Tunable propagation of surface plasmon-phonon polaritons in graphene-hBN metamaterials

We present a detailed study on the tunable propagation derived from the coupled surface plasmon-phonon polaritons (SPPPs) with the effective medium theory (EMT) in graphene-hBN metamaterials (MMs). Four reststrahlen bands (RBs) are observed, two of which mainly come from the hBN and the others originate from the effect of the graphene. The RBs frequency windows can be adjusted by the chemical potential and the filling ratio. An epsilon-near-zero-and-pole(eNZP)hyperbolic metamaterial (HMM) is detected at the precise frequency, chemical potential and filling ratio where the HMM undergoes a completely inversion of anisotropy. We derive the relative dispersion relation and demonstrate that the propagation of SPPP modes can be regulated by modifying the chemical potential. In addition, the tunability of the graphene-hBN MMs also can be improved by changing the thicknesses of the hBN and the number of graphene sheets. The energy-flux density in the graphenehBN MM seriously deviates from its wave vector and can be localized at a certain depth. Besides, the ghost SPPP modes with the oscillation-attenuation character are observed at some special conditions through checking the distribution of electric fields. The attenuation total reflection (ATR) measurement is established to examine these SPPP modes. The numerical results show that the observation of each SPPP modes requires different conditions dictated by material parameters and the polarization direction of the incident light.

Automated summary

By studying the coupled surface plasmon-phonon polaritons in graphene-hBN metamaterials, it is found that the propagation properties can be adjusted by changing the chemical potential and filling ratio. Additionally, tuning the material parameters such as thickness and number of layers can also improve the tunability of the metamaterial. Furthermore, the presence of ghost SPPP modes with oscillation-attenuation characteristics is observed under special conditions, demonstrating the complexity of the propagation behavior in the material system.