Tailoring Dirac Plasmons via Anisotropic Dielectric Environment by Design

Dirac plasmons in a two-dimensional (2D) crystal are strongly affected by the dielectric properties of the environment, due to interaction of their electric field lines with the surrounding medium. Using graphene as a 2D reservoir of free carriers, one can engineer a material configuration that provides an anisotropic environment to the plasmons. In this work, we discuss the physical properties of Dirac plasmons in graphene surrounded by an arbitrary anisotropic dielectric and exemplify how $h$-$\mathrm{BN}$–based heterostructures can be designed to bear the required anisotropic characteristics. We calculate how dielectric anisotropy impacts the spatial propagation of the plasmons and find that an anisotropy-induced plasmon mode emerges, together with a damping pathway, that stem from the out-of-plane off-diagonal elements in the dielectric tensor. Furthermore, we find that one can create hyperbolic plasmons by inheriting the dielectric hyperbolicity of the designed material environment. Strong control over plasmon propagation patterns can be realized in a similar manner. Finally, we show that in this way one can also control the polarization of the light-matter excitations that constitute the plasmon. Taken together, our results promote the design of the dielectric environment as an effective path to tailor the plasmonic response of graphene on the nanoscopic level.

Figure 1

The structure diagram of (a) the graphene heterostructure surrounded by an anisotropic dielectric environment in the coordinate system $(x_0,y_0,z_0)$ for Dirac plasmons in the coordinate system $(x,y,z)$, (b) the graphene/vertically placed $h$-$\mathrm{BN}$ layers without and with tilting angle ${\varphi }_{x_0}$, and (c) the graphene sandwich heterostructures with the top and bottom vertically placed $h$-$\mathrm{BN}$ layers with a twist angle ${\varphi }_{z_0}$ around the $z_0$ axis.

Figure 2

The isofrequency contours and the real-space profiles (insert) of elliptic and hyperbolic Dirac plasmons at the selected excitation frequencies.

Figure 3

The isofrequency contours of the two damped Dirac plasmons, (a) $k_l$ and (b) $k_p$, for the real part (left) and the imaginary part (right) at the selected frequency $\omega =35$ THz for different tilt angles ${\varphi }_{x_o}$.

Figure 4

The isofrequency contours and the real-space profiles (insert) of the anisotropic Dirac plasmons for different twist angles ${\varphi }_{z_o}$ at two selected excitation frequencies: (a) $\omega =10$ THz; (b) $\omega =35$ THz.

Figure 5

The dielectric functions ${\epsilon }_{\perp }$ and ${\epsilon }_{\parallel }$, respectively, for in-plane and out-of-plane $h$-$\mathrm{BN}$ layers. Regions I and II show the hyperbolic regions.