  We address the problem of barrier tunneling in the two-dimensional T_3
lattice (dice lattice). In particular we focus on the low-energy,
long-wavelength approximation for the Hamiltonian of the system, where the
lattice can be described by a Dirac-like Hamiltonian associated with a
pseudospin one. The enlarged pseudospin S = 1 (instead of S = 1/2 as for
graphene) leads to an enhanced "super" Klein tunneling through rectangular
electrostatic barriers. Our results are confirmed via numerical investigation
of the tight-binding model of the lattice. For a uniform magnetic field, we
discuss the Landau levels and we investigate the transparency of a rectangular
magnetic barrier. We show that the latter can mainly be described by
semiclassical orbits bending the particle trajectories, qualitatively similar
as it is the case for graphene. This makes it possible to confine particles
with magnetic barriers of sufficient width.
