Plasmon bands in multilayer graphene

Wachsmuth, Philipp; Hambach, Ralf; Benner, G.; Kaiser, Ute

doi:10.1103/physrevb.90.235434

Cited by 47 publications

(52 citation statements)

References 39 publications

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“…In experimental papers, Refs. [13,14], the authors also obtained π plasmon dispersion relation which is in accordance with our theoretical results and conclusions; however, they are also prone to describe it as √ Q behavior, with help of the hydrodynamic model [33,34].…”

Section: (E) and 2(f)]supporting

confidence: 88%

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Changing character of electronic transitions in graphene: From single-particle excitations to plasmons

2015

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In this paper we clarify the nature of π and π + σ electron excitations in pristine graphene. We clearly demonstrate the continuous transition from single particle to collective character of such excitations and how screening modifies their dispersion relations. We prove that π and π + σ plasmons do exist in graphene, though occurring only for a particular range of wave vectors and with finite damping rate. Particular attention is paid to comparing the theoretical results with available EELS measurements in optical (Q ≈ 0) and other (Q = 0) limits. The conclusions, based on microscopic numerical results, are confirmed in an approximate analytical approach.

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Section: (E) and 2(f)]supporting

confidence: 88%

“…And, finally, for even larger Q the collective nature of this mode in graphene is suppressed and they again emerge as the single-particle excitations. The same kind of dispersion is observed in [13][14][15], but the authors did not analyze it in detail.…”

Section: Introductionmentioning

confidence: 87%

Changing character of electronic transitions in graphene: From single-particle excitations to plasmons

2015

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“…These are counterparts to the π and σ-π interband plasmons observed in intrinsic MG [Figs. 2(a) and 2(b)], few-layer graphene and graphite [49][50][51][52]. Specifically, the π and π-σ structures of the GNRs exhibit a discontinuous dispersion vs q and ω, as they are split into more branches [Figs.…”

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confidence: 99%

Plasmon Modes of Graphene Nanoribbons with Periodic Planar Arrangements

et al. 2016

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Among their amazing properties, graphene and related low-dimensional materials show quantized charge-density fluctuations-known as plasmons-when exposed to photons or electrons of suitable energies. Graphene nanoribbons offer an enhanced tunability of these resonant modes, due to their geometrically controllable band gaps. The formidable effort made over recent years in developing graphene-based technologies is however weakened by a lack of predictive modeling approaches that draw upon available ab initio methods. An example of such a framework is presented here, focusing on narrow-width graphene nanoribbons organized in periodic planar arrays. Time-dependent density-functional calculations reveal unprecedented plasmon modes of different nature at visible to infrared energies. Specifically, semimetallic (zigzag) nanoribbons display an intraband plasmon following the energy-momentum dispersion of a two-dimensional electron gas. Semiconducting (armchair) nanoribbons are instead characterized by two distinct intraband and interband plasmons, whose fascinating interplay is extremely responsive to either injection of charge carriers or increase in electronic temperature. These oscillations share some common trends with recent nanoinfrared imaging of confined edge and surface plasmon modes detected in graphene nanoribbons of 100-500 nm width. Plasmons are quantized oscillations of the valence electron density in metals, metal-dielectric interfaces and nanostructures, being usually excited by light or electronbeam radiation. Plasmon-related technologies are expected to receive a burst from nanocarbon architectures [1-10], due to one of the fascinating features of monolayer graphene (MG) [11], i.e., its extrinsic plasmon modes at terahertz (THz) frequencies [12][13][14][15][16][17][18][19][20]. These show much stronger confinement, larger tunability and lower losses [21] compared to conventional plasmonic materials, such as silver or gold. Nowadays plasmons are launched, controlled, manipulated and detected in a variety of graphene-related materials and heterostructures, which suggests that graphene-based plasmonic devices are becoming closer to reality, with the potential to operate on the "THz gap", forbidden by either classical electronics or photonics [4,22,23]. Plasmons with widely tunable frequencies have been observed in graphene nanoribbons (GNRs)-from the nano-to microrange in width [12,14,24,25]. On the theoretical side, density functional and tight-binding (TB) approaches have explored the electronic structure of zigzag and armchair GNRs, with particular attention to the band-gap values of the intrinsic systems, being a major control factor of their plasmonic properties [26][27][28][29][30]. Far fewer studies have been focused on plasmon resonances in GNRs using either a semiclassical electromagnetic picture [31] or a TB scheme [5,32,33], and specializing to THz frequencies. A comprehensive characterization of the dielectric properties of such systems is, however, lacking.Here, we provide an ab initio study o...

