The effects of spin-orbit (SOC) and electron-phonon coupling on the collective excitation of doped monolayer Sb$_2$ are investigated using density functional and many-body perturbation theories. The spin-orbit coupling is exclusively important for the monolayer Sb$_2$ and it leads to the reconstruction of the electronic band structure. In particular, plasmon modes of monolayer Sb$_2$ are quite sensitive to the SOC and are characterized by very low damping rates owing to small electron-phonon scatterings. Our results show plasmons in antimonene are significantly less damped compared to monolayer graphene when plasmon energies are $\hbar ω> 0.2$ eV due to smaller plasmon-phonon coupling in the former material.
The collective excitation spectrum of two-dimensional (2D) antimonene is calculated beyond the low energy continuum approximation. The dynamical polarizability is computed using a 6-orbitals tight-binding model that properly accounts for the band structure of antimonene in a broad energy range. Electron-electron interaction is considered within the random phase approximation. The obtained spectrum is rich, containing the standard intra-band 2D plasmon and a set of single inter-band modes. We find that spin-orbit interaction plays a fundamental role in the reconstruction of the excitation spect…
We report on a theoretical study of collective electronic excitations in single-layer antimony crystals (antimonene), a novel two-dimensional semiconductor with strong spin-orbit coupling. Based on a tight-binding model, we consider electron-doped antimonene and demonstrate that the combination of spin-orbit effects with external bias gives rise to peculiar plasmon excitations in the mid-infrared spectral range. These excitations are characterized by low losses and negative dispersion at frequencies effectively tunable by doping and bias voltage. The observed behavior is attributed to the spin…
Plasmonics currently faces the problem of seemingly inevitable optical losses occurring in the metallic components that challenges the implementation of essentially any application. In this work we show that Ohmic losses are reduced in certain layered metals, such as the transition metal dichalcogenide TaS$_2$, due to an extraordinarily small density of states for scattering in the near-IR originating from their special electronic band structure. Based on this observation we propose a new class of band structure engineered van der Waals layered metals composed of hexagonal transition metal cha…
Anisotropic plasmon coupling in closely-spaced chains of Ag nanoparticles was visualized using the electron energy loss spectroscopy in a scanning transmission electron microscope. For dimers as the simplest chain, mapping the plasmon excitations with nanometers' spatial resolution and 0.27 eV energy resolution intuitively identified two coupling plasmons. The in-phase mode redshifted from the ultraviolet region as the inter-particle spacing was reduced, reaching the visible range at 2.7 eV. Calculations based on the discrete dipole approximation confirmed its optical activeness, where the lon…
In this article, we explore the anisotropic electron energy loss spectrum (EELS) in monolayer phosphorene based on ab-initio time dependent density functional theory calculations. Similar to black phosphorous, the EELS of undoped monolayer phosphorene is characterized by anisotropic excitonic peaks for energies in vicinity of the bandgap, and by interband plasmon peaks for higher energies. On doping, an additional intraband plasmon peak also appears for energies within the bandgap. Similar to other two dimensional systems, the intraband plasmon peak disperses as $ω_{\rm pl} \propto \sqrt{q}$ i…
Graphene plasmons were predicted to possess ultra-strong field confinement and very low damping at the same time, enabling new classes of devices for deep subwavelength metamaterials, single-photon nonlinearities, extraordinarily strong light-matter interactions and nano-optoelectronic switches. While all of these great prospects require low damping, thus far strong plasmon damping was observed, with both impurity scattering and many-body effects in graphene proposed as possible explanations. With the advent of van der Waals heterostructures, new methods have been developed to integrate graphe…
