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Register a new userThe Magic Angle Mystery in Electron Energy Loss Spectroscopy: Relativistic and Dielectric Corrections
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Recently it has been demonstrated that a careful treatment of both longitudinal and transverse matrix elements in electron energy loss spectra can explain the mystery of relativistic effects on the {it magic angle}. Here we show that there is an additional correction of order $(Zalpha)^2$ where $Z$ is the atomic number and $alpha$ the fine structure constant, which is not necessarily small for heavy elements. Moreover, we suggest that macroscopic electrodynamic effects can give further corrections which can break the sample-independence of the magic angle.
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A quantum mechanical scattering theory for relativistic, highly focused electron beams near nanoscopic platelets is presented, revealing a new excitation mechanism due to the electron wave scattering from the platelet edges. Radiative electromagnetic excitations within the light cone are shown to arise, allowed by the breakdown of momentum conservation along the beam axis in the inelastic scattering process. Calculated for metallic (silver and gold) and insulating (SiO2 and MgO) nanoplatelets, new radiative features are revealed above the main surface plasmon-polariton peak, and dramatic enhancements in the electron energy loss probability at gaps of the classical spectra, are found. The corresponding radiation should be detectable in the vacuum far-field zone, with e-beams exploited as sensitive tip-detectors of electronically excited nanostructures.
Exploiting the information provided by electron energy-loss spectroscopy (EELS) requires reliable access to the low-loss region where the zero-loss peak (ZLP) often overwhelms the contributions associated to inelastic scatterings off the specimen. Here we deploy machine learning techniques developed in particle physics to realise a model-independent, multidimensional determination of the ZLP with a faithful uncertainty estimate. This novel method is then applied to subtract the ZLP for EEL spectra acquired in flower-like WS$_2$ nanostructures characterised by a 2H/3R mixed polytypism. From the resulting subtracted spectra we determine the nature and value of the bandgap of polytypic WS$_2$, finding $E_{rm BG} = 1.6_{-0.2}^{+0.3},{rm eV}$ with a clear preference for an indirect bandgap. Further, we demonstrate how this method enables us to robustly identify excitonic transitions down to very small energy losses. Our approach has been implemented and made available in an open source Python package dubbed EELSfitter.
Transmission electron microscopy, scanning transmission electron tomography, and electron energy loss spectroscopy were used to characterize three-dimensional artificial Si nanostructures called metalattices, focusing on Si metalattices synthesized by high-pressure confined chemical vapor deposition in 30-nm colloidal silica templates with ~7 and ~12 nm meta-atoms and ~2 nm meta-bonds. The meta-atoms closely replicate the shape of the tetrahedral and octahedral interstitial sites of the face-entered cubic colloidal silica template. Composed of either amorphous or nanocrystalline silicon, the metalattice exhibits long-range order and interconnectivity in two-dimensional micrographs and three-dimensional reconstructions. Electron energy loss spectroscopy provides information on local electronic structure. The Si L2,3 core-loss edge is blue-shifted compared to the onset for bulk Si, with the meta-bonds displaying a larger shift (0.55 eV) than the two types of meta-atoms (0.30 and 0.17 eV). Local density of state calculations using an empirical tight binding method are in reasonable agreement.
The electronic properties of heterostructures of atomically-thin van der Waals (vdW) crystals can be modified substantially by Moire superlattice potentials arising from an interlayer twist between crystals. Moire-tuning of the band structure has led to the recent discovery of superconductivity and correlated insulating phases in twisted bilayer graphene (TBLG) near the so-called magic angle of $sim$1.1{deg}, with a phase diagram reminiscent of high T$_c$ superconductors. However, lack of detailed understanding of the electronic spectrum and the atomic-scale influence of the Moire pattern has so far precluded a coherent theoretical understanding of the correlated states. Here, we directly map the atomic-scale structural and electronic properties of TBLG near the magic angle using scanning tunneling microscopy and spectroscopy (STM/STS). We observe two distinct van Hove singularities (vHs) in the LDOS which decrease in separation monotonically through 1.1{deg} with the bandwidth (t) of each vHs minimized near the magic angle. When doped near half Moire band filling, the conduction vHs shifts to the Fermi level and an additional correlation-induced gap splits the vHs with a maximum size of 7.5 meV. We also find that three-fold (C$_3$) rotational symmetry of the LDOS is broken in doped TBLG with a maximum symmetry breaking observed for states near the Fermi level, suggestive of nematic electronic interactions. The main features of our doping and angle dependent spectroscopy are captured by a tight-binding model with on-site (U) and nearest neighbor Coulomb interactions. We find that the ratio U/t is of order unity, indicating that electron correlations are significant in magic angle TBLG. Rather than a simple maximization of the DOS, superconductivity arises in TBLG at angles where the ratio U/t is largest, suggesting a pairing mechanism based on electron-electron interactions.
The spatial distributions of anti-bonding $pi^ast$ and $sigma^ast$ states in epitaxial graphene multilayers are mapped using electron energy-loss spectroscopy in a scanning transmission electron microscope. Inelastic channeling simulations validate the interpretation of the spatially-resolved signals in terms of electronic orbitals, and demonstrate the crucial effect of the material thickness on the experimental capability to resolve the distribution of unoccupied states. This work illustrates the current potential of core-level electron energy-loss spectroscopy towards the direct visualization of electronic orbitals in a wide range of materials, of huge interest to better understand chemical bonding among many other properties at interfaces and defects in solids.
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