Barrier transmission of Dirac-like pseudospin-one particles

We address the problem of barrier tunneling in the two-dimensional T₃ 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.