Graphene sheets encapsulated between hexagonal Boron Nitride (hBN) slabs display superb electronic properties due to very limited scattering from extrinsic disorder sources such as Coulomb impurities and corrugations. Such samples are therefore expected to be ideal platforms for highly-tunable low-loss plasmonics in a wide spectral range. In this Article we present a theory of collective electron density oscillations in a graphene sheet encapsulated between two hBN semi-infinite slabs (hBN/G/hBN). Graphene plasmons hybridize with hBN optical phonons forming hybrid plasmon-phonon (HPP) modes. W…
In this paper we propose and discuss coherent terahertz sources based on charge density wave (plasmon) amplification in two dimensional graphene. The coupling of the plasmons to interband electron-hole transitions in population inverted graphene layers can lead to plasmon amplification through stimulated emission. Plasmon gain values in graphene can be very large due to the small group velocity of the plasmons and the strong confinement of the plasmon field in the vicinity of the graphene layer. We present a transmission line model for plasmon propagation in graphene that includes plasmon diss…
Graphene plasmonics is of great interest for compact optical devices working in broad frequency domains with ultrahigh speed and very low energy consumption. However, graphene plasmons damp out quickly on most substrates mainly due to scattering loss from substrate surface phonons and impurities. Here we discover a new hybridized plasmon-phonon polariton mode in graphene/h-BN van der Waals heterostructures, which enables ultralong hybrid plasmon lifetime up to 1.6 picosecond, the longest plasmon lifetime ever demonstrated. Such remarkably long lifetime arises from the coupling of long-lifetime…
High-resolution electron energy loss spectroscopy (HREELS) is one of the most powerful methods to detect the dispersion of plasmons. However, we find that in the HREELS measurement, the scattering geometric configuration will seriously affect the identification of plasmons. Here, taking graphene as an example, using the HREELS capable of two-dimensional energy-momentum mapping combined with the intensity distribution calculations, we visually display the intensity distribution of the scattering geometric factor. We demonstrate that the energy loss peaks from the scattering geometric effect may…
We study the TE polarized electromagnetic surface wave propagating along the interface between materials with positive and negative magnetic permeability. Contrary to the TM polarized surface wave, the TE surface wave exhibits almost no radiation losses when scattered at semi-infinite dielectric interfaces.
We explore the collective electronic excitations of bilayer molybdenum disulfide (MoS$_2$) using the density functional theory together with the random phase approximation. The many-body dielectric function and electron energy-loss spectra are calculated using an {\it ab initio} based model involving material-realistic physical properties. The electron energy-loss function of bilayer MoS$_2$ system is found to be sensitive to either electron or hole doping and it is owing to the fact that the Kohn-Sham band dispersions are not symmetric for energies above and below the zero Fermi level. Three …
Unlike conventional optics, plasmonics enables unrivalled concentration of optical energy well beyond the diffraction limit of light. However, a significant part of this energy is dissipated as heat. Plasmonic losses present a major hurdle in the development of plasmonic devices and circuits that can compete with other mature technologies. Until recently, they have largely kept the use of plasmonics to a few niche areas where loss is not a key factor, such as surface enhanced Raman scattering and biochemical sensing. Here, we discuss the origin of plasmonic losses and various approaches to eit…
We propose a composite layered structure for tunable, low-loss plasmon resonances, which con- sists of a noble-metal thin film coated in graphene and supported on a hexagonal boron nitride (hBN) substrate. We calculate electron energy loss spectra (EELS) for these structures, and nu- merically demonstrate that bulk plasmon losses in noble-metal films can be significantly reduced, and surface coupling enhanced, through the addition of a graphene coating and the wide-bandgap hBN substrate. Silver films with a trilayer graphene coating and hBN substrate demonstrated sur- face plasmon-dominant spe…
The inelastic scattering of electrons is one route to study the vibrational and electronic properties of materials. Such experiments, also called electron energy-loss spectroscopy, are particularly useful for the investigation of the collective excitations in metals, the charge carrier plasmons. These plasmons are characterized by a specific dispersion (energy-momentum relationship), which contains information on the sometimes complex nature of the conduction electrons in topical materials. In this review we highlight the improvements of the electron energy-loss spectrometer in the last years,…
