Dirac lines in the superconducting hyper-honeycomb lattice

Motivated by the recent discovery of the hyper-honeycomb $\beta$-Li$_2$IrO$_3$ studied in the context of Kitaev spin liquids, we investigate the possibility to realize superconductivity in the hyper-honeycomb lattice. Based on a t-J model we discuss the effect of the band structure and spin-orbit coupling on the most stable superconducting state. Using group theory we construct all symmetry allowed superconducting states and show that we naturally get Dirac line nodes protected by the non-symmorphic symmetries.