Momentum-resolved Electron Energy-loss Spectroscopy Research Articles

Mapping the energy-momentum dispersion of hBN excitons and hybrid plasmons in hBN-WSe2 heterostructures

Heterostructures obtained by combining two-dimensional (2D) sheets are widely investigated as a platform for designing new materials with customised characteristics. Transition metal dichalcogenides (TMDCs) are often combined with hexagonal boron nitride (hBN) to enhance their excitonic resonances. However, little is known about how stacking affects excitons and plasmons in TMDCs or their mutual interactions. Here, we combine momentum-resolved electron energy-loss spectroscopy with first-principles calculations to study the energy-momentum dispersion of plasmons in multi-layer WSe2-hBN heterostructures as well as in their isolated components. The dispersion of the high-momentum excitons of hBN, alone and in combination with WSe2, is mapped across the entire Brillouin zone. Signatures of hybridisation in the plasmon resonances and some of the excitons suggest that the contribution of hBN cannot be neglected when interpreting the response of such a heterostructure. The consequences of using hBN as an encapsulant for TMDCs are also discussed.

Investigation of Anisotropic Electronic Structure in Graphite by Momentum-Resolved Electron Energy Loss Spectroscopy (ω-q Mapping) and Electron Spectroscopic Diffraction Patterns

Investigation of Anisotropic Electronic Structure in Graphite by Momentum-Resolved Electron Energy Loss Spectroscopy (<i>ω</i>-<i>q</i> Mapping) and Electron Spectroscopic Diffraction Patterns

Probing the Polarization of Low-Energy Excitations in 2D Materials from Atomic Crystals to Nanophotonic Arrays Using Momentum-Resolved Electron Energy Loss Spectroscopy.

Spectroscopies utilizing free electron beams as probes offer detailed information on the reciprocal-space excitations of 2D materials such as graphene and transition metal dichalcogenide monolayers. Yet, despite the attention paid to such quantum materials, less consideration has been given to the electron-beam characterization of 2D periodic nanostructures such as photonic crystals, metasurfaces, and plasmon arrays, which can exhibit the same lattice and excitation symmetries as their atomic analogues albeit at drastically different length, momentum, and energy scales. Because of their lack of covalent bonding and influence of retarded electromagnetic interactions, important physical distinctions arise that complicate interpretation of scattering signals. Here we present a fully-retarded theoretical framework for describing the inelastic scattering of wide-field electron beams from 2D materials and apply it to investigate the complementarity in sample excitation information gained in the measurement of a honeycomb plasmon array versus angle-resolved optical spectroscopy in comparison to single monolayer graphene.

Momentum-resolved EELS and CL study on 1D-plasmonic crystal prepared by FIB method.

We investigate a one-dimensional plasmonic crystal (1D PlC) using momentum-resolved electron energy loss spectroscopy (EELS) and cathodoluminescence (CL) techniques, which are complementary in terms of available optical information. The PlC sample is fabricated from large aluminum grains through the focused ion beam (FIB) method. This approach allows curving nanostructures with high crystallinity, providing platforms for detailed analysis of plasmonic nanostructures using both EELS and CL. The momentum-resolved EELS visualizes dispersion curves outside the light cone, confirming the existence of the surface plasmon polaritons (SPP) and local modes, while the momentum-resolved CL mapping analysis identified these SPP and local modes. Such synergetic approach of two electron-beam techniques offers full insights into both radiative and non-radiative optical properties in plasmonic or photonic structures.

Automatic and Quantitative Measurement of Spectrometer Aberrations.

The performance of electron energy loss spectrometers can often be limited by their electron optical aberrations. Due to recent developments in high energy resolution and momentum-resolved electron energy loss spectroscopy (EELS), there is renewed interest in optimizing the performance of such spectrometers. For example, the "ω - q" mode of momentum-resolved EELS, which uses a small convergence angle and requires aligning diffraction spots with the slot aperture, presents a challenge in the realignments of the spectrometer required by the adjustment of the projection lenses. Automated and robust alignment can greatly benefit such a process. The first step toward this goal is automatic and quantitative measurement of spectrometer aberrations. We demonstrate the measurement of geometric aberrations and distortions in EELS within a monochromated scanning transmission electron microscope (STEM). To better understand the results, we present a wave mechanical simulation of the experiment. Using the measured aberration and distortion coefficients as inputs to the simulation, we find a good match between the simulation and experiment, verifying formulae used in the simulation. From verified simulations with known aberration coefficients, we can assess the accuracy of measurements. Understanding the errors and inaccuracies in the procedure can guide further progress in aberration measurement and correction for new spectrometer developments.

