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We describe a new class of spin liquids with global SU(2) spin rotationsymmetry in spin 1/2 systems on the triangular lattice, which have realMajorana fermion excitations carrying spin S = 1. The simplesttranslationally-invariant mean-field state on the triangular lattice breakstime-reversal symmetry and is stable to fluctuations. It generically possessesgapless excitations along 3 Fermi lines in the Brillouin zone. These intersectat a single point where the excitations scale with a dynamic exponent z = 3. Anexternal magnetic field has no orbital coupling to the SU(2) spinrotation-invariant fermion bilinears that can give rise to a transverse thermalconductivity, thus leading to the absence of a thermal Hall effect. The Zeemancoupling is found to gap out two-thirds of the z = 3 excitations near theintersection point and this leads to a suppression of the low temperaturespecific heat, the spin susceptibility and the Wilson ratio. We also computephysical properties in the presence of weak disorder and discuss possibleconnections to recent experiments on organic insulators.

SU(2)-invariant spin liquids on the triangular lattice with spinful Majorana excitations