  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.