Pines’ demon observed as a 3D acoustic plasmon in Sr2RuO4

The characteristic excitation of a metal is its plasmon, which is a quantized collective oscillation of its electron density. In 1956, David Pines predicted that a distinct type of plasmon, dubbed a ‘demon’, could exist in three-dimensional (3D) metals containing more than one species of charge carrier1. Consisting of out-of-phase movement of electrons in different bands, demons are acoustic, electrically neutral and do not couple to light, so have never been detected in an equilibrium, 3D metal. Nevertheless, demons are believed to be critical for diverse phenomena including phase transitions in mixed-valence semimetals2, optical properties of metal nanoparticles3, soundarons in Weyl semimetals4 and high-temperature superconductivity in, for example, metal hydrides3,5–7. Here, we present evidence for a demon in Sr2RuO4 from momentum-resolved electron energy-loss spectroscopy. Formed of electrons in the β and γ bands, the demon is gapless with critical momentum qc = 0.08 reciprocal lattice units and room-temperature velocity v = (1.065 ± 0.12) × 105 m s−1 that undergoes a 31% renormalization upon cooling to 30 K because of coupling to the particle–hole continuum. The momentum dependence of the intensity of the demon confirms its neutral character. Our study confirms a 67-year old prediction and indicates that demons may be a pervasive feature of multiband metals.

Electronic excitations in monoclinic hafnia as studied by spatially and momentum-resolved electron energy-loss spectroscopy and ab initio density functional theory calculations

Electronic excitations in monoclinic hafnia as studied by spatially and momentum-resolved electron energy-loss spectroscopy and <i>ab initio</i> density functional theory calculations

Imaging Vibrational Excitations in the Electron Microscope

Vibrational spectroscopy is a powerful tool for probing atomic motions in molecules and extended solids. Recent advances in aberration-corrected, monochromated-scanning transmission electron microscopy (STEM) now allow imaging of individual phonon modes at the nanoscale, overcoming the spatial limit imposed by diffraction-limited optical spectroscopy techniques. In this Perspective, we summarize the recent progress in high-resolution electron energy-loss spectroscopy (EELS), which now enables vibrational spectroscopy to be performed in the electron microscope. The high spatial and energy resolution of low-loss EELS can be used to directly image phonons inside or near inorganic and organic materials without considerable sample damage. Monochromated EELS can furthermore resolve isotope specific vibrational signatures and phonon modes arising from single-atom dopants. In parallel with these advances, we highlight the ability of spatial- and momentum-resolved EELS to measure the phonon dispersions at material interfaces, obtaining valuable knowledge about interfacial thermal and electrical transport phenomena. Before concluding, we illustrate how imaging infrared (IR) plasmons at high spatial resolution deepens our understanding of how plasmons interact with molecular vibrations. Taken together, these diverse studies illustrate the capability of monochromated STEM-EELS to image low-energy phonon and plasmon excitations at the nanoscale and the new insights from these studies can be leveraged to engineer the specific material properties needed for next-generation devices.

Deep ultra-violet plasmonics: exploiting momentum-resolved electron energy loss spectroscopy to probe germanium.

Germanium is typically used for solid-state electronics, fiber-optics, and infrared applications, due to its semiconducting behavior at optical and infrared wavelengths. In contrast, here we show that the germanium displays metallic nature and supports propagating surface plasmons in the deep ultraviolet (DUV) wavelengths, that is typically not possible to achieve with conventional plasmonic metals such as gold, silver, and aluminum. We measure the photonic band spectrum and distinguish the plasmonic excitation modes: bulk plasmons, surface plasmons, and Cherenkov radiation using a momentum-resolved electron energy loss spectroscopy. The observed spectrum is validated through the macroscopic electrodynamic electron energy loss theory and first-principles density functional theory calculations. In the DUV regime, intraband transitions of valence electrons dominate over the interband transitions, resulting in the observed highly dispersive surface plasmons. We further employ these surface plasmons in germanium to design a DUV radiation source based on the Smith-Purcell effect. Our work opens a new frontier of DUV plasmonics to enable the development of DUV devices such as metasurfaces, detectors, and light sources based on plasmonic germanium thin films.

