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Register a new userTheory of intraband plasmons in doped carbon nanotubes: rolled surface-plasmons of graphene
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A single-wall carbon nanotube possesses two different types of plasmons specified by the wavenumbers in the azimuthal and axial directions. The azimuthal plasmon that is caused by interband transitions has been studied, while the effect of charge doping is unknown. In this paper, we show that when nanotubes are heavily doped, intraband transitions cause the azimuthal plasmons to appear as a plasmon resonance in the near-infrared region of the absorption spectra, which is absent for light doping due to the screening effect. The axial plasmons that are inherent in the cylindrical waveguide structures of nanotubes, account for the absorption peak of the metallic nanotube observed in the terahertz region. The excitation of axial (azimuthal) plasmons requires a linearly polarized light parallel (perpendicular) to the tubes axis.
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Coupling of plasmons in graphene at terahert (THz) frequencies with surface plasmons in a heavily-doped substrate is studied theoretically. We reveal that a huge scattering rate may completely damp out the plasmons, so that proper choices of material and geometrical parameters are essential to suppress the coupling effect and to obtain the minimum damping rate in graphene. Even with the doping concentration 10^{19} - 10^{20} cm^{-3} and the thickness of the dielectric layer between graphene and the substrate 100 nm, which are typical values in real graphene samples with a heavily-doped substrate, the increase in the damping rate is not negligible in comparison with the acoustic-phonon-limited damping rate. Dependence of the damping rate on wavenumber, thicknesses of graphene-to-substrate and gate-to-graphene separation, substrate doping concentration, and dielectric constants of surrounding materials are investigated. It is shown that the damping rate can be much reduced by the gate screening, which suppresses the field spread of the graphene plasmons into the substrate.
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.
Graphene has raised high expectations as a low-loss plasmonic material in which the plasmon properties can be controlled via electrostatic doping. Here, we analyze realistic configurations, which produce inhomogeneous doping, in contrast to what has been so far assumed in the study of plasmons in nanostructured graphene. Specifically, we investigate backgated ribbons, co-planar ribbon pairs placed at opposite potentials, and individual ribbons subject to a uniform electric field. Plasmons in backgated ribbons and ribbon pairs are similar to those of uniformly doped ribbons, provided the Fermi energy is appropriately scaled to compensate for finite-size effects such as the divergence of the carrier density at the edges. In contrast, the plasmons of a ribbon exposed to a uniform field exhibit distinct dispersion and spatial profiles that considerably differ from uniformly doped ribbons. Our results provide a road map to understand graphene plasmons under realistic electrostatic doping conditions.
The two-dimensionality of graphene and other layered materials can be exploited to simplify the theoretical description of their plasmonic and polaritonic modes. We present an analytical theory that allows us to simulate these excitations in terms of plasmon wave functions (PWFs). Closed-form expressions are offered for their associated extinction spectra, involving only two real parameters for each plasmon mode and graphene morphology, which we calculate and tabulate once and for all. Classical and quantum-mechanical formulations of this PWF formalism are introduced, in excellent mutual agreement for armchaired islands with $>10,$nm characteristic size. Examples of application are presented to predict both plasmon-induced transparency in interacting nanoribbons and excellent sensing capabilities through the response to the dielectric environment. We argue that the PWF formalism has general applicability and allows us to analytically describe a wide range of 2D polaritonic behavior, thus facilitating their use for the design of actual devices.
A quantitative understanding of the electromagnetic response of materials is essential for the precise engineering of maximal, versatile, and controllable light--matter interactions. Material surfaces, in particular, are prominent platforms for enhancing electromagnetic interactions and for tailoring chemical processes. However, at the deep nanoscale, the electromagnetic response of electron systems is significantly impacted by quantum surface-response at material interfaces, which is challenging to probe using standard optical techniques. Here, we show how ultra-confined acoustic graphene plasmons (AGPs) in graphene--dielectric--metal structures can be used to probe the quantum surface-response functions of nearby metals, here encoded through the so-called Feibelman $d$-parameters. Based on our theoretical formalism, we introduce a concrete proposal for experimentally inferring the low-frequency quantum response of metals from quantum shifts of the AGPs dispersion, and demonstrate that the high field confinement of AGPs can resolve intrinsically quantum mechanical electronic length-scales with subnanometer resolution. Our findings reveal a promising scheme to probe the quantum response of metals, and further suggest the utilization of AGPs as plasmon rulers with r{a}ngstr{o}m-scale accuracy.
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