| The competition between Kitaev and Heisenberg interactions away from half filling is studied for the hole-doped Kitaev-Heisenberg t-JK-JH model on a honeycomb lattice. While the isotropic Heisenberg coupling supports a time-reversal violating d-wave singlet state, we find that the Kitaev interaction favors a time-reversal invariant p-wave superconducting phase, which obeys the rotational symmetries of the microscopic model, and is robust for JH < JK/2. Within the p-wave superconducting phase, a critical chemical potential μc ≈ t separates a topologically trivial phase for |μ| < μc from a topologically non-trivial Z2 time-reversal invariant spin-triplet phase for |μ| > μc. |
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