Effects of screening on the propagation of graphene surface plasmons

Electromagnetic fields bound tightly to charge carriers in a two-dimensional sheet, namely surface plasmons, are shielded by metallic plates that are a part of a device. It is shown that for epitaxial graphenes, the propagation velocity of surface plasmons is suppressed significantly through a partial screening of the electron charge by the interface states. On the basis of analytical calculations of the electron lifetime determined by the screened Coulomb interaction, we show that the screening effect gives results in agreement with those of a recent experiment.

Figure 1

(a) Schematic of a time-resolved transport experiment on epitaxial graphene [5]. Because the experiments were performed at 1.5 K, the finite temperature effect [7] can be safely ignored. (b) The waveform of the current at the detection gate is given as a function of time. The details of the waveform are dependent on $E_F$, which is controlled by a metal top gate covering the entire sample. This plot corresponds to $E_F\simeq 0.2$ eV. (c) The $E_F$ dependence of the propagation velocity.

Figure 2

The lower limit of the group velocity of the plasmons in graphene without a nearby metal top gate. The plasmons cannot exist (are damped) when $v_g/v_F$ is located below the solid line (dashed curve). Screening lowers the dashed curve: The dotted curve is when $e_{*}=e/10$.

Figure 3

Cross section of a device consisting of a graphene sheet (red) and a metal gate (blue). The gray regions represent a dielectric (dielectric constant $\varepsilon )$. (a) The arrows represent the electric fields $\mathbf{E}=(0,0,E_z)$ for nonradiative (acoustic) plasmons satisfying $q^{-1}\gg d$. We omit to draw an exponential decaying electric field which appears underneath the graphene sheet for clarity. (b) Interface states near to the graphene sheet, including the dangling bond states $\left(\delta \ll d\right)$, efficiently screen the electron charge.

Figure 4

The $q_c$ dependence of the waveform at $x=220$ $\mu$m. In this plot we assume $T=400$ ps and $v={10}^5$ m/s, and $q_c$ is given in the units of ${\left(10\mu \text{m}\right)}^{-1}$. The peak time of the $E_p$ component (blue) is $t=2.2$ ns, while that of the $E_d$ component (red) increases with increasing $q_c$. The sum of the two components $E_z$ is referred by yellow. Arrows represent peak time.