PHYSICAL REVIEW X 7, 031053 (2017)

Polaron-Driven Surface Reconstructions

Michele Reticcioli,1 Martin Setvin,2,* Xianfeng Hao,1,3 Peter Flauger,1 Georg Kresse,1 † Michael Schmid,2 Ulrike Diebold,2 and Cesare Franchini1, 1University of Vienna, Faculty of Physics and Center for Computational Materials Science, A-1090 Vienna, Austria 2Institute of Applied Physics, Technische Universität Wien, A-1040 Vienna, Austria 3Key Laboratory of Applied Chemistry, Yanshan University, Qinhuangdao 066004, People’s Republic of China (Received 24 May 2017; revised manuscript received 7 July 2017; published 25 September 2017) Geometric and electronic surface reconstructions determine the physical and chemical properties of surfaces and, consequently, their functionality in applications. The reconstruction of a surface minimizes its surface free energy in otherwise thermodynamically unstable situations, typically caused by dangling bonds, lattice stress, or a divergent surface potential, and it is achieved by a cooperative modification of the atomic and electronic structure. Here, we combined first-principles calculations and surface techniques (scanning tunneling microscopy, non-contact atomic force microscopy, scanning tunneling spectroscopy) to report that the repulsion between negatively charged polaronic quasiparticles, formed by the interaction between excess electrons and the lattice phonon field, plays a key role in surface reconstructions. As a paradigmatic example, we explain the (1 × 1)to(1 × 2) transition in rutile TiO2ð110Þ.

DOI: 10.1103/PhysRevX.7.031053 Subject Areas: Condensed Matter Physics, Physical Chemistry, Semiconductor Physics

I. INTRODUCTION lattice, and spins [1,12]. In this work, we find that charge trapping can cause surface reconstructions as well. The majority of surfaces undergo significant structural Excess charge in a flexible and ionic lattice is and electronic modifications with respect to the ideal bulk often present in the form of small polarons, i.e., trapped phase in order to minimize their surface free energy [1]. Typical mechanisms reduce the number of surface dangling electrons or holes coupled with the lattice phonon field. bonds, compensate intrinsic polarity, or decrease the lattice Manifestations include a local alteration of the bond lengths, stress [1–4]. Prototypical examples are the Sið111Þ-ð7 × 7Þ a change of the formal valence at the specific polaronic site, reconstruction [5,6], the (n × 1) and (2 × n) reconstructions and the emergence of a characteristic peak well localized in – occurring on the SrTiO3ð110Þ surface [7,8], and the (110) the gap region [13 17]. Polarons play a decisive role in missing-row or (100)-hexagonal structures observed on the electron transport, optical absorption, and chemical reac- fcc metals Au, Pt, and Ir [9–11], respectively. tivity, and have crucial implications in other diverse phe- Unraveling the physical mechanism that drives such nomena including high-Tc superconductivity [18], colossal surface reconstructions is essential to understand physical magnetoresistance [19,20], thermoelectricity [21], and and chemical properties of surfaces, and it helps optimize photochemistry [22]. Formation of polarons is particularly materials performance in applications such as microelec- favorable in transition-metal oxides, owing to the strength of tronics, catalysis, fuel cells, or surface engineering. The the electron-phonon interaction, and is further promoted stabilization process typically involves the displacements in the vicinity of a surface, where the crystal lattice is of surface atoms and electric charge transfer between more flexible and the necessary lattice relaxations cost less surface atoms, and often results in nonstoichiometric energy [23–25]. reconstructions; this mechanism can be affected by defects Titanium dioxide, TiO2,isanarchetypalpolaron and heating treatments, and by the interaction of orbitals, system. The surfaces of this material have been studied extensively in both theory and experiment [24,26,27]. *[email protected] TiO2 single crystals are often reduced, either chemically † [email protected] (by removing O from the lattice, i.e., by creating an V oxygen vacancy O) or electronically (by adding excess Published by the American Physical Society under the terms of electrons through the introduction of extrinsic dopants). the Creative Commons Attribution 4.0 International license. This reduction produces polarons that typically reside in Further distribution of this work must maintain attribution to 3þ the author(s) and the published article’s title, journal citation, subsurface Ti sites, although hopping can be thermally and DOI. activated [17,24].

