Topological Superconductivity in the Extended Kitaev-Heisenberg Model

We discover new superconducting pairing symmetries in the doped Kitaev-
Heisenberg model when taking into account the recently proposed symmetric
off-diagonal exchange Γ. We classify these phases in terms of lattice symme-
tries, pointing out the importance of the role of spin-orbit coupling, as well as
by calculating topological invariants. Performing self-consistent calculations,
we discover for Γ < 0 both a chiral state, breaking time-reversal symmetry,
classified by Chern number ±1, and a nematic state breaking the rotational
symmetry of the lattice. Both states yield clear experimental signatures that
distinguish them from the time-reversal symmetric, lattice symmetric super-
conducting state realized at Γ ≥ 0. For high doping levels, both time-reversal
symmetric states are classified by a non-trival Z 2 invariant. At lower doping,
we show that tuning into this non-trivial topological phase can alternatively be
achieved by including a symmetry-allowed spin-orbit coupling kinetic energy.