Barrier transmission of Dirac-like pseudospin-one particles

Abstract

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

Diverging dc conductivity due to a flat band in a disordered system of pseudospin-1 Dirac-Weyl fermions

“…These can be regarded as the pseudospin-1 generalization of the Dirac equation, [6][7][8][9][10] and arise in the family of higher pseudospin generalizations of the Dirac equation, proposed in Refs. 11-13. While many of their properties are well understood, including topology, not much is known about their transport properties, 10 which promise many excitement in light of the fascinating transport properties of their pseudospin-1/2 counterpart in graphene. There, the universal value of the minimal conductivity at half-filling 14 attracted significant attention over the years, whereby the decreasing number of charge carriers as the charge neutrality point is approached exactly compensates their increasingly long lifetime.…”

Existence of bulk chiral fermions and crystal symmetry

“…Indeed, one can check that, while the E = 0 component is longitudinally polarized, the other two are transverse, just like the propagating components of a photon. Pseudospin-one Dirac points have been reported in some two [29][30][31] and three-dimensional 32 systems.…”

Conical intersections for light and matter waves

“…Namely, wave propagation is governed by an integer pseudospin variant of the Dirac equation, which displays unique effects such as resonant all-angle Klein tunnelling through potential barriers [43,44]. In this case, the prototypical example for studying the properties of integer pseudospin intersections has been the square-like "Lieb lattice" shown in Fig.…”