Engineering Polarons at a Metal Oxide Surface

Time-Domain View of Polaron Dynamics in Metal Oxide Photocatalysts

The polaron is a fundamental physical phenomenon in transition metal oxides (TMOs), and it has been studied extensively for decades. However, the implication of a polaron on photochemistry is still ambiguous. As such, understanding the fundamental properties and controlling the dynamics of polarons at the atomistic level is desired. In this Perspective, we seek to highlight the recent advances in studying small polarons in TMOs, with a particular focus on nonadiabatic molecular dynamics at the ab initio level, and discuss the implications for photocatalysis from the aspects of the structure, intrinsic physical properties, formation, migration, and recombination of small polarons. Finally, various methods were proposed to advance our understanding of manipulating the small-polaron dynamics, and strategies to design high-performance TMO-based photoelectrodes were discussed.

Recent Progresses of Polarons: Fundamentals and Roles in Photocatalysis and Photoelectrocatalysis

Photocatalysis and photoelectrocatalysis are promising ways in the utilization of solar energy. To address the low efficiency of photocatalysts and photoelectrodes, in-depth understanding of their catalytic mechanism is in urgent need. Recently, polaron is considered as an influential factor in catalysis, which brings researchers a new approach to modify photocatalysts and photoelectrodes. In this review, brief introduction of polaron is given first, followed by which models and recent experimentally observations of polarons are reviewed. Studies about roles of polarons in photocatalysis and photoelectrocatalysis are listed in order to provide some inspiration in exploring the mechanism and improving the efficiency of photocatalysis and photoelectrocatalysis.

Tip-activated single-atom catalysis: CO oxidation on Au adatom on oxidized rutile TiO2 surface

Single-atom catalysis of carbon monoxide oxidation on metal-oxide surfaces is crucial for greenhouse recycling, automotive catalysis, and beyond, but reports of the atomic-scale mechanism are still scarce. Here, using scanning probe microscopy, we show that charging single gold atoms on oxidized rutile titanium dioxide surface, both positively and negatively, considerably promotes adsorption of carbon monoxide. No carbon monoxide adsorption is observed on neutral gold atoms. Two different carbon monoxide adsorption geometries on gold atoms are identified. We demonstrate full control over the redox state of adsorbed gold single atoms, carbon monoxide adsorption geometry, and carbon monoxide adsorption/desorption by the atomic force microscopy tip. On charged gold atoms, we activate Eley-Rideal oxidation reaction between carbon monoxide and a neighboring oxygen adatom by the tip. Our results provide unprecedented insights into carbon monoxide adsorption and suggest that the gold dual activity for carbon monoxide oxidation after electron or hole attachment is also the key ingredient in photocatalysis under realistic conditions.

Anomalous Dependence of Photocarrier Recombination Time on the Polaron Density of TiO2(110)

Polarons play a crucial role in energy conversion, but the microscopic mechanism remains unclear since they are susceptible to local atomic structures. Here, by employing ab initio nonadiabatic dynamic simulations, we investigate electron-hole (e-h) nonradiative recombination at the rutile TiO2(110) surface with varied amounts of oxygen vacancies (Vo). The isolated Vo facilitates e-h recombination through forming polarons compared to that in the defect-free surface. However, aggregated Vo forming clusters induce an order-of-magnitude acceleration of polaron diffusion by enhancing phonon excitations, which blocks the defect-mediated recombination and thus prolongs the photocarrier lifetime. We find that photoelectrons are driven to migrate toward the top surface due to polaron formation. Our results show the many-body effects of defects and polaron effects on determining the overall recombination rate, which has been ignored in the Shockley-Read-Hall model. The findings explain the controversial experimental observations and suggest that engineering Vo aggregation would instead improve photocatalysis efficiencies in polaronic materials.

