Influence of the Electron Charge Distribution on Surface-Plasmon Dispersion

Bennett, Alan J.

doi:10.1103/physrevb.1.203

Cited by 263 publications

(126 citation statements)

References 27 publications

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“…3 we plot ω/(qa) 1/4 for the monopole mode based on the numerical solution of Eq. (14). We see that the numerical results are in good agreement with the analytic argument.…”

Section: -3supporting

confidence: 79%

“…11 Xia and Quinn showed that systems with gradual edge density profiles support several types of edge waves (multipole modes) 12 that can be thought of as standing-wave plasmons fitting into the diffuse edge layer. This notation is very similar as 3D multipole surface plasmons [13][14][15][16][17][18] that have been observed experimentally on K, Na, and Ag surfaces 19,20 and, very recently, in graphene-coated Ir and SiC. 21 Basic requirements for the existence of such higher-multipole modes include gradual edge density profile and dispersion of bulk plasmon.…”

Section: Introductionmentioning

confidence: 99%

“…The numerical calculation must include a sufficient number of terms to guarantee convergence; we find that the results converge quickly and n = 20 yields the desired accuracy both for Eqs. (12) and (14). The potential at x > 0 can be obtained from Eqs.…”

Section: A a Semi-infinite Sheetmentioning

confidence: 99%

“…Interestingly, the main difference between the equations for a 2DEG and graphene is the different power of the edge profile f (x) that appears in Eqs. (12) and (14). This implies that for an abrupt edge, which is described by f (x) = 0 or f (x) = 1, there is no difference between a 2DEG and graphene as f (x) = √ f (x) (except for the differences arising from the prefactors ω 2 a ), and the edge plasmon dispersion relation is approximately given by ω(q) = (2/3) 1/2 ω B (q), where ω B (q) is the bulk plasma frequency.…”

Section: A a Semi-infinite Sheetmentioning

confidence: 99%

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Edge plasmons in graphene nanostructures

2011

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Plasmon modes in graphene are influenced by the unusual dispersion relation of the material. For bulk plasmons this results in a n 1/4 dependence of the plasma frequency on the charge density, as opposed to the n 1/2 dependence in two-dimensional electron gas (2DEG); yet, bulk plasmon dispersion in graphene follows a similar q 1/2 behavior as for other two-dimensional materials. In this work we consider finite graphene nanostructures, semi-infinite sheets, and circular disks and study edge plasmons that are confined to the boundaries of the structures. We find that, for abrupt edges, graphene edge plasmons behave analogously to those in 2DEGs, but, for gradual edge profiles, important distinctions arise. In particular, we show that for a linear edge profile, graphene supports fewer edge modes than a 2DEG at a given q, and the edge monopole plasmon dispersion in graphene follows a q 1/4 law in contrast to the q 0 behavior seen in 2DEGs.

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“…3 we plot ω/(qa) 1/4 for the monopole mode based on the numerical solution of Eq. (14). We see that the numerical results are in good agreement with the analytic argument.…”

Section: -3supporting

confidence: 79%

Section: Introductionmentioning

confidence: 99%

Section: A a Semi-infinite Sheetmentioning

confidence: 99%

Section: A a Semi-infinite Sheetmentioning

confidence: 99%

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Edge plasmons in graphene nanostructures

2011

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“…10 The multipole mode is a result of the nonlocal dielectric response at the surface. It was obtained by Feibelman 11 in the random-phase approximation ͑RPA͒ for the response function in a jellium model.…”

Section: Introductionmentioning

confidence: 99%

Dielectric screening and band-structure effects in low-energy photoemission

et al. 2010

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Nonlocal response of the surface to the incident light is included into an ab initio one-step photoemission theory. Surface-state normal emission spectra from Be͑0001͒ and Al͑100͒ are calculated by a full-potential scattering method and are found to agree well with the experiment in a wide energy range. The total exciting field is obtained within the random-phase approximation for jellium as well as for one-dimensional crystal models of the two surfaces. Material dependence of the multipole plasmon mode and strong effect of band structure on the photoyield is discussed.

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Electron Energy Loss Spectroscopy in Analysis of Surfaces

Erskine

2000

Encyclopedia of Analytical Chemistry

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Electron energy loss spectroscopy (EELS) is a versatile and sensitive probe of electronic and vibrational excitations at surfaces. The technique is extensively used as a research and analytical tool in a broad range of surface science applications including research on intrinsic physical and chemical properties of surfaces, chemisorption phenomena, and chemical processes at surfaces. The spectroscopy is based on measuring the energy loss and momentum transfer of electrons in a highly collimated, monochromatic (narrow energy spread) beam after the electrons scatter from a surface. Vibrational excitations of atoms and molecules adsorbed on surfaces, collective excitations of ordered chemisorbed structures, the intrinsic collective excitations of surface atoms (surface phonons), and collective electronic excitations (surface plasmons) can be studied using the technique. Under favorable conditions, vibrational losses from surface adsorbate concentrations below 10 −3 monolayer (10 12 atoms cm −2 ) can be detected. EELS is a surface science probe, typically requiring an ultrahigh vacuum (UHV) environment, and is generally employed in conjunction with complementary surface analytical probes such as Auger electron spectroscopy (AES), low‐energy electron diffraction (LEED) and thermal desorption mass spectroscopy (TDS). EELS is an ideal tool for determining surface chemical composition, and provides vibrational loss spectra similar to infrared reflection absorption spectroscopy (IRAS), Raman spectroscopy, and helium atom scattering spectroscopy (HAS).

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Influence of the Electron Charge Distribution on Surface-Plasmon Dispersion

Cited by 263 publications

References 27 publications

Edge plasmons in graphene nanostructures

Edge plasmons in graphene nanostructures

Dielectric screening and band-structure effects in low-energy photoemission

Electron Energy Loss Spectroscopy in Analysis of Surfaces

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