Automated Real-Space Lattice Extraction for Atomic Force Microscopy Images

Analyzing atomically resolved images is a time-consuming process requiring solid experience and substantial human intervention. In addition, the acquired images contain a large amount of information such as crystal structure, presence and distribution of defects, and formation of domains, which need to be resolved to understand a material's surface structure. Therefore, machine learning techniques have been applied in scanning probe and electron microscopies during the last years, aiming for automatized and efficient image analysis. This work introduces a free and open source tool (AiSurf: Automated Identification of Surface Images) developed to inspect atomically resolved images via Scale-Invariant Feature Transform (SIFT) and Clustering Algorithms (CA). AiSurf extracts primitive lattice vectors, unit cells, and structural distortions from the original image, with no pre-assumption on the lattice and minimal user intervention. The method is applied to various atomically resolved non-contact atomic force microscopy (AFM) images of selected surfaces with different levels of complexity: anatase TiO2(101), oxygen deficient rutile TiO2(110) with and without CO adsorbates, SrTiO3(001) with Sr vacancies and graphene with C vacancies. The code delivers excellent results and is tested against atom misclassification and artifacts, thereby facilitating the interpretation of scanning probe microscopy images.

Surface chemistry on a polarizable surface: Coupling of CO with KTaO3(001)

Polarizable materials attract attention in catalysis because they have a free parameter for tuning chemical reactivity. Their surfaces entangle the dielectric polarization with surface polarity, excess charge, and orbital hybridization. How this affects individual adsorbed molecules is shown for the incipient ferroelectric perovskite KTaO₃. This intrinsically polar material cleaves along (001) into KO- and TaO₂-terminated surface domains. At TaO₂ terraces, the polarity-compensating excess electrons form a two-dimensional electron gas and can also localize by coupling to ferroelectric distortions. TaO₂ terraces host two distinct types of CO molecules, adsorbed at equivalent lattice sites but charged differently as seen in atomic force microscopy/scanning tunneling microscopy. Temperature-programmed desorption shows substantially stronger binding of the charged CO; in density functional theory calculations, the excess charge favors a bipolaronic configuration coupled to the CO. These results pinpoint how adsorption states couple to ferroelectric polarization.

Competing electronic states emerging on polar surfaces

Excess charge on polar surfaces of ionic compounds is commonly described by the two-dimensional electron gas (2DEG) model, a homogeneous distribution of charge, spatially-confined in a few atomic layers. Here, by combining scanning probe microscopy with density functional theory calculations, we show that excess charge on the polar TaO₂ termination of KTaO₃(001) forms more complex electronic states with different degrees of spatial and electronic localization: charge density waves (CDW) coexist with strongly-localized electron polarons and bipolarons. These surface electronic reconstructions, originating from the combined action of electron-lattice interaction and electronic correlation, are energetically more favorable than the 2DEG solution. They exhibit distinct spectroscopy signals and impact on the surface properties, as manifested by a local suppression of ferroelectric distortions.

Defect-free surfaces with excess charge are typically described as a homogeneous 2D electron gas. Here, in contrast, the authors find that the KTaO₃(001) surface hosts a charge density wave coexisting with a pattern of electron polarons, highly localized states of excess electrons bound to a lattice distortion.

Role of Polarons in Single-Atom Catalysts: Case Study of Me1 [Au1, Pt1, and Rh1] on TiO2(110)

The local environment of metal-oxide supported single-atom catalysts plays a decisive role in the surface reactivity and related catalytic properties. The study of such systems is complicated by the presence of point defects on the surface, which are often associated with the localization of excess charge in the form of polarons. This can affect the stability, the electronic configuration, and the local geometry of the adsorbed adatoms. In this work, through the use of density functional theory and surface-sensitive experiments, we study the adsorption of Rh1, Pt1, and Au1 metals on the reduced TiO2(110) surface, a prototypical polaronic material. A systematic analysis of the adsorption configurations and oxidation states of the adsorbed metals reveals different types of couplings between adsorbates and polarons. As confirmed by scanning tunneling microscopy measurements, the favored Pt1 and Au1 adsorption at oxygen vacancy sites is associated with a strong electronic charge transfer from polaronic states to adatom orbitals, which results in a reduction of the adsorbed metal. In contrast, the Rh1 adatoms interact weakly with the excess charge, which leaves the polarons largely unaffected. Our results show that an accurate understanding of the properties of single-atom catalysts on oxide surfaces requires a careful account of the interplay between adatoms, vacancy sites, and polarons.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11244-022-01651-0.

