Plásmons de superfície localizados em uma folha de grafeno com uma deformação gaussiana

Abstract

Due to the unique electronic structure and intrinsic atomic thickness, graphene is considered an excellent plasmonic material and, consequently, a promising component for technological polaritonic applications related to light-matter interactions at the nanoscale. Plasmons in graphene present great advantages, when compared with standard 3D metallic plasmonic materials, (i) supporting strongly confined surface plasmons in mid-IR and in the THz spectral range, (ii) exhibiting a tunable frequency of plasmon resonances by controlling its Fermi level by means of chemical doping or electrostatic gating, and (iii) possessing a roughly low-loss propagation, i.e. being long-lived plasmons. One divides the plasmonic excitations into localized surface plasmons and surface plasmon polaritons, whether the polaritonic mode is a localized or a propagating surface wave, being the former excited by direct light illumination and used to concentrate the electromagnetic field in certain narrow regions. Studies concerning localized plasmonic modes have been reported in graphene nanostructures with different geometries and arrangements, isolated or partnered in periodic arrays (grating), such as ribbons, disks, and rings. An alternative route to enhance or attenuate the surface waves is the presence of roughness on the surface, which is hardly inevitable in any experimental growing/preparation process in solids. In this regard, several works in the 80s and 90s focused their attention in order to examine the consequences of rough/corrugated surfaces on the polaritonic properties of the localized and propagating waves. They observed that such modes are spatially localized in the vicinity of the defects (protuberance/groove/bump, indentation/wedge) and that the frequencies of these modes and the field distributions associated with them depend on the shape and dimensions of the defect. In this context, we investigate in this work the consequences of the spectrum of plasmon-polaritons in graphene by considering a corrugated graphene sheet. Within the electrostatic approximation, our theoretical approach allows us to consider different shapes of rough surfaces, with one-dimensional or two-dimensional profiles. We assume that the graphene sheet is corrugated to form a Gaussian one-dimensional groove localized in the interface between the vacuum and a dielectric substrate. Results for the dispersion relation and the behavior of the electric and magnetic fields for different geometric parameters are discussed and compared with planar graphene plasmon-polariton modes.