Spinon Fermi surface U(1) spin liquid in the spin-orbit-coupled triangular-lattice Mott insulator YbMgGaO4

Motivated by the recent progress in the spin-orbit-coupled triangular lattice spin liquid candidate ${\mathrm{YbMgGaO}}_{4}$, we carry out a systematic projective symmetry group analysis and mean-field study of candidate $U(1)$ spin-liquid ground states. Due to the spin-orbital entanglement of the Yb moments, the space-group symmetry operation transforms both the position and the orientation of the local moments, and hence it brings different features for the projective realization of the lattice symmetries from the cases with spin-only moments. Among the eight $U(1)$ spin liquids that we find with the fermionic parton construction, only one spin-liquid state, which was proposed and analyzed by Yao Shen et al. [Nature (London) 540, 559 (2016)] and labeled as U1A00 in the present work, stands out and gives a large spinon Fermi surface and provides a consistent explanation for the spectroscopic results in ${\mathrm{YbMgGaO}}_{4}$. Further connection of this spinon Fermi surface $U(1)$ spin liquid with ${\mathrm{YbMgGaO}}_{4}$ and the future directions are discussed. Finally, our results may apply to other spin-orbit-coupled triangular lattice spin-liquid candidates, and more broadly, our general approach can be well extended to spin-orbit-coupled spin-liquid candidate materials.