Atomic-scale manipulation of single-polaron in a two-dimensional semiconductor

Polaron is a composite quasiparticle derived from an excess carrier trapped by local lattice distortion, and it has been studied extensively for decades both theoretically and experimentally. However, atomic-scale creation and manipulation of single-polarons in real space have still not been achieved so far, which precludes the atomistic understanding of the properties of polarons as well as their applications. Herein, using scanning tunneling microscopy, we succeeded to create single polarons in a monolayer two-dimensional (2D) semiconductor, CoCl₂. Combined with first-principles calculations, two stable polaron configurations, centered at atop and hollow sites, respectively, have been revealed. Remarkably, a series of manipulation progresses - from creation, erasure, to transition - can be accurately implemented on individual polarons. Our results pave the way to understand the physics of polaron at atomic level, and the easy control of single polarons in 2D semiconductor may open the door to 2D polaronics including the data storage.

Manipulating single excess electrons in monolayer transition metal dihalide

Polarons are entities of excess electrons dressed with local response of lattices, whose atomic-scale characterization is essential for understanding the many body physics arising from the electron-lattice entanglement, yet difficult to achieve. Here, using scanning tunneling microscopy and spectroscopy (STM/STS), we show the visualization and manipulation of single polarons in monolayer CoCl₂, that are grown on HOPG substrate via molecular beam epitaxy. Two types of polarons are identified, both inducing upward local band bending, but exhibiting distinct appearances, lattice occupations and polaronic states. First principles calculations unveil origin of polarons that are stabilized by cooperative electron-electron and electron-phonon interactions. Both types of polarons can be created, moved, erased, and moreover interconverted individually by the STM tip, as driven by tip electric field and inelastic electron tunneling effect. This finding identifies the rich category of polarons in CoCl₂ and their feasibility of precise control unprecedently, which can be generalized to other transition metal halides.

Revealing the Polaron State at the MoS2/TiO2 Interface

Interfacial polarons determine the distribution of free charges at the interface and thus play important roles in manipulating the physicochemical properties of hybridized polaronic materials. In this work, we investigated the electronic structures at the atomically flat interface of the single-layer MoS₂ (SL-MoS₂) on the rutile TiO₂ surface using high-resolution angle-resolved photoemission spectroscopy. Our experiments directly visualized both the valence band maximum and the conduction band minimum (CBM) of SL-MoS₂ at the K point, which clearly defines a direct bandgap of ∼2.0 eV. Detailed analyses corroborated by density functional theory calculations demonstrated that the CBM of MoS₂ is formed by the trapped electrons at the MoS₂/TiO₂ interface that couple with the longitudinal optical phonons in the TiO₂ substrate through an interfacial Fröhlich polaron state. Such an interfacial coupling effect may register a new route for tuning the free charges in the hybridized systems of two-dimensional materials and functional metal oxides.

On-Surface Synthesis of Nanographenes and Graphene Nanoribbons on Titanium Dioxide

The formation of two types of nanographenes from custom designed and synthesized molecular precursors has been achieved through thermally induced intramolecular cyclodehydrogenation reactions on the semiconducting TiO₂(110)-(1×1) surface, confirmed by the combination of high-resolution scanning tunneling microscopy (STM) and spectroscopy (STS) measurements, and corroborated by theoretical modeling. The application of this protocol on differently shaped molecular precursors demonstrates the ability to induce a highly efficient planarization reaction both within strained pentahelicenes as well as between vicinal phenyl rings. Additionally, by the combination of successive Ullmann-type polymerization and cyclodehydrogenation reactions, the archetypic 7-armchair graphene nanoribbons (7-AGNRs) have also been fabricated on the titanium dioxide surface from the standard 10,10'-dibromo-9,9'-bianthryl (DBBA) molecular precursors. These examples of the effective cyclodehydrogenative planarization processes provide perspectives for the rational design and synthesis of molecular nanostructures on semiconductors.

