By using Gutzwiller projected fermionic wave functions and variational Monte Carlo technique, we study the spin-
1/2 Heisenberg model with the first-neighbor (
J1), second-neighbor (
J2), and additional scalar chiral interaction ${J}_{\ensuremath{\chi}}{\mathbf{S}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}({\mathbf{S}}_{j}\ifmmode\times\else\texttimes\fi{}{\mathbf{S}}_{k})$ on the triangular lattice. In the nonmagnetic phase of the ${J}_{1}\ensuremath{-}{J}_{2}$ triangular model with $0.08\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.16$, recent density-matrix renormalization group (DMRG) studies [Zhu and White, Phys. Rev. B 92, 041105(R) (2015) and Hu, Gong, Zhu, and Sheng, Phys. Rev. B 92, 140403(R) (2015)] find a possible gapped spin liquid with the signal of a competition between a chiral and a
Z2 spin liquid. Motivated by the DMRG results, we consider the chiral interaction ${J}_{\ensuremath{\chi}}{\mathbf{S}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}({\mathbf{S}}_{j}\ifmmode\times\else\texttimes\fi{}{\mathbf{S}}_{k})$ as a perturbation for this nonmagnetic phase. We find that with growing ${J}_{\ensuremath{\chi}}$, the gapless U(1) Dirac spin liquid, which has the best variational energy for ${J}_{\ensuremath{\chi}}=0$, exhibits the energy instability towards a gapped spin liquid with nontrivial magnetic fluxes and nonzero chiral order. We calculate topological Chern number and ground-state degeneracy, both of which identify this flux state as the chiral spin liquid with fractionalized Chern number
C=1/2 and twofold topological degeneracy. Our results indicate a positive direction to stabilize a chiral spin liquid near the nonmagnetic phase of the ${J}_{1}\ensuremath{-}{J}_{2}$ triangular model.
Recent work has shown that the triangular lattice spin-$\frac{1}{2} {J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg and XXZ antiferromagnets may exhibit coplanar or supersolid orders proximate to a gapless Dirac spin-liquid phase. We explore a distinct $\text{SU}(2N)\ifmmode\times\else\texttimes\fi{}\text{SU}(M)$ fermionic parton approach, complemented by variational Monte Carlo calculations for the spin-
21 model, to study the phase diagram of these models. We also calculate their dynamical spin response including parton interactions within a random-phase approximation, and discuss implications for neutron scattering on triangular lattice cobaltates
Ba3CoSb2O9,Na2BaCo(PO4)2,K2Co(SeO3)2,Rb2Co(SeO3)2, and Yb-based magnet
KYbSe2.