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I propose the emergence of the spin-orbital-coupled vector chirality in anon-frustrated Mott insulator with the strong spin-orbit coupling due to$ab$-plane's inversion-symmetry (IS) breaking. I derive the superexchangeinteractions for a $t_{2g}$-orbital Hubbard model on a square lattice with thestrong spin-orbit coupling and the IS-breaking-induced hopping integrals, andexplain the microscopic origins of the Dzyaloshinsky-Moriya (DM) -type and theKitaev-type interactions. Then, by adopting the mean-field approximation to aminimal model including only the Heisenberg-type and the DM-typenearest-neighbor interactions, I show that the IS breaking causes thespin-orbital-coupled chirality as a result of stabilizing the screw state. Ialso highlight the limit of the hard-pseudospin approximation in discussing thestability of the screw states in the presence of both the DM-type and theKitaev-type interactions, and discuss its meaning. I finally discuss theeffects of tetragonal crystal field and $J_{\textrm{eff}}=\frac{3}{2}$ states,and the application to the iridates near the $[001]$ surface ofSr$_{2}$IrO$_{4}$ and the interface between Sr$_{2}$IrO$_{4}$ andSr$_{3}$Ir$_{2}$O$_{7}$.

physical review. b./physical review. b

Vector chirality for effective total momentum $J_{\textrm{eff}}$ in a  nonfrustrated Mott insulator: Effects of strong spin-orbit coupling and  broken inversion symmetry