2160-3308=17=7(3)=031053(10) 031053-1 Published by the American Physical Society MICHELE RETICCIOLI et al. PHYS. REV. X 7, 031053 (2017)

1 2 For highly reduced rutile TiO2ð110Þ samples, the surface the five layers, which gives rise to two polarons per ( × ) assumes a (1 × 2) reconstruction rather than a (1 × 1) unit cell. termination that is observed on more stoichiometric crystals The stability of the surface, and the thermally activated [4,28,29].This(1 × 2) structure is then the low-temperature hopping behavior of the polarons, were inspected by phase; it can reversibly switch to the (1 × 1) phase when the combining FPMD at T ¼ 700 K and static T ¼ 0 K sample temperature is raised above approximately 1000 K DFT calculations using the following strategy: First, for c [30], and the transition is facilitated by the surface-to-bulk each phase and each VO , multiple series of FPMD runs mass flow [31]. Here, we evaluate the surface structure as a were conducted, each starting from an arbitrary polaronic function of oxygen vacancy concentration (at the surface), configuration and lasting 10 ps with a time step of 1 fs. This c leads to 10 000 different high-temperature structures for VO , using density functional theory (DFT), first-principles molecular dynamics (FPMD), scanning tunneling micros- each FPMD run. Second, we selected all inequivalent copy (STM), and atomic force microscopy (AFM). We find polaronic configurations from this set; about 200 for each V V that, with increasing O density, the resulting polarons tend phase and O concentration. Finally, we relaxed these at to form an optimum 3 × 1 arrangement in the (1 × 1) T ¼ 0 K and found the energetically most stable structure surface. When cV is further raised, the repulsive interaction by comparing the total DFT energies. This procedure was O V between these negatively charged quasiparticles increases repeated for the nine different O concentrations and for the surface free energy. The resulting energy instability is the Ti2O3 reconstructed model, by using the 9 × 2 cell. c ¼ 16 7% overtaken by the geometrical reconstruction into the A slightly lower ground-state energy for the VO . (1 × 2)phase. case was obtained by adopting a 6 × 2 unit cell, which allows for a more homogeneous distribution of oxygen vacancies as compared to the 9 × 2 cell at this particular c II. METHODS VO . The charge densities of polarons in the most stable configurations were used for simulating STM images A. Ab initio calculations within the Tersoff-Hamann approach [39]. The resulting We used DFT and FPMD to investigate the (1 × 1) and isosurface representations allow for comparison with our (1 × 2) surface phases of the TiO2ð110Þ rutile. The calcu- experimental data. lations were performed using the Vienna ab initio simu- The total energies of the most stable configurations were lation package (VASP) [32,33]. We adopted the generalized used to build a global surface phase diagram using standard gradient approximation (GGA) within the Perdew, Burke, ab initio atomistic thermodynamics [40]. By neglecting and Ernzerhof parametrization [34], with the inclusion of configurational entropy and phonon contributions, the an on-site effective U of 3.9 eV on Ti d-states. In our surface free energy ΔG can be approximated as follows: previous work [17], we calculated this value within the constrained random phase approximation (cRPA) [35] and 1 ΔG ¼ ½Eloc − n Ebulk þ μ ð2n − n Þ; ð1Þ confirmed that it correctly predicts the experimentally A Ti TiO2 O Ti O observed degree of localization in the TiO2 polymorphs rutile and anatase. We also checked the robustness of our where Eloc is the DFT total energy at T ¼ 0 K for the conclusions against other values of U (see Ref. [36]). The bulk surface slab with trapped polarons, and ETiO2 is the energy rutile TiO2ð110Þ surfaces were modeled with an asym- for the TiO2 bulk. The adimensional prefactor 1=A scales metric slab containing five Ti layers with a large two- the energy to the (1 × 1) surface cell. The weighted dimensional (2D) 9 × 2 unit cell, resulting in more than difference between the number of Ti (n ) and O (n ) 500 atoms. The bottom two layers were kept fixed, whereas Ti O atoms accounts for the deviation from the stoichiometric all the other atomic sites were relaxed using standard formula. The chemical potential μ of oxygen atoms was convergence criteria with a plane-wave energy cutoff O considered in terms of its deviation Δμ from the total of 300 eV (lowered to 250 eV for the FPMD runs) and O energy E of an isolated oxygen molecule: using the Γ point only for the integration in the reciprocal O2 space. For the (1 × 1) phase, up to nine oxygen vacancies   V ’ 1 ( O s) were homogeneously included in the top layer (S0) μ ¼ E þ Δμ : ð2Þ c ¼ 5 6% O 2 O2 O at different concentrations ( VO . , 11.1%, 16.7%, V 22.2%, 33.3%, 38.9%, 50.0%). This O distribution was chosen by taking into account the experimentally deter- We also constructed an additional phase diagram describing mined, spatially resolved, autocorrelation functions. More the stability of TiO2ð110Þ surfaces forced to have all the V details on this choice are provided in Ref. [36]. Each O electrons delocalized. The delocalized solution was supplies two excess electrons, which form two polarons. achieved by performing non-spin-polarized calculations. The (1 × 2) phase was constructed according to the Ti2O3 The surface free energy for the systems with all electrons model [4,37,38] by placing the reconstructed row on top of delocalized is given by replacing the Eloc term in Eq. (1) with

