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We theoretically investigate, within the Schwinger-Boson mean-field theory,the transition from a gapped $Z_{2}$ quantum spin-liquid, in a $J_1$-$J_2$Heisenberg spin-1/2 system in a honeycomb lattice, to a chiral $Z_2$ spinliquid phase under the presence of time-reversal symmetry breaking scalarchiral interaction (with amplitude $J_{\chi}$), with non-trivial Chern bands ofthe excitations. We numerically obtain a phase diagram of such$J_1$-$J_2$-$J_{\chi}$ system, where different phases are distinguished basedon the gap and the nature of excitation spectrum, topological invariant of theexcitations, the nature of spin-spin correlation and the symmetries of themean-field parameters. The chiral $Z_2$ state is characterized by non-trivialChern number of the excitation bands and lack of long-range magnetic order,which leads to large thermal Hall coefficient.

Schwinger-Boson mean-field study of spin-1/2 $J_1$-$J_2$-$J_{\chi}$ model in honeycomb lattice: thermal Hall signature