A periodic arrangement of 2D conducting planes is known to host a (bulk) plasmon dispersion that interpolates between the typical, gapped behavior of 3D metals and a gapless, acoustic regime as a function of the out-of-plane wavevector. The semi-infinite system -- the configuration relevant to Electron Energy Loss Spectroscopy (EELS) in a reflection geometry, as in High Resolution EELS (HREELS) -- is known to host a surface plasmon that ceases to propagate below a cutoff wavevector. As the f-sum rule requires a finite response whether or not there exist sharp excitations, we demonstrate that w…
Natural hyperbolic two-dimensional systems are a fascinating class of materials that could open alternative pathways to the manipulation of plasmon propagation and light-matter interactions. Here, we present a comprehensive study of the optical response in T$_d\,$-WTe$_2$ by means of density-functional and many-body perturbation theories. We show how monolayer WTe$_2$ with in-plane anisotropy sustains hyperbolic plasmon polaritons, which can be tuned via chemical doping and strain. The latter is able to extend the hyperbolic regime toward the near infrared with low losses. Moreover, with a mod…
A fully relativistic description of the electron energy loss and the induced radiation emission in arbitrary arrays of non-overlapping metallic cylinders is presented in terms of the multiple scattering method on the basis of vector cylindrical waves. Numerical analysis is given for dilute and dense arrays of Aluminum cylinders with a nanoscale diameter. The results of the electron energy loss spectrum are well correlated with the dispersion relation of coupled surface plasmon polaritons, and can be interpreted with an effective medium approximation when the electron runs inside the arrays. In…
Plasmons dispersion and nonvertical interband transitions in Bi2Se3 single crystals were investigated by electron energy-loss spectroscopy in conjunction with (scanning) transmission electron microscopy, (S)TEM-EELS. Both volume plasmons (π plasmon at 7 eV and π+σ plasmon at 17 eV) and surface plasmons (~5.5 and 10 eV) were demonstrated in STEM-EELS spectra and the corresponding spectral imaging in real space. In the further EELS experiments in reciprocal space, the momentum-dependent spectra reveal very different dispersion behavior between π and π+σ plasmons, with π+σ plasmons showing a typi…
Strontium molybdate (SrMoO3) thin films are shown to exhibit plasmonic behaviour with a zero crossover wavelength of the real part of the dielectric permittivity tunable between 600 and 950 nm (2.05 eV and 1.31 eV). The films are grown epitaxially on strontium titanate (SrTiO3), magnesium oxide (MgO), and lanthanum aluminate (LaAlO3) substrates by pulsed laser deposition. SrMoO3 is shown to have optical losses lower than those of gold at the point at which the real part of the dielectric permittivity is equal to -2, while possessing low electrical resistivity of 100E-6 Ohm cm at room temperatu…
We report on strong coupling of the charge carrier plasmon $ω_{PL}$ in graphene with the surface optical phonon $ω_{SO}$ of the underlying SiC(0001) substrate with low electron concentration ($n=1.2\times 10^{15}$ $cm^{-3}$) in the long wavelength limit ($q_\parallel \rightarrow 0$). Energy dependent energy-loss spectra give for the first time clear evidence of two coupled phonon-plasmon modes $ω_\pm$ separated by a gap between $ω_{SO}$ ($q_\parallel \rightarrow 0$) and $ω_{TO}$ ($q_\parallel >> 0$), the transverse optical phonon mode, with a Fano-type shape, in particular for higher primary e…
BaSnO$_3$ exhibits the highest carrier mobility among perovskite oxides, making it ideal for oxide electronics. Collective charge carrier oscillations, plasmons, are expected to arise in this material, thus providing a tool to control the nanoscale optical field for optoelectronics applications. Here, we demonstrate the existence of relatively long-lived plasmons supported by high-mobility charge carriers in La-doped BaSnO$_3$ (BLSO). By exploiting the high spatial and energy resolution of electron energy-loss spectroscopy with a focused beam in a scanning transmission electron microscope, we …
