Plasmon-Phonon-Polaritons in Encapsulated Phosphorene
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Plasmon-Phonon-Polaritons in Encapsulated Phosphorene Farnood Ghohroodi Ghamsari1,2
· Reza Asgari2,3
Received: 7 May 2019 / Accepted: 31 October 2019 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract 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. Keywords Dielectric properties · Surface plasmon · Surface plasmon-phonon-polariton (SPPP) · Encapsulated phosphorene · Hexagonal boron nitride (hBN) · Random-phase approximation (RPA)
Introduction Phosphorene is the monolayer counterpart of black phosphorus (BP); a single-atomic-layered material consisting of only phosphorus atoms [1, 2] with five outer shell electrons. In phosphorene, the phosphorus atoms are tightly packed in a rectangular lattice with the structure being slightly puckered—see Fig. 1a—giving rise to novel correlated electronic properties ranging from semiconducting to superconducting behaviors [3–9]. But unlike graphene (as a wellknown 2D material), this puckered structure of phosphorene impose a strong anisotropy in the band structure and therefore in the collective excitations like the standard plasmon mode and its extensions such as surface plasmon-phononpolariton modes in the related heterostructures described in the following. Farnood Ghohroodi Ghamsari
[email protected]; [email protected] 1
Department of Physics, Kharazmi University, Tehran, 15719-14911, Iran
2
School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5531, Iran
3
School of Nano Science, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5531, Iran
In order to trigger and measure plasmon modes, a scanning near-field optical microscope can be used in which the aperture radius is much smaller than the wavelength of incident light. The required in-plane momenta is provided by the near-field evanescent components of light coming out from the microscope. For example, plasmon modes in doped graphene [10–13] have been measured by using this technique with nanometer resolution. Two research groups carried out experiments on graphene plasmonics using a similar technique [14, 15]. Phonon-polaritons, on the other hand, are collective mod
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