New Dirac points and multiple Landau level crossings in biased trilayer graphene

TL;DR

This paper investigates how bias and trigonal warping in ABA-stacked trilayer graphene create new Dirac points and Landau level crossings, leading to tunable electronic properties and anomalous quantum Hall effects.

Contribution

It reveals the emergence of multiple tunable Dirac points and Landau level crossings in biased trilayer graphene, differing from bilayer graphene and enabling new quantum Hall phenomena.

Findings

Seven species of Dirac fermions emerge with bias-tunable masses.

New Landau level groups lead to anomalous quantum Hall steps of 3e^2/h.

Landau level degeneracies are highly sensitive to band structure parameters.

Abstract

Recently a new high-mobility Dirac material, trilayer graphene, was realized experimentally. The band structure of ABA-stacked trilayer graphene consists of a monolayer-like and a bilayer-like pairs of bands. Here we study electronic properties of ABA-stacked trilayer graphene biased by a perpendicular electric field. We find that the combination of the bias and trigonal warping gives rise to a set of new Dirac points: in each valley, seven species of Dirac fermions with small masses of order of a few meV emerge. The positions and masses of the emergent Dirac fermions are tunable by bias, and one group of Dirac fermions becomes massless at a certain bias value. Therefore, in contrast to bilayer graphene, the conductivity at the neutrality point is expected to show non-monotonic behavior, becoming of the order of a few e^2/h when some Dirac masses vanish. Further, we analyze the evolution of Landau level spectrum as a function of bias. Emergence of new Dirac points in the band structure translates into new three-fold-degenerate groups of Landau levels. This leads to an anomalous quantum Hall effect, in which some quantum Hall steps have a height of 3e^2/h. At an intermediate bias, the degeneracies of all Landau levels get lifted, and in this regime all quantum Hall plateaus are spaced by e^2/h. Finally, we show that the pattern of Landau level crossings is very sensitive to certain band structure parameters, and can therefore provide a useful tool for determining their precise values.