Quantum spin orbital liquids (QSOLs) are a novel phase of matter, similar to quantum spin liquids, with quantum fluctuations in both spin and orbital degrees of freedom. We use nonequilibrium Green's function theory to study out-of-equilibrium spin transport in an exactly solvable QSOL model put forward by Yao and Lee. We find that the spin transport problem can be mapped to that of a free fermion problem with effective fermionic baths that have a rapidly varying density of states. In the gapless phase, the spin current $I_s\text{−}{V}_s$ relation is thus highly nonlinear, while in the chiral gapped phase, the spin current conductance is quantized to be $1/2\pi$ provided that the contacts are sufficiently wide. The quantized conductance is a signature of the topological nature of the chiral gapped QSOL.

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• Spin liquid
• Transport phenomena
• Chiral symmetry
• Nonequilibrium Green's function