Real-space mapping of electronic orbitals

Abstract

Electronic states are responsible for most material properties, including chemical bonds, electrical and thermal conductivity, as well as optical and magnetic properties. Experimentally, however, they remain mostly elusive. Here, we report the real-space mapping of selected transitions between p and d states on theÅngström scale in bulk rutile (TiO 2 ) using electron energy-loss spectrometry (EELS), revealing information on individual bonds between atoms. On the one hand, this enables the experimental verification of theoretical predictions about electronic states. On the other hand, it paves the way for directly investigating electronic states under conditions that are at the limit of the current capabilities of numerical simulations such as, e.g., the electronic states at defects, interfaces, and quantum dots.Electronic states shape the world around us as their characteristics give rise to nearly all macroscopical properties of materials. Be it optical properties such as colour and refractive index, chemical properties such as bonding and valency, mechanical properties such as adhesion, strength and ductility, electromagnetic properties such as conductance and magnetisation, or the properties of trap states: ultimately, all these properties can be traced back to the electronic states in the material under investigation. Therefore, it is not surprising that electronic states are of paramount importance across many fields, including physics, materials science, chemistry and the life sciences. It does come as a surprise, however, that while some of their aspects can be inferred indirectly from macroscopical material properties or some diffraction techniques, the direct observation of individual electronic states in real space so far has succeeded only under very special circumstances (e.g. on an insulating surface using a scanning tunnelling microscope (STM) with a specially functionalised tip [1]) due to both experimental and theoretical challenges. In this work, we endeavour to remedy this situation by using a combination of transmission electron microscopy (TEM), electron energy-loss spectrometry (EELS), and state-of-the-art simulations.TEM is a well-known technique for studying materials on the nanoscale while EELS adds element-specific information. Both are widely-used on a regular basis in many fields and are readily commercially available. Owing to these two techniques, tremendous progress has been made over the last decade in mapping atom positions with ≈ 10 pm accuracy [2-4], determining charge densities [5][6][7], and performing atom-by-atom chemical mapping [8][9][10][11][12]. Furthermore, the fine-structures of the spectra allow the determination of the local chemical and structural environment as well as the hybridisation state of the scattering atoms [11][12][13][14][15][16][17][18] in the bulk, which can be substantially different from the surface states probed by STM. This suggests to use the EELS signal to probe the local environment in real-space and map, e.g., crystal fields, conduction states,...

Direct Detection Electron Energy-Loss Spectroscopy: A Method to Push the Limits of Resolution and Sensitivity

“…Compared to soft matter, oxides are relatively tolerant to electron irradiation, but beam-induced electronic and physical sample degradation may still occur 32 , 33 , 50 – 52 . Additionally, spatial resolution is paramount, thus reduced SI acquisition time is important to limit both sample drift and damage 34 . To this end, SIs were acquired with the short dwell time of 5 ms. Additional SI acquisition parameters are displayed in Table 2 .…”

“…Longer exposures can prohibit the study of highly beam sensitive samples 30 , 31 and potentially influence results from nominally stable materials 32 , 33 . For atomic resolution characterization where even small amounts of sample drift are problematic, extended exposures are not feasible, and the added noise can prevent quantitative data analysis 34 . For in situ EELS, added noise from ID sensors worsen time resolution, preventing dynamic spectroscopic tracking of certain chemical and physical processes.…”

Bridging nano-optics and condensed matter formalisms in a unified description of inelastic scattering of relativistic electron beams

“…For example, it has been demonstrated [18] that the so-called magic angle, at which the dependence of the core-loss electron scattering on the orientation of an anisotropic sample is canceled, strongly depends on the retarded character of the electron to target interaction, which had been considered as negligible in core-loss investigations before. Also, the description of the effect of interferences between inelastically scattered electrons, otherwise speaking, coherence effects, has been long discussed in terms of MDFF in the framework of inelastic holography of bulk plasmons [19] or EELS atomic resolution mapping [20][21][22], while coherence effects in surface plasmon excitations relied on Green's Dyad approaches [23]. Even more, electron magnetic circular dichroism (EMCD) [24] and phase-shaped EELS applied to plasmonics [8,23] relies physically on the same ingredients -electron phase manipulation to mimick the action of an X-ray or optical photon -yet are described within totally different frameworks.…”

Two-dimensional electron systems in perovskite oxide heterostructures: Role of the polarity-induced substitutional defects

“…By contrast, cross-sectional scanning probe microscopies and scanning transmission electron microscopy (STEM) offer high spatial resolution and have been widely used to study the local electronic properties relative to the 2DES of LAO/STO heterostructures [12,[29][30][31][32], but they cannot resolve the electronic/orbital states. Some advanced STEM studies were able to localize electronic states and hybridization [33] and image orbitals [34] but they are limited in the determination of orbital character due to low-q resolution [33] and subject to instrumental effects and delocalization of the inelastic scattering [35,36].…”