The U(1) Spin Liquids in a Spin-Orbit-Coupled Triangular Lattice Mott Insulator: the Projective Symmetry Group Analysis and Spectroscopic Study

Motivated by the recent progress on the spin-orbit-coupled triangular lattice spin liquid candidate material YbMgGaO$_4$, we carry out a systematic projective symmetry group analysis of the candidate spin liquid ground states. Due to the spin-orbit entanglement of the Yb$^{3+}$ $4f$ local moments, the space group symmetry operation transforms the position and the orientation of the local moments simultaneously, and hence brings new ingredients to the symmetry fractionalization and the projective realization in the candidate spin liquid phases. Based on the early proposal of the spinon Fermi surface U(1) spin liquid for YbMgGaO$_4$, we classify the U(1) spin liquid using the fermionic parton construction. We find eight U(1) spin liquids with distinct symmetry fractionalization patterns for the R$\bar{3}$m space group symmetry that is appropriate for YbMgGaO$_4$. The spectroscopic results are computed within the mean-field approximation for each U(1) spin liquid. The connection with the experiments in YbMgGaO$_4$ and the future directions are discussed.