  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.
