Abstract We theoretically studied Dyakonov-like surface polaritons in a hyperbolic crystal covered by a graphene monolayer. From the obtained dispersion equation, four Dyakonov-like surface polariton modes were found, and each mode is a di-hybrid Dyakonov-like surface polariton, namely the surface polaritons of polarization hybridization and plasmon–phonon hybridization. We investigated dispersion properties of these polaritons without damping effect for comparison with the existing results and found a new mode that is a highly localized mode with a large wave number and large attenuation constant. We discussed substantial effects of the graphene layer on the surface polaritons and the dispersion relation in several extreme cases. In a practical case, the dispersion equation with damping effect was further numerically calculated and the propagation distance of the surface polaritons was emphasized. It was found that there are huge differences in propagation distance and dispersion property among the surface polaritons. Our calculation results are based on the graphene-monolayer/hexagonal boron nitride heterostructure. The investigation provides a useful theoretical basis for the nano/micron photonics and technology in the mid-infrared range.
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