Massless Dirac-Weyl Fermions in a T_3 Optical Lattice

TL;DR

This paper proposes an experimental setup using a T_3 optical lattice with cold fermionic atoms to observe massless Dirac-Weyl fermions with a pseudo-spin of 1, revealing unique spectral features.

Contribution

It introduces a T_3 lattice setup that generalizes the Dirac-Weyl Hamiltonian to pseudo-spin 1, enabling the study of novel relativistic-like fermionic behavior in cold atom systems.

Findings

Identification of a T_3 lattice that hosts massless Dirac-Weyl fermions.

Discovery of a dispersionless localized state branch in the spectrum.

Discussion of Landau level implications for the T_3 lattice.

Abstract

We propose an experimental setup for the observation of quasi-relativistic massless Fermions. It is based on a T_3 optical lattice, realized by three pairs of counter-propagating lasers, filled with fermionic cold atoms. We show that in the long wavelength approximation the T_3 Hamiltonian generalizes the Dirac-Weyl Hamiltonian for the honeycomb lattice, however, with a larger value of the pseudo-spin 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.