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We study the effects of doping a Mott insulator on the honeycomb latticewhere spins interact via direction dependent Kitaev couplings J_K, and weakantiferromagnetic Heisenberg couplings J. This model is known to have a spinliquid ground state and may potentially be realized in correlated insulatorswith strong spin orbit coupling. The effect of hole doping is studied within at-J-J_K model, treated using the SU(2) slave boson formulation, which correctlycaptures the parent spin liquid. We find superconductor ground states with spintriplet pairing that spontaneously break time reversal symmetry. Interestingly,the pairing is qualitatively different at low and high dopings, and undergoes afirst order transition with doping. At high dopings, it is smoothly connectedto a paired state of electrons propagating with the underlying free particledispersion. However, at low dopings the dispersion is strongly influenced bythe magnetic exchange, and is entirely different from the free particle bandstructure. Here the superconductivity is fully gapped and topological,analogous to spin polarized electrons with px+ipy pairing. These results may berelevant to honeycomb lattice iridates such as A2IrO3 (A=Li or Na) on doping.

Doping a spin-orbit Mott Insulator: Topological Superconductivity from the Kitaev-Heisenberg Model and possible application to (Na2/Li2)IrO3