  We consider a system consists of a doped monolayer phosphorene embedded
between two hexagonal Boron Nitride (hBN) slabs along the heterostructure
direction. The wavevector azimuthal angle dependence of the plasmon-polariton
and plasmon-phonon-polariton modes of the hybrid system are calculated based on
the random phase approximation at finite temperature. The collective modes
illustrate strong anisotropy and strong coupling with phonon modes of the polar
media and furthermore, the Landau damping occurs due to the intraband processes
when plasmon enters intraband electron-hole continuum. Our numerical results
show that the plasmon mode is highly confined to the surface along the zigzag
direction. Owing to the strong electron-phonon interaction, the phonon
dispersions in the Reststrahlen bands are also angle-dependent. These results
are also in agreement with those of the semiclassical model obtained in our
calculations.
