  We study the electronic properties of a twisted trilayer graphene, where two
of the layers have Bernal stacking and the third one has a relative rotation
with respect to the AB-stacked layers. Near the Dirac point, the AB-twisted
trilayer graphene spectrum shows two parabolic Bernal-like bands and a
twisted-like Dirac cone. For small twist angles, the parabolic bands present a
gap that increases for decreasing rotation angle. There is also a shift in the
twisted-like Dirac cone with a similar angle dependence. We correlate the gap
in the trilayer with the shift of the Dirac cone in an isolated twisted
bilayer, which is due to the loss of electron-hole symmetry caused by
sublattice mixing in the rotated geometry. Using a tight-binding and a
continuum model, we derive an effective Hamiltonian which accounts for the
relevant low-energy properties of this system.
