Landau Level Spectrum of ABA- and ABC-stacked Trilayer Graphene

TL;DR

This paper analyzes the Landau level spectrum of ABA- and ABC-stacked trilayer graphene, deriving analytic expressions and exploring effects of electric fields, with implications for electronic transport and resonance experiments.

Contribution

It provides the first analytic low-energy expressions for the Landau levels in trilayer graphene with different stacking orders, validated by tight-binding calculations.

Findings

ABC stacking exhibits a zero-energy plateau under electric field due to a gap opening.

ABA stacking remains metallic under electric field.

Derived expressions aid analysis of cyclotron resonance measurements.

Abstract

We study the Landau level spectrum of ABA- and ABC-stacked trilayer graphene. We derive analytic low energy expressions for the spectrum, the validity of which is confirmed by comparison to a \pi -band tight-binding calculation of the density of states on the honeycomb lattice. We further study the effect of a perpendicular electric field on the spectrum, where a zero-energy plateau appears for ABC stacking order, due to the opening of a gap at the Dirac point, while the ABA-stacked trilayer graphene remains metallic. We discuss our results in the context of recent electronic transport experiments. Furthermore, we argue that the expressions obtained can be useful in the analysis of future measurements of cyclotron resonance of electrons and holes in trilayer graphene.