Photolysis versus Photothermolysis of N2O on a Semiconductor Surface Revealed by Nonadiabatic Molecular Dynamics

Identifying photolysis and photothermolysis during a photochemical reaction has remained challenging because of the highly non-equilibrium and ultrafast nature of the processes. Using state-of-the-art ab initio adiabatic and nonadiabatic molecular dynamics, we investigate N₂O photodissociation on the reduced rutile TiO₂(110) surface and establish its detailed mechanism. The photodecomposition is initiated by electron injection, leading to the formation of a N₂O^- ion-radical, and activation of the N₂O bending and symmetric stretching vibrations. Photothermolysis governs the N₂O dissociation when N₂O^- is short-lived. The dissociation is activated by a combination of the anionic excited state evolution and local heating. A thermal fluctuation drives the molecular acceptor level below the TiO₂ band edge, stabilizes the N₂O^- anion radical, and causes dissociation on a 1 ps timescale. As the N₂O^- resonance lifetime increases, photolysis becomes dominant since evolution in the anionic excited state activates the bending and symmetric stretching of N₂O, inducing the dissociation. The photodecomposition occurs more easily when N₂O is bonded to TiO₂ through the O rather than N atom. We demonstrate further that a thermal dissociation of N₂O can be realized by a rational choice of metal dopants, which enhance p-d orbital hybridization, facilitate electron transfer, and break N₂O spontaneously. By investigating the charge dynamics and lifetime, we provide a fundamental atomistic understanding of the competition and synergy between the photocatalytic and photothermocatalytic dissociation of N₂O and demonstrate how N₂O reduction can be controlled by light irradiation, adsorption configuration, and dopants, enabling the design of high-performance transition-metal oxide catalysts.

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.

Effects of oxygen vacancies on the photoexcited carrier lifetime in rutile TiO2

The photoexcited carrier lifetime in semiconductors plays a crucial role in solar energy conversion processes. The defects or impurities in semiconductors are usually proposed to introduce electron-hole (e-h) recombination centers and consequently reduce the photoexcited carrier lifetime. In this report, we investigate the effects of oxygen vacancies (O_V) on the carrier lifetime in rutile TiO₂, which has important applications in photocatalysis and photovoltaics. It is found that an O_V introduces two excess electrons which form two defect states in the band gap. The lower state is localized on one Ti atom and behaves as a small polaron, and the higher one is a hybrid state contributed by three Ti atoms around the O_V. Both the polaron and hybrid states exhibit strong electron-phonon (e-ph) coupling and their charge distributions become more and more delocalized when the temperature increases from 100 to 700 K. Such strong e-ph coupling and charge delocalization enhance the nonadibatic coupling between the electronic states along the hole relaxation path, where the defect states behave as intermediate states, leading to a distinct acceleration of e-h recombination. Our study provides valuable insights to understand the role of defects on photoexcited carrier lifetime in semiconductors.

CO Adsorbate Promotes Polaron Photoactivity on the Reduced Rutile TiO2(110) Surface

Polarons play a major role in determining the chemical properties of transition-metal oxides. Recent experiments show that adsorbates can attract inner polarons to surface sites. These findings require an atomistic understanding of the adsorbate influence on polaron dynamics and lifetime. We consider reduced rutile TiO₂(110) with an oxygen vacancy as a prototypical surface and a CO molecule as a classic probe and perform ab initio adiabatic molecular dynamics, time-domain density functional theory, and nonadiabatic molecular dynamics simulations. The simulations show that subsurface polarons have little influence on CO adsorption and CO can desorb easily. On the contrary, surface polarons strongly enhance CO adsorption. At the same time, the adsorbed CO attracts polarons to the surface, allowing them to participate in catalytic processes with CO. The CO interaction with polarons changes their orbital origin, suppresses polaron hopping, and stabilizes them at surface sites. Partial delocalization of polarons onto CO decouples them from free holes, decreasing the nonadiabatic coupling and shortening the quantum coherence time, thereby reducing charge recombination. The calculations demonstrate that CO prefers to adsorb at the next-nearest-neighbor five-coordinated Ti³⁺ surface electron polaron sites. The reported results provide a fundamental understanding of the influence of electron polarons on the initial stage of reactant adsorption and the effect of the adsorbate-polaron interaction on the polaron dynamics and lifetime. The study demonstrates how charge and polaron properties can be controlled by adsorbed species, allowing one to design high-performance transition-metal oxide catalysts.

