Plasmons in Dimensionally Mismatched Coulomb Coupled Graphene Systems

We calculate the plasmon dispersion relation for Coulomb coupled metallic armchair graphene nanoribbons and doped monolayer graphene. The crossing of the plasmon curves, which occurs for uncoupled 1D and 2D systems, is split by the interlayer Coulomb coupling into a lower and an upper plasmon branch. The upper branch exhibits an unusual behavior with end points at finite $q$. Accordingly, the structure factor shows either a single or a double peak behavior, depending on the plasmon wavelength. The new plasmon structure is relevant to recent experiments, its properties can be controlled by varying the system parameters and be used in plasmonic applications.

Figure 1

Plasmon dispersion in Coulomb coupled metallic armchair graphene nanoribbons and monolayer graphene. The green ($d=16\mathrm{nm}$) and blue ($d=2\mathrm{nm}$) solid curves show the energy dispersions of the upper and lower branches of the hybrid plasmons for two representative spacings. The dotted and dashed curves show the uncoupled 1D and 2D plasmon dispersions as a guide to the eye. The horizontal thin line at $\omega \approx 1.32E_F$ corresponds to the energy at which the 2D plasmon enters into the 2D interband EHC of graphene. The other two thin lines show the boundaries of the 2D inter and interband EHC in monolayer graphene. The nanoribbon width is $w=12\mathrm{nm}$ and the electron areal density in graphene monolayer $n_{\mathrm{gr}}=3\times {10}^{11}{\mathrm{cm}}^{-2}$ Inset: schematics of a dimensionally mismatched graphene nanostructure.

Figure 2

The imaginary part of the screening function in 1D-2D electronic systems along the upper (left) and the lower (right) hybrid plasmon branches. The solid and dashed curves correspond to interlayer spacing of $d=2$ and 16 nm. The values of other parameters are the same as in Fig. 1.

Figure 3

The dynamical structure factor (solid curve) and the real part of the screening function (dashed curve) in 1D-2D electronic bilayers as a function of the bosonic frequency $\omega$. In the panels from left to right the plots are calculated, respectively, for bosonic momenta $q_y\approx 0.3,0.43,0.51$, and $0.96k_F$ and for interlayer spacing $d=2\mathrm{nm}$. The values of other parameters are the same as in Fig. 1.