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Recently a new high-mobility Dirac material, trilayer graphene, was realizedexperimentally. The band structure of ABA-stacked trilayer graphene consists ofa monolayer-like and a bilayer-like pairs of bands. Here we study electronicproperties of ABA-stacked trilayer graphene biased by a perpendicular electricfield. We find that the combination of the bias and trigonal warping gives riseto a set of new Dirac points: in each valley, seven species of Dirac fermionswith small masses of order of a few meV emerge. The positions and masses of theemergent Dirac fermions are tunable by bias, and one group of Dirac fermionsbecomes massless at a certain bias value. Therefore, in contrast to bilayergraphene, the conductivity at the neutrality point is expected to shownon-monotonic behavior, becoming of the order of a few e^2/h when some Diracmasses vanish. Further, we analyze the evolution of Landau level spectrum as afunction of bias. Emergence of new Dirac points in the band structuretranslates into new three-fold-degenerate groups of Landau levels. This leadsto an anomalous quantum Hall effect, in which some quantum Hall steps have aheight of 3e^2/h. At an intermediate bias, the degeneracies of all Landaulevels get lifted, and in this regime all quantum Hall plateaus are spaced bye^2/h. Finally, we show that the pattern of Landau level crossings is verysensitive to certain band structure parameters, and can therefore provide auseful tool for determining their precise values.

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