Motivated by exploring correlated metals with frustrating bond-dependent exchange interactions, we study hole- and electron-doped Kitaev Mott insulators on the triangular lattice. Using homogeneous parton mean-field theory, we find that the stripe antiferromagnetic (AFM) order for Kitaev coupling $K>0$ and the ferromagnetic (FM) order for $K<0$, both vanish at sufficiently large doping, beyond which we find regimes with chiral $d\pm id$ singlet pairing and $p\pm ip$ triplet pairing, respectively. Our tensor network computations, however, reveal that the superconducting correlations are strongly suppressed; while FM order stubbornly persists for the doped $K<0$ model, the doped $K>0$ model features emergent spin-charge modulated stripe orders. At higher hole doping for $K>0$, where AFM order is more strongly suppressed than for the electron-doped case, incorporating a sufficiently strong nearest-neighbor attraction yields evidence for singlet $d$-wave superconductivity with Luttinger parameter $K_{\mathrm{sc}}<1$. Our work sets the stage for a broader exploration of doping effects in triangular lattice magnets such as ${\mathrm{NaRuO}}_2$ that feature bond-dependent exchange interactions.

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• Density matrix renormalization group
• Density matrix methods
• Kitaev model
• t-J model