Hyperbolic metamaterials based on multilayer graphene structures

We propose metamaterials for THz frequencies based on multilayer graphene structures. We calculate the dielectric permittivity tensor of the effective nonlocal medium with a periodic stack of graphene layers and demonstrate that tuning from elliptic to hyperbolic dispersion can be achieved with an external gate voltage. We reveal that such graphene structures can demonstrate a giant Purcell effect that can be used for boosting the THz emission in semiconductor devices. Tunability of these structures can be enhanced further with an external magnetic field which leads to the unconventional hybridization of the TE and TM polarized waves.

Figure 1

Geometry of the effective hyperbolic metamaterial composed of a periodic structure of graphene layers with conductivity $\sigma$ separated by dielectric slabs with the thickness $d$ and dielectric constant $\epsilon$.

Figure 2

Isofrequency contours of the graphene metamaterial for the different values of the gate voltage and a fixed frequency of 4 meV.

Figure 3

(a) Dependence of the component ${\varepsilon }_{xx}$ on the in-plane wave vector $\beta$. Frequency is 40 meV; local approximation result is shown with a straight dashed line. Inset shows the dependence on $K$. (b) Frequency dependence of the component ${\varepsilon }_{xx}$ for different values of $\beta$.

Figure 4

Purcell factor vs frequency for both TE and TM polarizations. Temperature is 4 K.

Figure 5

(a) Frequency dependence of the Hall and longitudinal conductivities in the presence of static magnetic field of 0.1 T. Temperature is 4 K. (b) Isofrequency contours for the frequency 100 meV for the first (red solid line) and second (blue dashed line) hybrid electromagnetic modes.