031053-2 POLARON-DRIVEN SURFACE RECONSTRUCTIONS PHYS. REV. X 7, 031053 (2017)

Edeloc the so-obtained, delocalized, ground-state energy relax , (O adatom). In our experience, this is the only tip model where the atoms were allowed to relax again. where the attractive force above the highest O atoms (O2c) Moreover, the most stable configurations were analyzed is negligible and the repulsive regime is entered directly. E E in terms of the polaron formation energy POL. POL With CO-functionalized tips [45], the same AFM contrast represents the convenience for the system to trap electrons, was obtained above the (1 × 2) reconstruction, but no good and it is calculated as images were obtained on the (1 × 1) phase.

E ¼ Eloc − Edeloc: ð Þ III. RESULTS POL relax 3 1 1 1 2 E The transition from a ( × )toa( × ) structure at the The stability of a polaron, quantified by POL, is the result rutile TiO2ð110Þ surface is well documented in the literature of the competition between the structural cost needed to E [4,28]. The large-area STM image in Fig. 1 shows a surface distort the lattice in order to accommodate polarons ( ST) typical for a strongly reduced TiO2ð110Þ sample. The bulk- and the electronic energy gained by localizing the electron 1 1 E terminated ( × ) structure with isolated oxygen vacancies in the distorted lattice ( EL): V ’ 1 2 ( O s) coexists with stripes of the ( × ) reconstruction. E ¼ E þ E ð4Þ When a pristine (stoichiometric) TiO2 sample is introduced POL EL ST into UHV, it shows only the (1 × 1) surface. The standard where E is defined as sample treatments described above, i.e., sputtering and ST high-temperature annealing, reduce the crystals and, at first, V ’ E ¼ Edeloc − Edeloc ð Þ result in the appearance of isolated surface O s at the 2-fold ST constr relax 5 coordinated oxygen (O2c) sites. Eventually, the (1 × 2) Edeloc stripes shown in Fig. 1(a) appear; their density increases where constr is the energy of the system forced to have only delocalized electrons and constrained into the structure of upon further reduction until they cover the whole surface [28]. Here, we have only isolated (1 × 2) stripes [not a full the system hosting polarons. 1 2 Finally, the results of the FPMD runs were also used to ( × ) superstructure, which would be detectable by perform a statistical analysis of the polarons and their diffraction techniques]. This phase separation into (1 × 1) and (1 × 2) regions hopping behavior. For each phase and cV , we determined O allows an accurate determination of the critical concen- the number of occurrences of charge trapping in each tration of V ’s where the transition occurs. In the samples layer. We computed the polaron-polaron correlation func- O considered here, it is measured as a 16.7 0.2% (≈1=6) tion, defined as the distribution of the distance between monolayer. two polarons at a given time step, averaged over all A zoom-in of the (1 × 1) phase and a detail of the FPMD steps. (1 × 2) reconstruction are shown in Figs. 1(f)–1(h) and – B. Experiments Figs. 1(i) 1(k), respectively. Using an nc-AFM with an O tip termination allows us to image the O sublattice. On the Combined STM/AFM measurements were performed at well-known (1 × 1) phase [Fig. 1(f)], the image shows the T ¼ 78 V ’ K in an ultrahigh vacuum (UHV) chamber with a O2c atoms in the regime of repulsive forces; O s appear base pressure below 2 × 10−9 Pa, equipped with a com- as missing spots in the rows. This imaging mode is mercial Omicron q-Plus LT head. Synthetic single crystal particularly valuable on the (1 × 2) reconstruction samples (Crystec) were cleaned in an adjoining preparation [Fig. 1(i)], where the structural model is still under debate chamber by repeated sputtering with 1 keV Arþ ions and [4,37,38,47–50]. AFM allows a precise measurement of the annealing to 1000 K. All data were measured on a sample positions of the surface O atoms in the x-y plane, which that was strongly reduced by more than 100 cycles of prior helps us exclude most of the proposed structures. Our sputtering and annealing. Tuning-fork-based AFM sensors results confirm the Ti2O3 model [Fig. 1(c)] initially with a separate wire for the tunneling current were used proposed by Onishi and Iwasawa [4], recently refined by (k ¼ 3750 N=m, f0 ¼ 47 500 Hz, Q ≈ 50 000) [41]. Wang et al. [37] via DFT-based genetic algorithms, and Glued to each tuning fork was an electrochemically etched supported by total-reflection high-energy positron diffrac- W tip, which was cleaned in situ by field emission and self- tion studies [38]. Here, the stripes have a Ti2O3 stoichi- −4 sputtering in 10 Pa argon [42]. The tips were purposely ometry; i.e., their composition can be viewed as Ti2O4 with V ’ 1 1 1 2 functionalized by an O adatom. Here, the rutile surface was 50% of O s. The atom labeling for the ( × ) and ( × ) exposed to O2, and bias pulses applied above adsorbed O2 phases used in the discussion is specified graphically in molecules occasionally resulted in a single O atom being Figs. 1(b) and 1(c). picked up. Comparing force-distance curves (see Ref. [36]) While STM images [Figs. 1(g), 1(h), 1(j), and 1(k)] measured above the clean (1 × 1) surface to previous provide supplementary information about the geometric experimental AFM works [43,44] leads us to conclude structure, their importance resides in unraveling the elec- that the tip is terminated by a single-coordinated O atom tronic structure of the two phases. In the empty-states STM

