Interaction of charged particles with surface plasmons in cylindrical channels in solids

Abstract

The interaction between swift charged particles and the electronic surface modes of a cylindrical cavity is described according to classical and quantum-mechanical formulations. We perform a quantization of the collective modes and obtain expressions for the coupling with external probes moving with arbitrary trajectories. We study the case of particles moving parallel to the channel axis and derive the probabilities of single and multiple plasmon excitation and the average energy loss. A correspondence between the classical and quantum pictures is shown. The scaling properties of the interaction terms are studied and general scaling functions are obtained, which may be applied to a wide range of particle velocities and cavity sizes, including microcapillaries and nanotubes.

Strong coupling between a metallic nanoparticle and a single molecule

“…Here γ λ = 2n 0 /(ω λ β λ ), and a λ is an expansion coefficient for the eigenmode λ. Inserting this expression into equation (2) and performing the standard quantization procedure via a canonical transformation, 25,26,35 then brings us to the plasmon Hamiltonian in secondquantized form…”

Excitations of bulk and surface plasmons in solids and nanostructures

“…The electrostatic surface modes of a given system are obtained from the solutions of the Laplace equation, r Using the Drude approximation for the dielectric function (Eqn (1)), we can evaluate the different excitation modes and calculate the average number of plasmon excitations Q v in the frame of the semiclassical description or using the plasmon quantization technique. 24,25 In a previous work, we demonstrated that both methods produce equivalent results. 26 We also showed 24 -28 that plasmon excitations include a great variety of modes and frequencies, but when the radius of the cylinder grows, the frequencies of all modes go to that of the surface plasmons characteristic of a plane surface.…”

Charge–Metal Interaction of a Carbon Nanotube

“…The results of the mathematical treatment are fit to two simple three-dimensional functions of 1) the radius of the tube and 2) the distance of the charge from either its inner or outer surfaces that are readily amenable to use in the treatment of experimental data or in molecular modeling. Arista et al used a similar approach to investigate the interactions between a metal cylinder and a moving charge, [5] and their results were used by Granger et al to support the idea of the existence of image states around nanotubes.[6] For a charge outside/inside a hollow cylinder with internal/external radius a¼rÀx=2 and b¼rþx=2 where r is the tube radius and x is its thickness, the electrostatic potential induced on the position of the charge, can written in terms of a modified Bessel functions I m (x) and K m (x) [12] , see the Appendix for the derivation of Equations (1a) and (1b): …”

“…[5, 6] This is not to say that interactions between SWCNTs and molecules have not been studied, but rather that the additional metallic contribution to the interaction with a (partial) charge has often been left unquantified or even neglected. And yet, this is not a trivial issue because prior to many of the practical applications advocated for SWCNTs there is the separation of metallic from semiconducting tubes that could be based on the larger adsorption energy of charged molecules when bound to metallic nanotubes.…”

“…The set of Figure 1 illustrates the functions and shows that the additional stabilizing contribution of the interaction of a metallic nanotube with a charge of an electron (in absolute value) is up to one electronvolt. Although not directly comparable, B3LYP/SVP calculations of alkali cations on a section of a [5,5] nanotube give total binding energies, that include van der Waals, electro- Figure 1. The metal-charge interaction energy of a metallic SWCNT with zero thickness with a charge of one atomic unit.…”