Momentum-resolved Electron Energy Loss Research Articles

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.

Investigation of Electronic Excitations in Monoclinic HfO2 Studied by Energy-Filtered Transmission Electron Microscopy-Spectrum-Imaging and Momentum-Resolved Electron Energy Loss ω-q Mapping Techniques.

Investigation of Electronic Excitations in Monoclinic HfO2 Studied by Energy-Filtered Transmission Electron Microscopy-Spectrum-Imaging and Momentum-Resolved Electron Energy Loss ω-q Mapping Techniques.

Extracting Inelastic Scattering Cross Sections for Finite and Aperiodic Materials from Electronic Dynamics Simulations.

Explicit time-dependent electronic structure theory methods are increasingly prevalent in the areas of condensed matter physics and quantum chemistry, with the broad-band optical absorptivity of molecular and small condensed-phase systems nowadays routinely studied with such approaches. In this paper, it is demonstrated that electronic dynamics simulations can similarly be employed to study cross sections for the scattering-induced electronic excitations probed in nonresonant inelastic X-ray scattering and momentum-resolved electron energy loss spectroscopies. A method is put forth for evaluating the electronic dynamic structure factor, which involves the application of a momentum boost-type perturbation and transformation of the resulting reciprocal space density fluctuations into the frequency domain. Good agreement is first demonstrated between the dynamic structure factor extracted from these electronic dynamics simulations and the corresponding transition matrix elements from linear response theory. The method is then applied to some extended (quasi)one-dimensional systems, for which the wave vector becomes a good quantum number in the thermodynamic limit. Finally, the dispersion of many-body excitations in a series of hydrogen-terminated graphene flakes (and twisted bilayers thereof) is investigated to highlight the utility of the presented approach for capturing morphology-dependent effects in the inelastic scattering cross sections of nanostructured and/or noncrystalline materials.

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.

Deciphering the Intense Postgap Absorptions of Monolayer Transition Metal Dichalcogenides.

Rich valleytronics and diverse defect-induced or interlayer pre-bandgap excitonics have been extensively studied in transition metal dichalcogenides (TMDCs), a system with fascinating optical physics. However, more intense high-energy absorption peaks (∼3 eV) above the bandgaps used to be long ignored and their underlying physical origin remains to be unveiled. Here, we employ momentum resolved electron energy loss spectroscopy to measure the dispersive behaviors of the valley excitons and intense higher-energy peaks at finite momenta. Combined with accurate Bethe-Salpeter equation calculations, non-band-nesting transitions at the Q valley and at the midpoint of KM are found to be responsible for the high-energy broad absorption peaks in tungsten dichalcogenides and present spin polarizations similar to A excitons, in contrast with the band-nesting mechanism in molybdenum dichalcogenides. Our experiment-theory joint research will offer insights into the physical origins and manipulation of the intense high-energy excitons in TMDC-based optoelectronic devices.

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.

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.

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.

Anisotropic 2D metallicity: plasmons in Ge(1 0 0)-Au

The low-energy plasmonic excitations of the Ge(0 0 1)-Au close to one monolayer coverage of Au were investigated by momentum-resolved high resolution electron energy loss spectroscopy. A very weak plasmonic loss was identified dispersing along the chain direction of the formed at these Au coverages. The measured dispersion was compared with the Tomonaga–Luttinger-liquid (TLL) model and with a model for an anisotropic Fermi liquid. Using the TLL model both for single and arrays of wires, no consistent picture turned up that could describe all available data. On the contrary, a quasi-one-dimensional model of a confined 2D electron gas gave a satisfactorily consistent description of the data. From these results for the collective low-energy excitations we conclude that the Ge(0 0 1)-Au system is reasonably well described by a strongly anisotropic 2D Fermi liquid, but is incompatible with a TLL.

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.

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.

Quantum gyroelectric effect: Photon spin-1 quantization in continuum topological bosonic phases

Topological phases of matter arise in distinct fermionic and bosonic flavors. The fundamental differences between them are encapsulated in their rotational symmetries - the spin. Although spin quantization is routinely encountered in fermionic topological edge states, analogous quantization for bosons has proven elusive. To this end, we develop the complete electromagnetic continuum theory characterizing 2+1D topological bosons, taking into account their intrinsic spin and orbital angular momentum degrees of freedom. We demonstrate that spatiotemporal dispersion (momentum and frequency dependence of linear response) captures the matter-mediated interactions between bosons and is a necessary ingredient for topological phases. We prove that the bulk topology of these 2+1D phases is manifested in transverse spin-1 quantization of the photon. From this insight, we predict two unique bosonic phases - one with even parity $C=\pm 2$ and one with odd $C=\pm 1$. To understand the even parity phase $C=\pm 2$, we introduce an exactly solvable model utilizing non-local optical Hall conductivity and reveal a single gapless photon at the edge. This unidirectional photon is spin-1 helically quantized, immune to backscattering, defects, and exists at the boundary of the $C=\pm 2$ bosonic phase and any interface - even vacuum. The contrasting phenomena of transverse quantization in the bulk, but longitudinal (helical) quantization on the edge is addressed as the quantum gyro-electric effect (QGEE). We also validate our bosonic Maxwell theory by direct comparison with the supersymmetric Dirac theory of fermions. To accelerate the discovery of such bosonic phases, we suggest two new probes of topological matter with broken time-reversal symmetry: momentum-resolved electron energy loss spectroscopy and cold atom near-field measurement of non-local optical Hall conductivity.