Anderson transition in stoichiometric Fe2VAl: high thermoelectric performance from impurity bands

Discovered more than 200 years ago in 1821, thermoelectricity is nowadays of global interest as it enables direct interconversion of thermal and electrical energy via the Seebeck/Peltier effect. In their seminal work, Mahan and Sofo mathematically derived the conditions for ’the best thermoelectric’—a delta-distribution-shaped electronic transport function, where charge carriers contribute to transport only in an infinitely narrow energy interval. So far, however, only approximations to this concept were expected to exist in nature. Here, we propose the Anderson transition in a narrow impurity band as a physical realisation of this seemingly unrealisable scenario. An innovative approach of continuous disorder tuning allows us to drive the Anderson transition within a single sample: variable amounts of antisite defects are introduced in a controlled fashion by thermal quenching from high temperatures. Consequently, we obtain a significant enhancement and dramatic change of the thermoelectric properties from p-type to n-type in stoichiometric Fe₂VAl, which we assign to a narrow region of delocalised electrons in the energy spectrum near the Fermi energy. Based on our electronic transport and magnetisation experiments, supported by Monte-Carlo and density functional theory calculations, we present a novel strategy to enhance the performance of thermoelectric materials.

The mathematical conditions for the best thermoelectric is well known but never realised in real materials. Here, the authors propose the Anderson transition in a narrow impurity band as a physical realisation of this seemingly unrealisable scenario.

Modeling polarons in density functional theory: lessons learned from TiO2

Density functional theory (DFT) is nowadays one of the most broadly used and successful techniques to study the properties of polarons and their effects in materials. Here, we systematically analyze the aspects of the theoretical calculations that are crucial to obtain reliable predictions in agreement with the experimental observations. We focus on rutile TiO₂, a prototypical polaronic compound, and compare the formation of polarons on the (110) surface and subsurface atomic layers. As expected, the parameterUused to correct the electronic correlation in the DFT +Uformalism affects the resulting charge localization, local structural distortions and electronic properties of polarons. Moreover, the polaron localization can be driven to different sites by strain: due to different local environments, surface and subsurface polarons show different responses to the applied strain, with impact on the relative energy stability. An accurate description of the properties of polarons is key to understand their impact on complex phenomena and applications: as an example, we show the effects of lattice strain on the interaction between polarons and CO adsorbates.

Electronic State Unfolding for Plane Waves: Energy Bands, Fermi Surfaces, and Spectral Functions

Present day computing facilities allow for first-principles density functional theory studies of complex physical and chemical phenomena. Often such calculations are linked to large supercells to adequately model the desired property. However, supercells are associated with small Brillouin zones in the reciprocal space, leading to folded electronic eigenstates that make the analysis and interpretation extremely challenging. Various techniques have been proposed and developed to reconstruct the electronic band structures of super cells unfolded into the reciprocal space of an ideal primitive cell. Here we propose an unfolding scheme embedded directly in the Vienna Ab initio Simulation Package (VASP) that requires modest computational resources and allows for an automatized mapping from the reciprocal space of the supercell to the primitive cell Brillouin zone. This algorithm can compute band structures, Fermi surfaces, and spectral functions by using an integrated postprocessing tool (bands4vasp). Here the method is applied to a selected variety of complex physical situations: the effect of doping on the band dispersion in the BaFe_2(1-x)Ru_2x As₂ superconductor, the interaction between adsorbates and polaronic states on the TiO₂(110) surface, and the band splitting induced by noncollinear spin fluctuations in EuCd₂As₂.