Chemical Modification of Polaronic States in Anatase TiO2(101)

Two polymorphs of TiO₂, anatase and rutile, are employed in photocatalytic applications. It is broadly accepted that anatase is the more catalytically active and subsequently finds wider commercial use. In this work, we focus on the Ti³⁺ polaronic states of anatase TiO₂(101), which lie at ∼1.0 eV binding energy and are known to increase catalytic performance. Using UV-photoemission and two-photon photoemission spectroscopies, we demonstrate the capability to tune the excited state resonance of polarons by controlling the chemical environment. Anatase TiO₂(101) contains subsurface polarons which undergo sub-band-gap photoexcitation to states ∼2.0 eV above the Fermi level. Formic acid adsorption dramatically influences the polaronic states, increasing the binding energy by ∼0.3 eV. Moreover, the photoexcitation oscillator strength changes significantly, resonating with states ∼3.0 eV above the Fermi level. We show that this behavior is likely due to the surface migration of subsurface oxygen vacancies.

Polaron-Adsorbate Coupling at the TiO2(110)-Carboxylate Interface

Understanding how adsorbates influence polaron behavior is of fundamental importance in describing the catalytic properties of TiO₂. Carboxylic acids adsorb readily at TiO₂ surfaces, yet their influence on polaronic states is unknown. Using UV photoemission spectroscopy (UPS), two-photon photoemission spectroscopy (2PPE), and density functional theory (DFT) we show that dissociative adsorption of formic and acetic acids has profound, yet different, effects on the surface density, crystal field, and photoexcitation of polarons in rutile TiO₂(110). We also show that these variations are governed by the contrasting electrostatic properties of the acids, which impacts the extent of polaron-adsorbate coupling. The density of polarons in the surface region increases more in formate-terminated TiO₂(110) relative to acetate. Consequently, increased coupling gives rise to new photoexcitation channels via states 3.83 eV above the Fermi level. The onset of this process is 3.45 eV, likely adding to the catalytic photoyield.

Capturing the Electron-Phonon Renormalization in Molecules from First-Principles

Since the interaction between electrons and atomic nuclei can affect the electronic structure, in recent years, first-principles-based electron-phonon renormalization methods have been applied in the condensed matter physics community to account for the influence of the electron-phonon coupling in solid systems. However, little is yet known about the behavior and trends of the electron-phonon renormalization in the molecules. In this work, the method for the electron-phonon renormalization in molecules has been derived, using which, we exhaustively investigate the zero-point renormalization in 32 molecules with three different density functions. We find that the renormalization of the highest occupied molecular orbital-lowest unoccupied molecular orbital gap due to electron-vibration coupling does not relate to the atomic masses but quite relates to the electronic structure properties of the molecules.

Dynamics of Photoexcited Small Polarons in Transition-Metal Oxides

The dynamics of photoexcited polarons in transition-metal oxides (TMOs), including their formation, migration, and quenching, plays an important role in photocatalysis and photovoltaics. Taking rutile TiO₂ as a prototypical system, we use ab initio nonadiabatic molecular dynamics simulation to investigate the dynamics of small polarons induced by photoexcitation at different temperatures. The photoexcited electron is trapped by the distortion of the surrounding lattice and forms a small polaron within tens of femtoseconds. Polaron migration among Ti atoms is strongly correlated with quenching through an electron-hole (e-h) recombination process. At low temperature, the polaron is localized on a single Ti atom and polaron quenching occurs within several nanoseconds. At increased temperature, as under solar cell operating conditions, thermal phonon excitation stimulates the hopping and delocalization of polarons, which induces fast polaron quenching through the e-h recombination within 200 ps. Our study proves that e-h recombination centers can be formed by photoexcited polarons, which provides new insights to understand the efficiency bottleneck of photocatalysis and photovoltaics in TMOs.