Functions to map photoelectron distributions in a variety of setups in angle-resolved photoemission spectroscopy.

The distribution of photoelectrons acquired in angle-resolved photoemission spectroscopy can be mapped onto the energy-momentum space of the Bloch electrons in the crystal. The explicit forms of the mapping function f depend on the configuration of the apparatus as well as on the type of the photoelectron analyzer. We show that the existence of the analytic forms of f-1 is guaranteed in a variety of setups. The variety includes the case when the analyzer is equipped with a photoelectron deflector. Thereby, we provide a demonstrative mapping program implemented by an algorithm that utilizes both f and f-1. The mapping methodology is also usable in other spectroscopic methods such as momentum-resolved electron-energy loss spectroscopy.

Modelling relativistic effects in momentum-resolved electron energy loss spectroscopy of graphene

ABSTRACTWe present an analytical model for the electron energy loss through a two-dimensional (2D) layer of graphene, fully taking into account relativistic effects. Using two different models for graphene's 2D conductivity, one a two-fluid hydrodynamic model with an added correction to account for the inter-band electron transitions near the Dirac point in undoped graphene, the other derived from ab initio plane-wave time-dependent density functional theory in the frequency domain (PW-TDDFT-ω) calculations applied on a graphene superlattice, we derive various different expressions for the probability density of energy and momentum transfer from the incident electron to graphene. To further compare with electron energy loss spectroscopy (EELS) experiments that use setups like scanning Transmission Electron Microscopy, we integrated our energy loss functions over a range of wavenumbers, and compared how the choice of range directly affects the shape, position, and relative heights of graphene's π → π* and σ → σ* transition peaks. Comparisons were made with experimental EELS data under different model inputs, revealing again the strong effect that the choice of wavenumber range has on the energy loss.

Anomalous lattice vibrations in self-nanostructured graphene on Ru(0001)

Momentum-resolved high-resolution electron energy loss spectroscopy has been used to probe the phonon dispersion of periodically rippled graphene grown on Ru(0001). Optical phonons in this system show anomalies with respect to other graphene/metal interfaces. Novel modes with weak intensity are observed at ∼86 and ∼150 meV. Moreover, the dispersion relation of the highest optical branches in the Γ-K direction strongly deviates from the expected behavior. These unusual features in the phonon dispersion should be related to the corrugated and chiral structure of the graphene overlayer on Ru(0001).

Higgs modes in the pair density wave superconducting state

The pair density wave (PDW) superconducting state has been proposed to explain the layer- decoupling effect observed in the compound La$_{2-x}$Ba$_x$CuO$_4$ at $x=1/8$ (Phys. Rev. Lett. 99, 127003). In this state the superconducting order parameter is spatially modulated, in contrast with the usual superconducting (SC) state where the order parameter is uniform. In this work, we study the properties of the amplitude (Higgs) modes in a unidirectional PDW state. To this end we consider a phenomenological model of PDW type states coupled to a Fermi surface of fermionic quasiparticles. In contrast to conventional superconductors that have a single Higgs mode, unidirectional PDW superconductors have two Higgs modes. While in the PDW state the Fermi surface largely remains gapless, we find that the damping of the PDW Higgs modes into fermionic quasiparticles requires exceeding an energy threshold. We show that this suppression of damping in the PDW state is due to kinematics. As a result, only one of the two Higgs modes is significantly damped. In addition, motivated by the experimental phase diagram, we discuss the mixing of Higgs modes in the coexistence regime of the PDW and uniform SC states. These results should be observable directly in a Raman spectroscopy, in momentum resolved electron energy loss spectroscopy, and in resonant inelastic X-ray scattering, thus providing evidence of the PDW states.

Quasiparticle interference and strong electron–mode coupling in the quasi-one-dimensional bands of Sr2RuO4

The single-layered ruthenate Sr$_2$RuO$_4$ has attracted a great deal of interest as a spin-triplet superconductor with an order parameter that may potentially break time reversal invariance and host half-quantized vortices with Majorana zero modes. While the actual nature of the superconducting state is still a matter of controversy, it has long been believed that it condenses from a metallic state that is well described by a conventional Fermi liquid. In this work we use a combination of Fourier transform scanning tunneling spectroscopy (FT-STS) and momentum resolved electron energy loss spectroscopy (M-EELS) to probe interaction effects in the normal state of Sr$_2$RuO$_4$. Our high-resolution FT-STS data show signatures of the \beta-band with a distinctly quasi-one-dimensional (1D) character. The band dispersion reveals surprisingly strong interaction effects that dramatically renormalize the Fermi velocity, suggesting that the normal state of Sr$_2$RuO$_4$ is that of a 'correlated metal' where correlations are strengthened by the quasi 1D nature of the bands. In addition, kinks at energies of approximately 10meV, 38meV and 70meV are observed. By comparing STM and M-EELS data we show that the two higher energy features arise from coupling with collective modes. The strong correlation effects and the kinks in the quasi 1D bands may provide important information for understanding the superconducting state. This work opens up a unique approach to revealing the superconducting order parameter in this compound.