Massless Dirac-Weyl fermions in aT3optical lattice

Abstract

We propose an experimental setup for the observation of quasirelativistic massless fermions. It is based on a ${\mathcal{T}}_3$ optical lattice, realized by three pairs of counterpropagating lasers, filled with fermionic cold atoms. We show that in the long wavelength approximation the ${\mathcal{T}}_3$ Hamiltonian generalizes the Dirac-Weyl Hamiltonian for the honeycomb lattice, however, with a larger value of the pseudospin $S=1$. In addition to the Dirac cones, the spectrum includes a dispersionless branch of localized states producing a finite jump in the atomic density. Furthermore, implications for the Landau levels are discussed.