The split-off terahertz radiating dipoles on thermally reduced α-V2O5 (001) surface

The trapped electron states on a pliable lattice have different localization and physical chemistry characteristics. Here, terahertz time-domain measurements suggest that the formation of vanadyl oxygen defect, in the presence of the surface potential traps and mobile charge carriers, leads to a transient charge distribution that forms terahertz radiating dipoles in V2O5. The emergence of radiating dipoles is evidenced by terahertz responses with a two-valley feature of the thermally reduced α-V2O5 (001) thin films in the temperature range of 300-700 K. The two photoconductance valleys on a several millielectron volts interval are related to two emergent split-off traps, which originate from the VO6 octahedra distortion upon the vanadyl oxygen desorption on the surface. The pliable surface lattices plays a decisive role. So long as the α-V2O5 (001) thin films are covered by a 30 nm-thick Al2O3 capping layer, the distinct two-valley feature disappears completely in the full temperature range. The terahertz radiating dipoles with a fine energy structure is potentially a new measure for charge dynamics on the α-V2O5 (001) surface.

Imaging Charge Localization in a Conjugated Oligophenylene

Polaron formation in conjugated polymers has a major impact on their optical and electronic properties. In polyphenylene, the molecular conformation is determined by a delicate interplay between electron delocalization and steric effects. Injection of excess charges is expected to increase the degree of conjugation, leading to structural distortions of the chain. Here we investigated at the single-molecule level the role of an excess charge in an individual oligophenylene deposited on sodium chloride films. By combining sub-molecular-resolved atomic force microscopy with redox-state-selective orbital imaging, we characterize both structural and electronical changes occurring upon hole injection. While the neutral molecule exhibits a delocalized frontier orbital, for the cationic radical the excess charge is observed to localize, inducing a partial planarization of the molecule. These results provide direct evidence for self-trapping of the excess charge in oligophenylenes, shedding light on the interplay of charge localization and structural distortion.

Probing Nonequilibrium Dynamics of Photoexcited Polarons on a Metal-Oxide Surface with Atomic Precision

Understanding the nonequilibrium dynamics of photoexcited polarons at the atomic scale is of great importance for improving the performance of photocatalytic and solar-energy materials. Using a pulsed-laser-combined scanning tunneling microscopy and spectroscopy, here we succeeded in resolving the relaxation dynamics of single polarons bound to oxygen vacancies on the surface of a prototypical photocatalyst, rutile TiO_{2}(110). The visible-light excitation of the defect-derived polarons depletes the polaron states and leads to delocalized free electrons in the conduction band, which is further corroborated by ab initio calculations. We found that the trapping time of polarons becomes considerably shorter when the polaron is bound to two surface oxygen vacancies than that to one. In contrast, the lifetime of photogenerated free electrons is insensitive to the atomic-scale distribution of the defects but correlated with the averaged defect density within a nanometer-sized area. Those results shed new light on the photocatalytically active sites at the metal-oxide surface.

Photoemission core level binding energies from multiple sized nanoparticles on the same support: TiO2(110)/Au

A novel method of measuring the core level binding energies of multiple sized nanoparticles on the same substrate is demonstrated using the early stage of Au nanoparticle growth on reduced r-TiO₂(110). This method employed in situ scanning tunneling microscopy (STM) and microfocused X-ray photoemission spectroscopy. An STM tip-shadowing method was used to synthesize patterned areas of Au nanoparticles on the substrate with different coverages and sizes. Patterns were identified and imaged using a UV photoelectron emission microscope. The Au 4f core level binding energies of the nanoparticles were investigated as a function of Au nanoparticle coverage and size. A combination of initial and final state effects modifies the binding energies of the Au 4f core levels as the nanoparticle size changes. When single Au atoms and Au₃ clusters are present, the Au 4f_7/2 binding energy, 84.42 eV, is similar to that observed at a high coverage (1.8 monolayer equivalent), resulting from a cancellation of initial and final state effects. As the coverage is increased, there is a decrease in binding energy, which then increases at a higher coverage to 84.39 eV. These results are consistent with a Volmer-Weber nucleation-growth model of Au nanoparticles at oxygen vacancies, resulting in electron transfer to the nanoparticles.