031053-3 MICHELE RETICCIOLI et al. PHYS. REV. X 7, 031053 (2017)

FIG. 1. The (1 × 1) and (1 × 2) surface phases of TiO2ð110Þ. (a) Large-area STM image of a reduced rutile (110) single crystal. Unreconstructed (1 × 1) regions with single oxygen vacancies VO appear together with reconstructed (1 × 2)Ti2O3 stripes. (b,c) Structural models of the (1 × 1) and (1 × 2) phases, respectively. (d,e) STS spectra (line) taken above (1 × 1) and (1 × 2), together with calculated polaronic gap states (filled area), shifted upwards by ≈0.25 eV to align the center of mass of the Ti3þ (polaronic) peaks with E the experiment (in this way, the DFT peak positions are also in better agreement with the calculated vertical excitation energy EL [46]). (f)–(k) High-resolution images of the (1 × 1) and (1 × 2) regions marked in panel (a), overlaid with the respective structural models. AFM images (i,f) show the highest O atoms (O2c and Orec) on the surface, and STM images show the empty (g,j) and filled (h,k) states. images of the (1 × 1) phase [the imaging mode most- Therefore, the number of polarons that form in this V ’ V widely employed in the literature, Fig. 1(g)], the O s structure is in accordance with a nominal O concentration A appear as bright spots between the surface TiS0 atoms. of 50% (i.e., one missing oxygen per unit cell). This value More interesting, however, are filled-states STM images is also in agreement with the electronic structure results that collect the gap states seen in STS [Fig. 1(d)]; the image shown in Fig. 1(e): The significant jump in the off- in Fig. 1(h) directly shows the distribution of trapped stoichiometry from the (1 × 1)to(1 × 2) reconstruction, V ’ polarons originating from the O s, as is discussed below. 16.7% to (locally) 50%, implies a high concentration of The lattice of the (1 × 2) reconstruction is very flexible and polarons and causes the broadening of the in-gap peak in subject to surface buckling; see the DFT ground-state the DOS and filled-states STS [51–53] of the reconstructed structural model shown in Fig. 1(c). Both experiment surface [compare Figs. 1(d) and 1(e)]. and DFT find competing structures with different degrees We now turn our attention to the distribution of polarons of buckling (discussed in Ref. [36]). When the buckling is in the (1 × 1) structure. It is generally agreed that excess – V ’ small, like in Figs. 1(i) 1(k), the STM signal comes from electrons originating from impurities (such as O s but also α;β other defects, e.g., interstitial Ti atoms [54]) form polarons the O3c [empty states, Fig. 1(j)] and TiSO [in-gap states, 3þ A Fig. 1(k)] atoms, the latter is attributed to Ti polaronic- preferentially located in the subsurface TiS1 [001] rows. like states originating from the deviation of the Ti2O3 These can easily hop to surface sites when thermally reconstruction from the stoichiometric formula. Our activated [17,24,55–58], while a polaron trapping deeper DFT calculations show that the reconstructed Ti2O3 in the bulk is significantly less favorable energetically, (1 × 2) surface hosts two polarons per (1 × 2) unit cell. comparable to delocalized electrons [59]. We followed the