Resolving the adsorption of molecular O2 on the rutile TiO2(110) surface by noncontact atomic force microscopy

Interaction of molecular oxygen with semiconducting oxide surfaces plays a key role in many technologies. The topic is difficult to approach both by experiment and in theory, mainly due to multiple stable charge states, adsorption configurations, and reaction channels of adsorbed oxygen species. Here we use a combination of noncontact atomic force microscopy (AFM) and density functional theory (DFT) to resolve [Formula: see text] adsorption on the rutile [Formula: see text](110) surface, which presents a longstanding challenge in the surface chemistry of metal oxides. We show that chemically inert AFM tips terminated by an oxygen adatom provide excellent resolution of both the adsorbed species and the oxygen sublattice of the substrate. Adsorbed [Formula: see text] molecules can accept either one or two electron polarons from the surface, forming superoxo or peroxo species. The peroxo state is energetically preferred under any conditions relevant for applications. The possibility of nonintrusive imaging allows us to explain behavior related to electron/hole injection from the tip, interaction with UV light, and the effect of thermal annealing.

Spin fluctuation induced Weyl semimetal state in the paramagnetic phase of EuCd2As2

Weyl fermions as emergent quasiparticles can arise in Weyl semimetals (WSMs) in which the energy bands are nondegenerate, resulting from inversion or time-reversal symmetry breaking. Nevertheless, experimental evidence for magnetically induced WSMs is scarce. Here, using photoemission spectroscopy, we observe that the degeneracy of Bloch bands is already lifted in the paramagnetic phase of EuCd2As2. We attribute this effect to the itinerant electrons experiencing quasi-static and quasi-long-range ferromagnetic fluctuations. Moreover, the spin-nondegenerate band structure harbors a pair of ideal Weyl nodes near the Fermi level. Hence, we show that long-range magnetic order and the spontaneous breaking of time-reversal symmetry are not essential requirements for WSM states in centrosymmetric systems and that WSM states can emerge in a wider range of condensed matter systems than previously thought.

Doping-induced insulator-metal transition in the Lifshitz magnetic insulator NaOsO3

By means of first principles schemes based on magnetically constrained density functional theory and on the band unfolding technique we study the effect of doping on the conducting behaviour of the Lifshitz magnetic insulator NaOsO₃. Electron doping is treated within a supercell approach by replacing sodium with magnesium at different concentrations ([Formula: see text], [Formula: see text]). Undoped NaOsO₃ is subjected to a temperature-driven Lifshitz transition involving a continuous closing of the gap due to longitudinal and rotational spin fluctuations (Kim et al 2016 Phys. Rev. B 94 241113). Here we find that Mg doping suppresses the insulating state, gradually drives the system to a metallic state (via an intermediate bad metal phase) and the transition is accompanied by a progressive lowering of the Os magnetic moment. We inspected the role of longitudinal spin fluctuations by constraining the amplitude of the local Os moments and found that a robust metal state can be achieved below a critical moment. In analogy with the undoped case we conjecture that the decrease of the local moment can be controlled by temperature effects, in accordance with the theory of itinerant electron magnetism.

Interplay between Adsorbates and Polarons: CO on Rutile TiO_{2}(110)

Polaron formation plays a major role in determining the structural, electrical, and chemical properties of ionic crystals. Using a combination of first-principles calculations, scanning tunneling microscopy, and atomic force microscopy, we analyze the interaction of polarons with CO molecules adsorbed on the reduced rutile TiO_{2}(110) surface. Adsorbed CO shows attractive coupling with polarons in the surface layer, and repulsive interaction with polarons in the subsurface layer. As a result, CO adsorption depends on the reduction state of the sample. For slightly reduced surfaces, many adsorption configurations with comparable adsorption energies exist and polarons reside in the subsurface layer. At strongly reduced surfaces, two adsorption configurations dominate: either inside an oxygen vacancy, or at surface Ti_{5c} sites, coupled with a surface polaron. Similar conclusions are predicted for TiO_{2}(110) surfaces containing near-surface Ti interstitials. These results show that polarons are of primary importance for understanding the performance of polar semiconductors and transition metal oxides in catalysis and energy-related applications.