Photoresponses of Supported Au Single Atoms on TiO2(110) through the Metal-Induced Gap States

When a metal single-atom (SA) catalyst is supported on a semiconducting photocatalyst, the charge transfer of the photoexcited carriers to metal SAs can provide a synergetic activity for the co-catalysts. Here, we report the interfacial electronic coupling of the Au SAs on the TiO₂(110) surface using scanning tunneling microscopy/spectroscopy, in combination with first-principles calculations. Distinct energy and spatial distributions of the metal-induced gap states (MIGSs) are experimentally revealed for the Au SAs adsorbed at the terminal Ti sites and the oxygen vacancies. The localized MIGS below the Fermi level provides a dedicated channel for the transfer of a photoexcited hole from the TiO₂ substrate to the adsorbed Au SAs. The hole can weaken the Ti-Au bonding and activate the diffusion of Au SAs. Our results shed light on combining the advantages of photocatalysis and metal SA catalysis using a co-catalyst, which is promising to promote chemical reactions at low temperatures.

Tip-Induced Control of Charge and Molecular Bonding of Oxygen Atoms on the Rutile TiO2 (110) Surface with Atomic Force Microscopy

We study a low-temperature on-surface reversible chemical reaction of oxygen atoms to molecules in ultrahigh vacuum on the semiconducting rutile TiO₂(110)-(1 × 1) surface. The reaction is activated by charge transfer from two sources, natural surface/subsurface polarons and experimental Kelvin probe force spectroscopy as a tool for electronic charge manipulation with single electron precision. We demonstrate a complete control over the oxygen species not attainable previously, allowing us to deliberately discriminate in favor of charge or bond manipulation, using either direct charge injection/removal through the tip-oxygen adatom junction or indirectly via polarons. Comparing our ab initio calculations with experiment, we speculate that we may have also manipulated the spin on the oxygens, allowing us to deal with the singlet/triplet complexities associated with the oxygen molecule formation. We show that the manipulation outcome is fully governed by three experimental parameters, vertical and lateral tip positions and the bias voltage.

Adsorption Features of Formaldehyde on TiO2(110) Surface Probed by High-Resolution Scanning Tunnelling Microscopy

We report a real-space imaging of formaldehyde (HCHO) adsorption on a TiO₂(110) surface probed by high-resolution scanning tunnelling microscopy (STM). Density functional theory calculations (DFT) were carried out to assign the observed features. The adsorptions occur exclusively on 5-fold coordinated Ti (Ti_5c) sites and oxygen vacancies (OVs). The well-resolved configurations on the Ti_5c sites feature the overlapping of the two "dumbbell" structures which are originated from the empty orbitals of HCHO. The STM images for the physical adsorption of HCHO on the OV sites appear fuzzy because of the rapid switching of HCHO among the three stable orientations, while those for the chemical adsorption are much clearer, revealing a distinctive difference between chemical and physical adsorptions. This work presents a systematic characterization of the topological features of HCHO/TiO₂(110) and provides useful information for mechanical understanding of the reaction mechanism of HCHO on the surfaces.

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.

The role of surface reduction in the formation of Ti interstitials

Density functional theory simulations are used to investigate the formation and mobility of Ti interstitial ions, Ti_i, at the (110) surface of rutile TiO₂.

The electronic structure and the formation of polarons in Mo-doped BiVO4 measured by angle-resolved photoemission spectroscopy

We experimentally investigated the electronic structure of Mo-doped BiVO₄ high-quality single-crystals with synchrotron radiation-excited angle-resolved photoelectron spectroscopy (ARPES). By photon-energy dependent ARPES, we measured the bulk-derived valence band dispersion along the direction normal to the (010) cleavage plane, while the dispersion along the in-plane directions is obtained by angle-dependent measurements at fixed photon energy. Our data show that the valence band has a width of about 4.75 eV and is composed of many peaks, the two most intense have energies in good agreement with the theoretically calculated ones. A non-dispersive feature is observed in the fundamental gap, which we attribute to quasiparticle excitations coupling electrons and phonons, i.e. polarons. The determination of the polaron peak binding energy and bulk band gap allows to fix the value of the theoretical mixing parameter necessary in hybrid Hartree–Fock calculations to reproduce the experimental data. The attribution of the in-gap peak to polarons is strengthened by our discussion in the context of experimental transport data and ab initio theory.

