Gapless Spin Liquids on the Three-Dimensional Hyperkagome Lattice of Na4Ir3O8

Recent experiments indicate that Na4Ir3O8, a material in which s=1/2 Ir local moments live on a three-dimensional hyperkagome lattice of corner-sharing triangles, may have a quantum spin liquid ground state with gapless spin excitations. Using a combination of exact diagonalization, symmetry analysis of fermionic mean field ground states and Gutzwiller projected variational wave functions studies, we propose a quantum spin liquid with spinon Fermi surfaces as a favorable candidate for the ground state of the Heisenberg model on this lattice. We point out implications of this proposal for thermodynamic properties and discuss possible weak instabilities of the spinon Fermi surfaces.