution

It provides a comprehensive analysis of Landau levels in multilayer graphene with various stacking configurations, highlighting new theoretical features and their experimental implications.

Findings

Landau levels split into N groups based on stacking

Distinct Landau level behaviors for AA, AB, and ABC stackings

Predicted novel features not yet experimentally verified

Abstract

Essential properties of multilayer graphenes are diversified by the number of layers and the stacking configurations. For an $N$-layer system, Landau levels are divided into $N$ groups, with each identified by a dominant sublattice associated with the stacking configuration. We focus on the main characteristics of Landau levels, including the degeneracy, wave functions, quantum numbers, onset energies, field-dependent energy spectra, semiconductor-metal transitions, and crossing patterns, which are reflected in the magneto-optical spectroscopy, scanning tunneling spectroscopy, and quantum transport experiments. The Landau levels in AA-stacked graphene are responsible for multiple Dirac cones, while in AB-stacked graphene the Dirac properties depend on the number of graphene layers, and in ABC-stacked graphene the low-lying levels are related to surface states. The Landau-level mixing leads to anticrossings patterns in energy spectra, which are seen for intergroup Landau levels in AB-stacked graphene, while in particular, a formation of both intergroup and intragroup anticrossings is observed in ABC-stacked graphene. The aforementioned magneto-electronic properties lead to diverse optical spectra, plasma spectra, and transport properties when the stacking order and the number of layers are varied. The calculations are in agreement with optical and transport experiments, and novel features that have not yet been verified experimentally are presented.