031053-4 POLARON-DRIVEN SURFACE RECONSTRUCTIONS PHYS. REV. X 7, 031053 (2017) hopping in FPMD calculations and increased the polaron Figure 2 also presents the charge density isosurfaces of c density by considering slabs with increasing VO from 5.6% polarons in their energetically most favorable configuration c for each cV . The stable configurations at low V concen- to 50.0%. Indeed, we found that at any VO, the polarons are O O S0 S1 c ≤ 16 7% mostly located in the topmost two layers, and ,as tration ( VO . ) are characterized by polarons reported by the histogram bars in Fig. 2. This result does trapped only in S1 sites [Figs. 2(a)–2(c)]. At higher c ≥ 22 2% not depend on the thickness of the simulated slab, cor- concentrations ( VO . ), it is energetically more roborating the conclusion that in the (1 × 1) phase excess favorable to also host polarons in S0 sites rather than electrons form near-surface polarons [17,24] and avoid increasing their density in the S1 layer [Fig. 2(d)]. c the bulk states suggested in recent literature [60]. At the Interestingly, this VO value in the calculations agrees with c ¼ 5 6% V 1 1 smallest concentration, VO . , the polarons are the O concentration of 16.7%, where the ( × ) and located in the S1 layer 95% of the time and undergo inter- (1 × 2) phases are found to coexist in our experiment. A S1 and intra-TiS1 row hopping [histogram bar of Fig. 2(a)]. Thus, the limited capacity of the subsurface ( ) layer to Hopping into surface sites is very rare, with polarons accommodate the polarons appears to be the driving force being trapped in S0 for 5% of the time only. With behind forming the (1 × 2) reconstruction. c In order to explain this characteristic feature of the increasing VO in the surface (S0) layer [histogram bars of Figs. 2(b)–2(d)], i.e., with an increasing number of polarons polaronic distribution as a function of the concentration in the system, hopping into S0 sites becomes more likely. of oxygen vacancies, we recall here that polarons are negatively charged quasiparticles. Therefore, their Coulomb-like repulsion should increase with decreasing polaron-polaron distance. Indeed, during the FPMD runs, the probability of finding two polarons at adjacent sites is c – very low at any VO. This is seen in Figs. 3(c) 3(e), where we report the polaron-polaron autocorrelation functions A along the TiS1 [001] rows. The highest probability is found for values that maximize the distance between polarons in the row, corresponding to three or four lattice constants V – apart, depending on the O density [Figs. 3(c) 3(e)]. This result is in excellent agreement with experiment, in c ¼ 16 7% 3 1 particular, at VO . where a clear ( × ) periodicity is observed in the autocorrelation analysis of filled-states V STM images [Fig. 3(g)]. We notice that, at larger O c ≥ 22 2% concentration ( V O . ), the peak of the calculated correlation function is not shifted to smaller distances, although the polaron density in the cell increases: The (3 × 1) pattern in S1 is preserved [Fig. 3(e)], and polarons populate the S0 layer more often [histogram bar of Fig. 2(d)]. This can be understood by inspecting the spatial extension of the polaron charge density. While most of the polaron charge has dz2 symmetry [see inner yellow isosur- face in Fig. 3(b)], a non-negligible amount of charge A A spreads across the adjacent TiS0 and TiS1 sites [see external isosurface in Fig. 3(b)]. This extended cloud gives rise to the STM contrast observed in experiment [Fig. 3(f)]—a characteristic dimerlike shape [Fig. 3(a)]—and clarifies the correlation between the distribution of polarons in S1 and the STM spots. The 3 × 1 periodicity of polarons along the A TiS1 row [sketched in Fig. 3(h)] avoids the overlap of two adjacent extended repulsive polaron clouds [Fig. 3(b)], thereby reducing the polaron-polaron repulsion, as recently confirmed in the literature [60]. In the FPMD runs at higher V concentrations, polarons are pushed into S0 sites in FIG. 2. Polaron distribution in TiO2ð110Þ. (a)–(d), Most stable O S1 polaron configurations obtained by FPMD and subsequent order to preserve the optimal concentration in the layer. relaxations at the various VO concentrations specified in each We also note that the polaron-polaron repulsion is per- panel. The histograms illustrate how often the polarons are found turbed by the attracting Coulomb interaction between S0 S1 V in (orange) and (green) Ti sites during the FPMD runs. polarons and the immobile O centers [16,61], which

