Hydrodynamic approximation for the nonlinear response of a metal surface

Bergara, Aitor; Pitarke, J. M.; Ritchie, R.H.

doi:10.1103/physrevb.60.16176

Cited by 7 publications

(9 citation statements)

References 37 publications

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“…(8) and (9) in the Heisenberg picture. Our results [23] reproduce previous calculations for the image potential [defined as half the induced potential at the position of the charged particle that creates it] of a static (v = 0) external charged particle [5], which in the case of a non-dispersive electron gas (β = 0) coincides with the classical image potential [24] V im (z) = −(4z) −1 . The energy loss per unit path length of a moving charged particle can be obtained as the retarding force that the polarization charge distribution in the electron gas exerts on the projectile itself [25]:…”

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confidence: 88%

Plasmon excitation by charged particles interacting with metal surfaces

1999

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Recent experiments (R. A. Baragiola and C. A. Dukes, Phys. Rev. Lett. 76, 2547 (1996)) with slow ions incident at grazing angle on metal surfaces have shown that bulk plasmons are excited under conditions where the ions do not penetrate the surface, contrary to the usual statement that probes exterior to an electron gas do not couple to the bulk plasmon. We here use the quantized hydrodynamic model of the bounded electron gas to derive an explicit expression for the probability of bulk plasmon excitation by external charged particles moving parallel to the surface. Our results indicate that for each q (the surface plasmon wave vector) there exists a continuum of bulk plasmon excitations, which we also observe within the semi-classical infinite-barrier (SCIB) model of the surface.It is well known that charged particles interacting with solid surfaces can create electronic collective excitations in the solid. These are bulk [1] and surface [2] plasmons. In the absence of electron-gas dispersion, the scalar electric potential due to bulk plasmons vanishes outside the surface [3]; hence, in this case probes exterior to the solid can only generate surface excitations. That electron-gas dispersion allows external probes to interact with bulk plasmons was discussed by Barton [4] and Eguiluz [5], and more recently by Nazarov et al [6]. Nevertheless, the fact that within a non-local description of screening bulk plasmons do give rise to a potential outside the solid has been ignored over the years [7,8], even when electrongas dispersion has been included; also, current non-local theories of plasmon excitation by external charges have not shown evidence for bulk plasmon excitation outside the solid [8][9][10]. Recently, Baragiola and Dukes [11] have studied the emission spectra produced by slow ions that were incident at grazing angle; their data indicate that the bulk plasmon is importantly involved in the emission process, though the projectiles are not expected to have penetrated into the solid. Bulk plasmon excitation in electron emission spectra produced by slow multiply charged ions has also been investigated [12], with projectiles that may enter the solid.In this letter we derive, within the quantized hydrodynamic model of the bounded electron gas [13], an explicit expression for the probability of bulk plasmon excitation by external charged particles moving parallel to a jellium surface. Our model, which assumes a sharp electron density profile at the surface, neatly displays the role of bulk plasmon excitations in the interaction of charged particles moving near a metal surface. We also demonstrate that our results for the total energy-loss probability agree with standard calculations [14] derived either by solving the linearized Bloch hydrodynamic equations [15] or within the semi-classical infinite-barrier (SCIB) model of the surface [16,17] with the hydrodynamic approximation for the bulk dielectric function. Though it has been generally believed that when charged particles move outside the solid the energy l...

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confidence: 88%

Plasmon excitation by charged particles interacting with metal surfaces

1999

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“…Our derivation of the quantized SPP Hamiltonian H SPP and its coupling to electrons H SPP-el follows the procedure used in Ref. 80, in which the SPPs are obtained from quantization of the classical plasmon field. The classical plasmon field is derived within the hydrodynamical model, which treats plasmons as irrotational deformations of the conduction electrons.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Kinetic theory of surface plasmon polariton in semiconductor nanowires

Yin

2013

Phys. Rev. B

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Based on the semiclassical model Hamiltonian of the surface plasmon polariton and the nonequilibrium Green-function approach, we present a microscopic kinetic theory to study the influence of the electron scattering on the dynamics of the surface plasmon polariton in semiconductor nanowires. The damping of the surface plasmon polariton originates from the resonant absorption by the electrons (Landau damping), and the corresponding damping exhibits size-dependent oscillations and distinct temperature dependence without any scattering. The scattering influences the damping by introducing a broadening and a shifting to the resonance. To demonstrate this, we investigate the damping of the surface plasmon polariton in InAs nanowires in the presence of the electron-impurity, electron-phonon and electron-electron Coulomb scatterings. The main effect of the electron-impurity and electron-phonon scatterings is to introduce a broadening, whereas the electron-electron Coulomb scattering can not only cause a broadening, but also introduce a shifting to the resonance. For InAs nanowires under investigation, the broadening due to the electron-phonon scattering dominates. As a result, the scattering has a pronounced influence on the damping of the surface plasmon polariton: The size-dependent oscillations are smeared out and the temperature dependence is also suppressed in the presence of the scattering. These results demonstrate the the important role of the scattering on the surface plasmon polariton damping in semiconductor nanowires.Comment: 21 pages, 11 figure

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“…However, these corrections have been shown to be less important when the charged particle moves outside the solid [56]. Hence, in the case of a bounded three-dimensional electron gas we restrict the calculations to linear-response theory.…”

Section: Bounded Electron Gasmentioning

confidence: 99%

Nonlinear, Band-Structure, and Surface Effects in the Interaction of Charged Particles with Solids

Pitarke¹,

Gurtubay²,

Nazarov³

2004

Advances in Quantum Chemistry

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A survey is presented of various aspects of the interaction of charged particles with solids. In the framework of many-body perturbation theory, we study the nonlinear interaction of charged particles with a free gas of interacting electrons; in particular, nonlinear corrections to the stopping power are analyzed, and special emphasis is made on the separate contributions that are originated in the excitation of either electron-hole pairs, single plasmons, or double plasmons. Ab initio calculations of the electronic energy loss of ions moving in real solids are also presented, and the energy loss of charged particles interacting with simple metal surfaces is addressed.

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Hydrodynamic approximation for the nonlinear response of a metal surface

Cited by 7 publications

References 37 publications

Plasmon excitation by charged particles interacting with metal surfaces

Plasmon excitation by charged particles interacting with metal surfaces

Kinetic theory of surface plasmon polariton in semiconductor nanowires

Nonlinear, Band-Structure, and Surface Effects in the Interaction of Charged Particles with Solids

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