Competition between spin-singlet and -triplet superconducting states in the doped extended Kitaev-Heisenberg model

Recently, the extended Kitaev-Heisenberg model has been proposed to describe spin-orbital Mott insulators, such as iridate oxides and ruthenium chloride with honeycomb lattice. Using mean-field theory, we obtain the linear gap equations to find all possible superconducting phases in terms of different exchanges and doping levels. Our calculation based  on the hole-doped model, in the presence of the off-diagonal exchange  , shows the spin-triplet states can be stable in a larger area related to the doped Kitaev-Heisenberg model with K<0 and JH>0. However, the finite ferromagnetic off-diagonal exchange solely cannot generate the triplet pairing instabilities in competition with the antiferromagnetic-Heisenberg and -Kitaev exchanges.