Extracting correlation effects from momentum-resolved electron energy loss spectroscopy: Synergistic origin of the dispersion kink in Bi2.1Sr1.9CaCu2O8+x

We employ Momentum-Resolved Electron Energy Loss Spectroscopy (M-EELS) on Bi2.1Sr1.9CaCu2O8+x to resolve the issue of the kink feature in the electron dispersion widely observed in the cuprates. To this end, we utilize the GW approximation to relate the density response function measured in in M-EELS to the self-energy, isolating contributions from phonons, electrons, and the momentum dependence of the effective interaction to the decay rates. The phononic contributions, present in the M-EELS spectra due to electron-phonon coupling, lead to kink features in the corresponding single-particle spectra at energies between 40 meV and 80 meV, independent of the doping level. We find that a repulsive interaction constant in momentum space is able to yield the kink attributed to phonons in ARPES. Hence, our analysis of the M-EELS spectra points to local repulsive interactions as a factor that enhances the spectroscopic signatures of electron-phonon coupling in cuprates. We conclude that the strength of the kink feature in cuprates is determined by the combined action of electron-phonon coupling and electron-electron interactions.

Plasmons in holographic graphene

We demonstrate how self-sourced collective modes – of which the plasmon is a prominent example due to its relevance in modern technological applications – are identified in strongly correlated systems described by holographic Maxwell theories. The characteristic \omega \propto \sqrt{k}ω∝k plasmon dispersion for 2D materials, such as graphene, naturally emerges from this formalism. We also demonstrate this by constructing the first holographic model containing this feature. This provides new insight into modeling such systems from a holographic point of view, bottom-up and top-down alike. Beyond that, this method provides a general framework to compute the dynamical charge response of strange metals, which has recently become experimentally accessible due to the novel technique of momentum-resolved electron energy-loss spectroscopy (M-EELS). This framework therefore opens up the exciting possibility of testing holographic models for strange metals against actual experimental data.

Investigation of anisotropic π plasmon induced by the intrinsic crystallographic defects in topological crystalline insulator material—tin-substitutional lead selenide (Pb1−xSnxSe)

The presence of intrinsic defects in topological crystalline insulator materials has been predicted to improve the thermoelectric figure-of-merit values in the literature. Performing atomic-resolved high angle annular dark field imaging, momentum-resolved electron energy loss spectroscopy, and electron spectroscopic diffraction, we observed those intrinsic defects, including interstitial Se atoms and Se vacancies, to cause localized mirror symmetry breaking and further result in the anisotropic π-plasmon dispersion along the ΓX¯ and ΓM¯ directions in single-crystal Pb1−xSnxSe (x = 0 and 0.34). In addition to the anisotropic π plasmon dispersion, the splitting lines along the ΓX¯ direction were revealed with selected π plasmon energy in the electron spectroscopic diffraction pattern.

Probing Exciton Dispersions of Freestanding Monolayer WSe2 by Momentum-Resolved Electron Energy-Loss Spectroscopy

Excitons, as bound electron-hole paired quasiparticle, play an essential role in the energy transport in the optical-electric properties of semiconductors. Their momentum-energy dispersion relation is a fundamental physical property of great significance to understand exciton dynamics. However, this dispersion is seldom explored especially in two-dimensional transition metal dichalcogenides with rich valleytronic properties. In this work, momentum resolved electron energy-loss spectroscopy was used to measure the dispersions of excitons in freestanding monolayer WSe_{2}. Besides the parabolically dispersed valley excitons, a subgap dispersive exciton was observed at nonzero momenta for the first time, which can be introduced by the prolific Se vacancies. Our work provides a paradigm to directly probe exciton dispersions in 2D semiconductors and could be generalized to many low-dimensional systems.

Dynamical charge susceptibility in the Hubbard model

We compute the dynamical charge susceptibility in the two-dimensional Hubbard model within the dynamical cluster approximation. In order to understand the connection between charge susceptibility and pseudogap, we investigate the momentum, doping, and temperature dependence. We find that as a function of frequency, the dynamical charge susceptibility is well represented by a single peak at a characteristic frequency. It shows little momentum or temperature dependence, while the doping dependence is more evident, and no clear signature of the pseudogap is observed. Data for the doping evolution of the static susceptibility and for fluctuation diagnostics are presented. Our susceptibilities should be directly measurable in future Momentum-resolved electron energy-loss spectroscopy experiments.

Emergence of point defect states in a plasmonic crystal

Plasmonic crystals are well known to have band structure including a band gap, enabling the control of surface plasmon propagation and confinement. The band dispersion relation of bulk crystals has been generally measured by momentum-resolved spectroscopy using far field optical techniques while the defects introduced in the crystals have separately been investigated by near field imaging techniques so far. Particularly, defect related energy levels introduced in the plasmonic band gap have not been observed experimentally. In order to investigate such a localized mode, we performed electron energy-loss spectroscopy (EELS) on a point defect introduced in a plasmonic crystal made up of flat cylinders protruding out of a metal film and arranged on a triangular lattice. The energy level of the defect mode was observed to lie within the full band-gap energy range. This was confirmed by a momentum-resolved EELS measurement of the band gap performed on the same plasmonic crystal. Furthermore, we experimentally and theoretically investigated the emergence of the defect states by starting with a corral of flat cylinders protrusions and adding sequentially additional shells of those in order to eventually form a plasmonic band-gap crystal encompassing a single point defect. It is demonstrated that a defectlike state already forms with a crystal made up of only two shells.

