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

The magnetic properties of 4d and 5d transition-metal insulating compounds with the honeycomb structure are believed to be described by the Heisenberg–Kitaev model, which contains both the isotropic Heisenberg interaction J and anisotropic Kitaev interaction K. In this paper, we study the single-hole propagation of the t–J–K model in various magnetically ordered phases by the self-consistent Born approximation. We find that there are low-energy coherent quasiparticle (QP) excitations in all of these phases which appear firstly around the K point in the first Brillouin zone (BZ), but the bandwidths of these QPs are very small due to the hole–magnon coupling. Interestingly, in the zigzag phase relevant to recent experiments, though the QP weights are largely suppressed in the physical spectra in the first BZ, we find that they recover in the extended BZs. Moreover, our results reveal that the low-energy QP spectra are reduced with the increase of K. (paper)