Coexistence of spin-1/2 and spin-1 Dirac-Weyl fermions in the edge-centered honeycomb lattice

We investigate the properties of an edge-centered honeycomb lattice, and show that this lattice features both spin-1/2 and spin-1 Dirac-Weyl fermions at different filling fractions f (f=1/5,4/5 for spin-1/2 and f=1/2 for spin-1). This five-band system is the simplest lattice that can support simultaneously the two different paradigmatic Dirac-Weyl fermions with half-integer spin and integer spin. We demonstrate that these pseudo-relativistic structures, including a flat band at half-filling, can be deduced from the underlying Kagome sublattice. We further show that the signatures of the two kinds of relativistic fermions can be clearly revealed by several perturbations, such as a uniform magnetic field, a Haldane-type spin-orbit term, and charge density waves. We comment on the possibility to probe the similarities and differences between the two kinds of relativistic fermions, or even to isolate them individually. We present a realistic scheme to realize such a system using cold atoms.