Experimental investigation of the electronic structure of Mo-doped BiVO₄ high-quality single-crystals with synchrotron radiation-excited angle-resolved photoelectron spectroscopy (ARPES).

Inhomogeneous dynamical mean-field theory of the small polaron problem

We present an inhomogeneous dynamical mean field theory (I-DMFT) that is suitable to investigate electron-lattice interactions in non-translationally invariant and/or inhomogeneous systems. The presented approach, whose only assumption is that of a local, site-dependent self-energy, recovers both the exact solution of an electron for a generic random tight-binding Hamiltonian in the non-interacting limit and the DMFT solution for the small polaron problem in translationally invariant systems. To illustrate its full capabilities, we use I-DMFT to study the effects of defects embedded on a two-dimensional surface. The computed maps of the local density of states reveal Friedel oscillations, whose periodicity is determined by the polaron mass. This can be of direct relevance for the interpretation of scanning-tunneling microscopy experiments on systems with sizable electron-lattice interactions. Overall, the easy numerical implementation of the method, yet full self-consistency, allows one to study problems in real-space that were previously difficult to access.

Direct observation of atomic step edges on the rutile TiO2(110)-(1 × 1) surface using atomic force microscopy

Clarifying the atomic configuration of step edges on a rutile TiO2 surface is crucial for understanding its fundamental reactivity, and the direct observation of atomic step edges is still a challenge. AFM is a powerful tool for investigating surface structures with true atomic resolution, and it provides the opportunity to resolve the real structure of step edges with improved techniques. In this work, we successfully imaged the atomic configuration of 001 and 1-11 step edges on the surface of rutile TiO2(110)-(1 × 1), and we present the direct observation of oxygen vacancies along the 1-11 step edges, indicating that one 1-11 step edge site corresponds to one oxygen vacancy using AFM. We also made use of the simultaneous AFM/STM measurements to explore the electronic structure of step edges, which enhanced the evidence of oxygen vacancies existing along the 1-11 step edges and further demonstrated that the 001 step edge was terminated by an O row. The effect of the reduced 1-11 step edges was explored by probing the O2 adsorption and the nucleation behavior of gold clusters. It was found that oxygen vacancies along the 1-11 step edges could contribute to O2 dissociative adsorption and there was no obvious difference compared with the oxygen vacancies on the flat terrace. The reduced step edge and terrace likewise acted as nucleation and growth sites for gold atoms/nanoparticles, in line with previous reports. The present study provides a complete characterization of the atomic configuration of the step edges on the TiO2(110) surface and plays an important role in investigating the surface chemistry of metal oxides.

Visualization of Water-Induced Surface Segregation of Polarons on Rutile TiO2(110)

Water-oxide surfaces are ubiquitous in nature and of widespread importance to phenomena like corrosion as well as contemporary industrial challenges such as energy production through water splitting. So far, a reasonably robust understanding of the structure of such interfaces under certain conditions has been obtained. Considerably less is known about how overlayer water modifies the inherent reactivity of oxide surfaces. Here we address this issue experimentally for rutile TiO₂(110) using scanning tunneling microscopy and photoemission, with complementary density functional theory calculations. Through detailed studies of adsorbed water nanoclusters and continuous water overlayers, we determine that excess electrons in TiO₂ are attracted to the top surface layer by water molecules. Measurements on methanol show similar behavior. Our results suggest that adsorbate-induced surface segregation of polarons could be a general phenomenon for technologically relevant oxide materials, with consequences for surface chemistry and the associated catalytic activity.

