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

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 pair 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 nonmonotonic behavior, becoming of the order of a few ${e}^{2}/h$ when some Dirac masses vanish. Further, we analyze the evolution of the Landau level spectrum as a function of bias. The emergence of new Dirac points in the band structure translates into new threefold-degenerate groups of Landau levels. This leads to an anomalous quantum Hall effect, in which some quantum Hall steps have a height of $3{e}^{2}/h$. 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.