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The magnetic properties of 4d and 5d transition-metal insulating compoundswith the honeycomb structure are believed to be described by theHeisenberg-Kitaev model, which contains both the isotropic Heisenberginteraction J and anisotropic Kitaev interaction K. In this paper, toinvestigate the charge dynamics in these materials, we study the single-holepropagation of the t-J-K model in various magnetically ordered phases by theself-consistent Born approximation. We find that there are low-energy coherentquasiparticle (QP) excitations in all of these phases which appear firstlyaround the K point in the Brillouin zone (BZ), but the band-widths of these QPsare very small due to the hole-magnon coupling. Interestingly, in the zigzagphase relevant to recent experiments, though the QP weights are largelysuppressed in the physical spectra in the first BZ, we find that they recoverin the extended BZs. Moreover, our results reveal that the low-energy QPspectra are reduced with the increase of K.

Dynamics of a single hole in the Heisenberg-Kitaev model: a self-consistent Born approximation study