Hyperbolic Plasmon in Black Phosphorus¶

Optical Conductivity of bilayer black phosphorus¶

Imaginary Part	Real Part

• The imaginary part of the optical conductivity of bilayer black phosphorus in units of ${\sigma }_0=\pi e^2/2h$, showing a hyperbolic region (shaded) where $\text{Im}({\sigma }_{xx})\cdot \text{Im}({\sigma }_{yy})<0$ starting at $\omega =2.8eV$.
• $\text{Im}({\sigma }_{xx})$ is negative throughout the spectrum (solid red line), $\text{Im}({\sigma }_{yy})$ goes from negative to positive around (solid blue line) ${\omega }_h$= 2.8 eV, which results in a hyperbolic region starting at that frequency.

• Under compressive strain, the band gap of bilayer black phosphorus becomes smaller. As a result, the optical peaks shift to lower frequencies and ${\omega }_h$ goes down.
• For increasing bias in the bilayer case [Figs. 4(e) and 4(f)], the hyperbolic onset frequency ${\omega }_h$ first goes up, because the bands corresponding to the excitation causing the second peak move away from one another. Then it goes down as the band gap closes, and a new peak appears in between the two existing peaks, because breaking the mirror symmetry in the z direction allows for new hybrid transitions.

Related Links : - Surface Plasmons and Polaritons - Plasma oscillation