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“…Apart from high-resolution imaging, we take advantage of the exceptionally low background noise of the SALVE microscopy at low voltages enabling the investigation of plasmons in single [36] and multi-layer graphene using angle-resolved electron energy loss spectroscopy [37]. In addition, we show that graphene can now serve as an extreme thermal platform for physisorbed carbon species whose transformations can be imaged under the influence of Joule heat and electron irradiation atom-by-atom [38].…”

mentioning

confidence: 99%

“…The new Cc/Cs-corrector has been successfully installed into the SALVE microscope and we will show first results from this voltage-tuneable microscope (20-80kV (120kV)). We will discuss the motivation for flexibility in voltage-tuning by means of the complexity of beam-sample interactions in calcite [34] and metal-filled single-walled carbon nanotubes [35].Apart from high-resolution imaging, we take advantage of the exceptionally low background noise of the SALVE microscopy at low voltages enabling the investigation of plasmons in single [36] and multi-layer graphene using angle-resolved electron energy loss spectroscopy [37]. In addition, we show that graphene can now serve as an extreme thermal platform for physisorbed carbon species whose transformations can be imaged under the influence of Joule heat and electron irradiation atom-by-atom [38].…”

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confidence: 99%

Current Status of the Sub-Angstrom Low-Voltage Electron Microscopy (SALVE) Project

Kaiser¹

2013

Microsc Microanal

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The technical realization of the spherical aberration correction in transmission electron microscopes (TEM) [1,2] presently enables atomically-resolved analysis of electron-beam sensitive low-dimensional and low-atomic-number materials down to about 60kV. However, the maximum electron dose which the material can tolerate limits decisively the achievable specimen resolution in TEM images [3]. Low-dose modes combined with appropriate image processing techniques in the past a domain in biological sciences needs to be applied and developed for materials science applications [4,5]. Using such techniques, microscopists begin to discover new physics and chemistry of low-dimensional materials on the atomic level. In the past these task have been tackled solely by means of computer simulations and analytical theory. The two-dimensional objects are very thin and have an exactly defined thickness. Therefore, their images are well suited for quantitative comparison with those obtained from image calculations. Scientists now can determine (a) the exact atomic structure of point defects [6][7][8][9][10][11], (b) the knock-on damage thresholds in 2D materials [12,13], (c) electron energy-and dose-dependent structural rearrangements of defects from atomically resolved image sequences [14,15], (d) bonding effects information in high-resolution TEM images of covalently bonded light elements [16], (e) the structure of grain boundaries and dislocations and their dynamics [17][18][19][20][21][22], (f) new transformation routes between carbon nanostructures [23][24][25], and moreover (g) the structure of the two-dimensional amorphous phase on the atom-by-atom base [26,27]. Above 80kV, the low intrinsic contrast and the high susceptibility of these materials to electron-beam induced knock-on damage prevents an atomically resolved analysis, Recent low-voltage microscope developments address electron energies down to 40keV [28], 30keV [29], or 20keV [30] because materials, in particular low-Z materials, often require imaging at energies appreciably lower than 80keV or 60keV. To obtain high image contrast and high resolution at these low energies, it is mandatory to compensate for the spherical aberration and the chromatic aberration of the objective lens [31]. We demonstrate by means of image calculations [32,33] at 20keV and 40keV that in the case of spherical and chromatic correction the image contrast cannot be described by means of the weak phase-object approximation, even not even for graphene, a mono-atomic layer of carbon atoms. Because at these voltages all atoms are strong scatters, we must incorporate the effect of inelastic scattering in the image simulation of low-Z specimens because the inelastic scattering cross-section is about 20/Z times the elastic scattering cross-section. We show first results for simulated energy-filtered elastic and inelastic images of graphene and silicon [33]. The new Cc/Cs-corrector has been successfully installed into the SALVE microscope and we will show first results from this voltage-tuneabl...

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Plasmon bands in multilayer graphene

Cited by 47 publications

References 39 publications

Changing character of electronic transitions in graphene: From single-particle excitations to plasmons

Changing character of electronic transitions in graphene: From single-particle excitations to plasmons

Plasmon Modes of Graphene Nanoribbons with Periodic Planar Arrangements

Current Status of the Sub-Angstrom Low-Voltage Electron Microscopy (SALVE) Project

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