Competition between d-wave and topological p-wave superconductivity in the doped Kitaev-Heisenberg model

The competition between Kitaev and Heisenberg interactions away from half filling is studied for the the hole-doped Kitaev-Heisenberg $t$-$J_K$-$J_H$ 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 $J_H<J_K/2$. Within the p-wave superconducting phase, a critical chemical potential $\mu_c \approx t$ separates a topologically trivial phase for $|\mu|< \mu_c$ from a topologically non-trivial $Z_2$ time-reversal invariant spin-triplet phase for $|\mu|>\mu_c$.