Investigation of the π plasmon and plasmon-exciton coupling in titanium diselenide (TiSe2) by momentum-resolved electron energy loss spectroscopy

In this work, π-plasmon dispersion and plasmon-exciton coupling in single-crystal 1T-TiSe2 along the ΓM¯ direction were investigated by using momentum (q)-resolved electron energy loss spectroscopy (EELS), ω-q map. Both the π plasmon at 7 eV and the π + σ plasmon at ∼19.7 eV were observed in the EELS spectrum. Furthermore, the π plasmon exhibits an unexpected dispersion behavior that transitions from a square root of q dependence (q1/2) to a quadratic dependence (q2) with increasing q values. A low energy excitation at ∼2.3 eV was also observed, which can be attributed to the plasmon-exciton coupling excitation mode (or plexciton) with a linear positive dispersion turning to negative dispersion by following the band structure along the ΓM¯ direction.

Fast electrons interacting with a natural hyperbolic medium: bismuth telluride.

Fast electrons interacting with matter have been instrumental for probing bulk and surface photonic excitations including Cherenkov radiation and plasmons. Additionally, fast electrons are ideal to investigate unique bulk and longitudinal photonic modes in hyperbolic materials at large wavevectors difficult to probe optically. Here, we use momentum-resolved electron energy loss spectroscopy (k-EELS) to perform the first experimental demonstration of high-k modes and hyperbolic Cherenkov radiation in the natural hyperbolic material Bi2Te3. This work establishes Bi2Te3 as one of the few viable natural hyperbolic materials in the visible and paves the way for k-EELS as a fundamental tool to probe hyperbolic media.

Collective mode in the SU(2) theory of cuprates

Recent advances in momentum-resolved electron energy-loss spectroscopy (MEELS) and resonant inelastic X-ray scattering (RIXS) now allow one to access the charge response function with unprecedented versatility and accuracy. This allows for the study of excitations which were inaccessible recently, such as low-energy and finite momentum collective modes. The SU(2) theory of the cuprates is based on a composite order parameter with SU(2) symmetry fluctuating between superconductivity and charge order. The phase where it fluctuates is a candidate for the pseudogap phase of the cuprates. This theory has a signature, enabling its strict experimental test, which is the fluctuation between these two orders, corresponding to a charge 2 spin 0 mode at the charge ordering wave-vector. Here we derive the influence of this SU(2) collective mode on the charge susceptibility in both strong and weak coupling limits, and discuss its relation to MEELS, RIXS and Raman experiments. We find two peaks in the charge susceptibility at finite energy, whose middle is the charge ordering wave-vector, and discuss their evolution in the phase diagram.

Extreme ultraviolet plasmonics and Cherenkov radiation in silicon

Silicon is widely used as the material of choice for semiconductor and insulator applications in nanoelectronics, micro-electro-mechanical systems, solar cells, and on-chip photonics. In stark contrast, in this paper, we explore silicon’s metallic properties and show that it can support propagating surface plasmons, collective charge oscillations, in the extreme ultraviolet (EUV) energy regime not possible with other plasmonic materials such as aluminum, silver, or gold. This is fundamentally different from conventional approaches, where doping semiconductors is considered necessary to observe plasmonic behavior. We experimentally map the photonic band structure of EUV surface and bulk plasmons in silicon using momentum-resolved electron energy loss spectroscopy. Our experimental observations are validated by macroscopic electrodynamic electron energy loss theory simulations as well as quantum density functional theory calculations. As an example of exploiting these EUV plasmons for applications, we propose a tunable and broadband thresholdless Cherenkov radiation source in the EUV using silicon plasmonic metamaterials. Our work can pave the way for the field of EUV plasmonics.

Holographic plasmons

Since holography yields exact results, even in situations where perturbation theory is not applicable, it is an ideal framework for modeling strongly correlated systems. We extend previous holographic methods to take the dynamical charge response into account and use this to perform the first holographic computation of the dispersion relation for plasmons. As the dynamical charge response of strange metals can be measured using the new technique of momentum-resolved electron energy-loss spectroscopy (M-EELS), plasmon properties are the next milestone in verifying predictions from holographic models of new states of matter.