In our previous publications 1-4, we studied the effects of plasmon-phonon hybridization in a sandwich-like structure consisting of two doped graphene sheets separated by a layer of aluminum oxide (Al2O3) 1-4, silicon dioxide (SiO2) 4, and hafnium dioxide (HfO2) 4. In all those publications, we considered only isotropic insulators between two graphene sheets. In this work, we investigate for the first time two graphene layers separated by an insulating slab that exhibits anisotropy of a uniaxial crystal. We choose an anisotropic layer of hexagonal boron nitride (hBN) because van der Waals heterostructures based on graphene and hBN layers with different stacking modes have been attracting a great deal of interest in the last few years owing to their potential applications 5-8. The objective is to explore the effects of anisotropy of hBN in the graphene-hBN-graphene heterostructure. In particular, we examine the plasmon-phonon hybridization in the range of frequencies corresponding to the Reststrahlen bands of hBN, where the phonon modes of this material exhibit hyperbolic dispersion. The expression for the effective surface electron energy loss (EEL) function (the imaginary part of the negative value of the surface response function 9) of the graphene-hBN-graphene composite system is derived following and generalizing the continued fraction method of Ref. 10. The response function of each graphene is obtained using the dynamic polarization function of doped graphene within the random phase approximation for its π electrons described as Dirac’s fermions. The response of the anisotropic hBN layer is described by a diagonal dielectric tensor consisting of the in-plane and axial components. We compare the effective surface EEL functions of the graphene-hBN-graphene systems in the cases of the anisotropic and fictitious isotropic (with the dielectric functions equal to the in-plane or axial components) hBN layers.
Radović et al. (2025) studied this question.