Plasmons in anisotropic Dirac systems

We consider the plasmon excitations in anisotropic two-dimensional Dirac systems, be it either anisotropic graphene or surfaces of topological insulators. Generalizing the exact density-density response function one finds a plasmon dispersion that is anisotropic already at the lowest frequencies. Asymptotic expressions are obtained for the dispersion in this regime. We show that the plasmon properties of the complete material class of anisotropic Dirac systems are characterized by just two dimensionless material parameters. The strong anisotropy can be used to guide the plasmon modes, introducing new functionalities to the field of Dirac plasmonics.

Figure 1

Real part of the zero-order density-density response function ${\chi }_0/C$ for $\nu =\hslash \omega /{\varepsilon }_F=0.6$. Compared are the exact expression (red, full line) with the approximative one [Eq. (10), blue dash-dotted line] and the parabolic approximation [Eq. (11), green dashed line].

Figure 2

Plasmon dispersion for material parameters $\beta =2.0$ and $A=1.5$ for the two extremal plasmon propagation directions $\alpha =0$ (left) and $\alpha =\pi /2$ (right) using the exact expression or the two approximate ones (see Fig. 1) together with the corresponding boundaries of the continuum of electron-hole excitations (yellow) shown by dotted lines.

Figure 3

Plasmon dispersion for material parameters $\beta =0.4$ and $A=6.0$ for the two extremal plasmon propagation directions $\alpha =0$ (left) and $\alpha =\pi /2$ (right) using the exact expression or the two approximate ones (see Figs. 1 and 2). The continuum of electron-hole excitations is indicated in yellow.

Figure 4

Contour plot of the anisotropic plasmon dispersion with lines of constant plasmon energy in the $q_x\text{−}{q}_y$ plane for material parameters $\beta =2.0$ and $A=2.5$.