Plasmonic phenomena are exhibited in light-matter interaction involving materials whose real parts of permittivity functions attain negative values at operating wavelengths. However, such materials usually suffer from dissipative losses, thus limiting the performance of plasmon-based optical devices. Here, we utilize an alternative methodology that mimics a variety of plasmonic phenomena by exploiting the well-known structural dispersion of electromagnetic modes in bounded guided-wave structures filled with only materials with positive permittivity. A key issue in design of such structures is …
The nature of low energy plasmon excitations plays an important role in understanding the low energy electronic properties and coupling mechanism of different superconducting compounds such as CaC$_6$. Recent ab-initio studies predict a charge carrier intraband plasmon in keeping with a low energy acoustic plasmon. Here, we have studied the low-energy electronic excitations of CaC$_6$ using high-resolution electron energy-loss spectroscopy in transmission at low temperatures. The analysis of the core-level excitations leads to the conclusion that hybridization between graphite and calcium stat…
We investigate the effects of crystal lattice vibrations on the dispersion of plasmons. The loss function of the homogeneous electron gas (HEG) in two and three dimensions is evaluated numerically in presence of electronic coupling to an optical phonon mode. Our calculations are based on many-body perturbation theory for the dielectric function as formulated by the Hedin-Baym equations in the Fan-Migdal approximation. The coupling to phonons broadens the spectral signatures of plasmons in the electron-energy loss spectrum (EELS) and it induces the decay of plasmons on timescales shorter than 1…
In previous work a different and powerful, analytical, technique was used to get data, such as the absolute atom concentration (AAC), specimen thickness etc., from public domain boron nitride EELS spectrum collected under a collection semi-angle, $β$, less than the plasmon cutoff angle, $θ_{c}$, but large relative to incident beam convergence, $α$. Here, seeking for some completeness, another, numerical, technique usable together with, also, $β< θ_{c}$ is described in minute detail and applied to data obtained with $β/α< 2$, so necessitating incident beam convergence-related corrections. A lot…
Graphene-based hyperbolic metamaterials have been predicted to transport evanescent fields with extraordinarily large vacuum wave-vectors. It is particularly at much higher wave vector values that the commonly employed descriptional models involving structure homogenization and assumptions of an approximatively local graphene conductivity start breaking down. Here, we combine a non-local quantum conductivity model of graphene with an exact mathematical treatment of the periodic structure in order to develop a tool-set for determining the hyperbolic behavior of these graphene-based hyperbolic m…
We report on a combined far- and near-field study of surface plasmon polaritons on freestanding perforated gold films. The samples are fabricated by focused ion beam milling of {a periodic hole array into} a carbon membrane followed by thermal evaporation of gold and plasma ashing of the carbon film. Optical transmission spectra show a series of characteristic features, which can be attributed to the excitation of surface plasmon modes via the periodic nanohole array. The corresponding near-field distributions are mapped by electron energy-loss spectroscopy. Besides the optically bright surfac…
Low-loss electron energy loss spectroscopy (EELS) has emerged as a technique of choice for exploring the localization of plasmonic phenomena at the nanometer level, necessitating analysis of physical behaviors from 3D spectral data sets. For systems with high localization, linear unmixing methods provide an excellent basis for exploratory analysis, while in more complex systems large numbers of components are needed to accurately capture the true plasmonic response and the physical interpretability of the components becomes uncertain. Here, we explore machine learning based analysis of low-los…
Transparent conducting oxides (TCO) are emerging as possible alternative constituent materials to replace noble metals such as silver and gold for low-loss plasmonic and metamaterial (MMs) applications in the near infrared (NIR) regime. The optical characteristics of TCOs have been studied to evaluate the functionalities and potential of these materials as metal substitutes in plasmonic and MM devices, even apart from their usual use as electrode materials. However, patterning TCOs at the nanoscale, which is necessary for plasmonic and MM devices, is not well-studied. This paper investigates n…
