Theory for surface polaritons supported by a black-phosphorus monolayer

Abstract

A theory is presented for surface polaritons that may propagate along the electrostatically doped phosphorene layer (black-phosphorus monolayer) surrounded by two insulating media of different dielectric constants. It is shown that the phosphorene layer in such a structure supports three types of strongly localized surface polariton modes: the transverse magnetic (TM), the transverse electric (TE), and the hybrid TE-TM. Both the TM and TE modes can propagate only along the phosphorene's ``armchair'' and ``zigzag'' crystallographic axes, while the in-plane wave vector $\mathbf{q}$ of the hybrid TE-TM modes makes a finite angle with respect to both the abovementioned axes. It is found that there exists such a critical value ${q}_{C}$ of the polariton mode wave number $q$, peculiar to each type of mode, that the mode ceases from propagating at $qg{q}_{C}$. The critical value of polariton frequency, corresponding to this critical wave number, lies either below the phosphorene's interband absorption threshold or slightly above it, depending on the type of the polariton mode, its propagation direction, and the doping level of the phosphorene. Our findings suggest that the phosphorene, in which the charge carrier density is tuned by an external gate voltage, could be promising for polariton waveguiding applications in future planar nanophotonic devices operating at near-infrared wavelengths.