Exotic S=1 spin liquid state with fermionic excitations on triangular lattice

Motivated by recent experiments on the material Ba_3NiSb_2O_9 we consider a spin-one quantum antiferromagnet on a triangular lattice with the Heisenberg bilinear and biquadratic exchange interactions and a single-ion anisotropy. Using a fermionic "triplon" representation for spins, we study the phase diagram within mean field theory. In addition to a fully gapped spin-liquid ground state, we find a state where one gapless triplon mode with Fermi surface coexists with d + id topological pairing of the other triplons. Despite the existence of a Fermi surface, this ground state has fully gapped bulk spin excitations. Such a state has linear in temperature specific heat and constant in plane spin susceptibility, with an unusually high Wilson ratio.