Probing Plasmons by EELS in Chiral Array of Graphene Nano-Ribbons

We have obtained the energy loss spectra of a graphene nano-ribbon array (GNR) in the effective media approximation. The GNR layer conductivity becomes a tensor, with a strong nonlocal component. This approach is valid in the long wavelength limit where one can neglect the polarization across the GNR. The quasi 1D longitudinal plasmons are probed using electron energy loss spectroscopy (EELS). In the perfectly aligned configuration the plasmonic propagation constant is contracted along oblique directions. This allows for plasmon probing with much lower electron energies as compared to the uniform graphene and offers drastic modification of the energy loss probability. The system is similar to a thin uni-axial crystal supporting extraordinary refracted beams with negative group velocity. We investigate the existence of plasmonic resonances by probing the system with a parallel moving electronic beam using EELS. We argue that EELS is capable of picking up two different resonances when there is a mismatch between the direction of the beam and that of the GNR. For several twisted GNR layers one may observe peculiar interference effects between the ordinary and extraordinary plasmon modes.