The global phase diagram of a doped Kitaev-Heisenberg model is studied using an SU(2) slave-boson mean-field method. Near the Kitaev limit, p-wave superconducting states which break the time-reversal symmetry are stabilized as reported by You {it et al.} [Phys. Rev. B {bf 86}, 085145 (2012)] irrespective of the sign of the Kitaev interaction. By further doping, a d-wave superconducting state appears when the Kitaev interaction is antiferromagnetic, while another p-wave superconducting state appears when the Kitaev interaction is ferromagnetic. This p-wave superconducting state does not break the time-reversal symmetry as reported by Hyart {it et al.} [Phys. Rev. B {bf 85}, 140510 (2012)], and such a superconducting state also appears when the antiferromagnetic Kitaev interaction and the ferromagnetic Heisenberg interaction compete. This work, thus, demonstrates the clear difference between the antiferromagnetic Kitaev model and the ferromagnetic Kitaev model when carriers are doped while these models are equivalent in the undoped limit, and how novel superconducting states emerge when the Kitaev interaction and the Heisenberg interaction compete.
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