Hunting for superconductivity in doped triangular lattice Kitaev magnets

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 $d\pm i d$ 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 $K_{\rm sc} < 1$. Our work sets the stage for a broader exploration of doping effects in triangular lattice magnets such as NaRuO$_2$ which feature bond-dependent exchange interactions.