Intrinsic charge trapping in amorphous oxide films: status and challenges

We review the current understanding of intrinsic electron and hole trapping in insulating amorphous oxide films on semiconductor and metal substrates. The experimental and theoretical evidences are provided for the existence of intrinsic deep electron and hole trap states stemming from the disorder of amorphous metal oxide networks. We start from presenting the results for amorphous (a) HfO₂, chosen due to the availability of highest purity amorphous films, which is vital for studying their intrinsic electronic properties. Exhaustive photo-depopulation spectroscopy measurements and theoretical calculations using density functional theory shed light on the atomic nature of electronic gap states responsible for deep electron trapping observed in a-HfO₂. We review theoretical methods used for creating models of amorphous structures and electronic structure calculations of amorphous oxides and outline some of the challenges in modeling defects in amorphous materials. We then discuss theoretical models of electron polarons and bi-polarons in a-HfO₂ and demonstrate that these intrinsic states originate from low-coordinated ions and elongated metal-oxygen bonds in the amorphous oxide network. Similarly, holes can be captured at under-coordinated O sites. We then discuss electron and hole trapping in other amorphous oxides, such as a-SiO₂, a-Al₂O₃, a-TiO₂. We propose that the presence of low-coordinated ions in amorphous oxides with electron states of significant p and d character near the conduction band minimum can lead to electron trapping and that deep hole trapping should be common to all amorphous oxides. Finally, we demonstrate that bi-electron trapping in a-HfO₂ and a-SiO₂ weakens Hf(Si)-O bonds and significantly reduces barriers for forming Frenkel defects, neutral O vacancies and O^2- ions in these materials. These results should be useful for better understanding of electronic properties and structural evolution of thin amorphous films under carrier injection conditions.

Application of the Lany-Zunger polaron correction for calculating surface charge trapping

Defect calculations, using density functional theory in a local or semi-local approximation, in transition metal oxides are severely handicapped by the electron self-interaction error. The underestimation of the band gap may cause incorrect occupation of defect states and wrong formation energies, and the underestimated localization of the states disfavors the formation of small polarons. These problems can be avoided by using higher level approximations (GW or a correctly chosen hybrid functional), but those methods are computationally too expensive to be used for calculating surface defects in a periodic slab model. Lany and Zunger have suggested a convenient (low-cost) solution for solving the band-gap and charge delocalization problem, by applying a correction scheme to the standard local or semi-local approximations. Most importantly, the linearity of the total energy as a function of the fractional occupation numbers, is restored, leading to the fulfillment of the generalized Koopmans' theorem. The method works well in the bulk but, as we show here, it is not accurate on the surface due to the different screening environment. We also show that by making the atom- and angular-momentum dependent parameters of the Lany-Zunger polaron-correction also coordination dependent, it is possible to correctly describe charge trapping in small polaron states on the anatase (1 0 1) and rutile (1 1 0) surfaces at a low computational cost.

Scenarios of polaron-involved molecular adsorption on reduced TiO2(110) surfaces

The polaron introduced by the oxygen vacancy (Vo) dominates many surface adsorption processes and chemical reactions on reduced oxide surfaces. Based on IR spectra and DFT calculations of NO and CO adsorption, we gave two scenarios of polaron-involved molecular adsorption on reduced TiO₂(110) surfaces. For NO adsorption, the subsurface polaron electron transfers to a Ti:3d-NO:2p hybrid orbital mainly on NO, leading to the large redshifts of vibration frequencies of NO. For CO adsorption, the polaron only transfers to a Ti:3d state of the surface Ti_5c cation underneath CO, and thus only a weak shift of vibration frequency of CO was observed. These scenarios are determined by the energy-level matching between the polaron state and the LUMO of adsorbed molecules, which plays a crucial role in polaron-adsorbate interaction and related catalytic reactions on reduced oxide surfaces.

Surface point defects on bulk oxides: atomically-resolved scanning probe microscopy

Metal oxides are abundant in nature and they are some of the most versatile materials for applications ranging from catalysis to novel electronics.