Three-dimensional Dirac-like fermions in an optical lattice

We present a scheme to realize three-dimensional Dirac-like fermions with an edge-centered cubic optical lattice. We propose a method to construct the optical edge-centered cubic crystals and then determine the parameters required for the description of the systems with a tight-binding model. Interestingly, we show that the low-energy quasiparticles are three-dimensional massive or massless Dirac-like fermions determined by the parameters of the system. In addition, two three-dimensional degenerate flat bands lie between the upper and the lower branches of the Dirac dispersion. Furthermore, we demonstrate that the Dirac dispersion relation and the flat bands can be verified by the density profile measurement.