Dirac loops in trigonally connected 3D lattices
  We consider different generalizations of the honeycomb lattice to three dimensional structures. We address the family of the hyper-honeycomb lattice, which is made up of alternating layers of 2D honeycomb nano-ribbons, with each layer rotated by $\pi/2$ with the layer below. When the orbitals of the lattice sites are symmetric with respect to the planes of the trigonal links, these structures can produce a Dirac loop, a closed line of Dirac nodes in momentum space. For orbitals that break that symmetry, such as the carbon $p$-wave orbitals, hyper-honeycomb lattices do not possess the loop structure. We also consider a new structure, the screw hyper-honeycomb, in which the successive layers of parallel units are rotated by $2\pi/3$. This structure has a Dirac loop if reflection symmetry in the unit cell is imposed, regardless the symmetry of the onsite orbitals. We discuss the implementation of those systems in optical lattices. 
Kieran Mullen, Bruno Uchoa, Bin Wang and Daniel Glatzhofer
cond-mat.mes-hall