  We report on the transport properties of ABC and ABA stacked trilayer
graphene using dual, locally gated field effect devices. The high efficiency
and large breakdown voltage of the HfO2 top and bottom gates enables
independent tuning of the perpendicular electric field and the Fermi level over
an unprecedentedly large range. We observe a resistance change of six orders of
magnitude in the ABC trilayer, which demonstrates the opening of a band gap.
Our data suggest that the gap saturates at a large displacement field of D ~ 3
V/nm, in agreement with self-consistent Hartree calculations. In contrast, the
ABA trilayer remains metallic even under a large perpendicular electric field.
Despite the absence of a band gap, the band structure of the ABA trilayer
continues to evolve with increasing D. We observe signatures of two-band
conduction at large D fields. Our self-consistent Hartree calculation
reproduces many aspects of the experimental data, but also points to the need
for more sophisticated theory.
