Anisotropic 2D Materials for Tunable Hyperbolic Plasmonics

Motivated by the recent emergence of a new class of anisotropic 2D materials, we examine their electromagnetic modes and demonstrate that a broad class of the materials can host highly directional hyperbolic plasmons. Their propagation direction can be manipulated on the spot by gate doping, enabling hyperbolic beam reflection, refraction, and bending. The realization of these natural 2D hyperbolic media opens up a new avenue in dynamic control of hyperbolic plasmons not possible in the 3D version.

Figure 1

Real (a) and imaginary (b) parts of the conductivity of the 2D material. The parameters of the 2D material are $m_x=0.2m_0$, $m_y=m_0$, $\eta =0.01\mathrm{eV}$, $w_x=1\mathrm{eV}$, $s_x=1.7s_0$, $w_y=0.35\mathrm{eV}$, and $s_y=3.7s_0$. $s_0=e^2/4\hslash$; $m_0$ is the free-electron mass.

Figure 2

(a)–(e) Spatial distribution (log scale) of the electric field $|\mathbf{E}|$ of a surface plasmon excited by a $y$-polarized electric dipole [green arrow in panels (a)–(e)] in a $2\times 2\mu \mathrm{m}$ sheet of a 2D material placed in the plane $z=0$ [dashed black line in panels (b) and (d)]. The distribution of the electric field is calculated in the planes $z=10\mathrm{nm}$ (a),(c),(e) and $x=0.6\mu \mathrm{m}$ (b),(d). (a),(b) $n={10}^{14}{\mathrm{cm}}^{-2}$, $\hslash \omega =0.165\mathrm{eV}$. (c),(d) $n={10}^{14}{\mathrm{cm}}^{-2}$, $\hslash \omega =0.3\mathrm{eV}$. (e) $n=3\times {10}^{13}{\mathrm{cm}}^{-2}$, $\hslash \omega =0.3\mathrm{eV}$. (f) $k$ surfaces, $\omega (q_x,q_y)=\text{const}$, for plasmons in panels (a)–(e).

Figure 3

Angle between plasmon beam direction and the $x$ axis, for $\eta =0.01\mathrm{eV}$, $m_x=0.2m_0$, $m_y=m_0$, $s_x=s_y=2s_0$, $\hslash {\omega }_x=1\mathrm{eV}$, $\hslash {\omega }_y=0.35\mathrm{eV}$, $n=5\times {10}^{13}{\mathrm{cm}}^{-2}$, and $\hslash \omega =0.3\mathrm{eV}$, unless stated otherwise in the figure.

Figure 4

Plasmon launched by a $y$-polarized electric dipole in a layered medium made by placing sheets of 2D materials with different electron concentrations next to each other. The dipole position is designated by a green arrow. The parameters of the 2D materials are the same as in Fig. 1. (a),(b) The concentration of electrons in the material above the dashed white line is $n={10}^{14}{\mathrm{cm}}^{-2}$, while below the white line it is $n=3\times {10}^{13}{\mathrm{cm}}^{-2}$. (c) The electron concentration varies gradually from $n={10}^{14}{\mathrm{cm}}^{-2}$ (upper layer) to $n=2\times {10}^{13}{\mathrm{cm}}^{-2}$ (lower layer).