Topological superconductivity in the extended Kitaev-Heisenberg model

Abstract

We study superconducting pairing in the doped Kitaev-Heisenberg model by taking into account the recently proposed symmetric off-diagonal exchange Γ. By performing a mean-field analysis, we classify all possible superconducting phases in terms of symmetry, explicitly taking into account effects of spin-orbit coupling. Solving the resulting gap equations self-consistently, we map out a phase diagram that involves several topologically nontrivial states. For Γ<0, we find a competition between a time-reversal symmetry-breaking chiral phase with Chern number ±1 and a time-reversal symmetric nematic phase that breaks the rotational symmetry of the lattice. On the other hand, for Γ≥0 we find a time-reversal symmetric phase that preserves all the lattice symmetries, thus yielding clearly distinguishable experimental signatures for all superconducting phases. Both of the time-reversal symmetric phases display a transition to a Z2 nontrivial phase at high doping levels. Finally, we also include a symmetry-allowed spin-orbit coupling kinetic energy and show that it destroys a tentative symmetry-protected topological order at lower doping levels. However, it can be used to tune the time-reversal symmetric phases into a Z2 nontrivial phase even at lower doping.

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