Plasmon oscillations in two-dimensional arrays of ultranarrow graphene nanoribbons

The recent ability to manipulate graphene-like structures at the atomic scale is opening up new challenges in electronics and photonics, with a key focus on the bulk and edges of the systems, which generate peculiar and interfering charge density oscillations, quantized as plasmons. These quasiparticles are here scrutinized in planar periodic distributions (two-dimensional arrays) of parallel and atomically wide graphene nanoribbons. Time-dependent density functional theory is used, with a specifically developed adjustment on the random phase approximation, suitable for two-dimensional materials. Several extrinsic conditions (for doped or gated nanoribbon arrays) are simulated to characterize the propagation and interplay of the bulk and edge plasmons, at far infrared to visible energies, and over a broad range of momentum transfers. The main technological interest is on the bulk mode, which is dominant and propagates undamped, at energies below the band gap of the intrinsic systems. On the other hand, the edge mode is always well defined at energies above the band gap, and highly dependent on the band gap value, though it decays via electron-hole excitations between the first valence and conduction bands. Particular attention is paid to the interaction or overlap region of the two plasmons, explaining its sensitivity to induced Fermi level shifting, transferred momentum, ribbon type, and geometry, with the inclusion of many-body, GW-like effects. More importantly, the lower-terahertz behavior of the bulk plasmon is explored, highlighting the limits of available non-ab initio approaches, suitable for stripes of graphene being tenths of nanometers wide. Then, an effective model is derived from the ab initio framework, which reasonably accounts for the two-plasmon response of the studied, ultranarrow nanoribbon systems, at small momentum transfers. The range of applicability of the same derivation procedure may be extended to more complex nanoribbon heterostructures available for synthesis, which emphasizes the need for an ab initio guide to a reliable design of nanoplasmonic devices.