031053-5 MICHELE RETICCIOLI et al. PHYS. REV. X 7, 031053 (2017)

most favorable configuration. When polaron formation is included in the calculations, the phase diagram in Fig. 4(b) shows that the Ti2O3 reconstruction becomes the most V stable one above the critical O concentration of 22.2%. This is slightly larger than the critical concentration measured experimentally, which could be attributable to effects not included in our calculations, such as the presence of additional dopants (e.g., interstitial Ti [54]), V the O distribution, and the specific type of approximation (DFT þ U) chosen to treat the localization effect [63]. Note, however, that the delocalized solution shown in Fig. 4(a) predicts that the reduced (1 × 1) phase remains V the most stable structure even at high O concentrations: The Ti2O3 reconstruction [inset in Fig. 4(a)] is just as stable 1 1 c ¼ 50 0% as the ( × )at VO . .

IV. DISCUSSION To understand this polaron-mediated change of the surface stability, it is instructive to analyze the energy E gained upon polaron formation, POL [46]. It is defined as the total-energy difference between the polaronic and fully delocalized free-carrier solution, and it results from the competition between the strain energy required to distort E E the lattice, ST, and the electronic energy EL gained by localizing the electron at a Ti site in such a distorted lattice. E Figure 5(a) shows POL for the most stable configuration c at each considered VO . For low concentrations, up to c ≃ 20% 1 1 E A V in the ( × ) structure, POL decreases with FIG. 3. Polaron distribution along the TiS1 row. (a) Simulated O filled-states STM (at 2 Å from the surface) of an isolated polaron increasing concentration; it becomes more favorable to A c > 22 2% around a TiS1 site. (b) The corresponding charge density isosur- form polarons in the system. For VO . , however, A E face shows the high-density dz2 -like orbital localized at TiS1 POL remains constant and ultimately increases. Figure 5(a) (yellow) and the large, low-density cloud extending across the also includes the polaron energy for the reconstructed A A nearby TiS1 and TiS0 sites. (c)–(e) Calculated polaron-polaron surface [64]. It has the highest negative value of all A A autocorrelation functions along TiS1 and TiS0 rows extracted from configurations considered, and the resulting convex hull cV ¼ 5 6% 1 1 FPMD runs at O . , 16.7%, and 22.2%. (f) Experimental clearly shows that the reduced ( × ) phases are unstable filled-states STM image at cV ¼ 16.7%, and (g) corresponding c > 22 2% O for VO . . The surface undergoes a structural polaron-polaron autocorrelation function along the [001] rows. reconstruction above this critical value. A (h) Sketch of the 3 × 1 periodicity in the TiS1 row. E c The trend of POL as a function of VO becomes clear if one considers the energy cost that is required to locally modifies the optimum patterns, including the 3 × 1 (see distort the lattice in order to accommodate an electron Ref. [36] for more details). and the energy gained by localizing an electron in such a V lattice [46]. Figure 5(b) reports this strain energy E The measured maximum O concentration of 16.7% on ST the (1 × 1) patches of the partially reconstructed surface for the most stable configuration at each considered V cV . E decreases with increasing cV , but it shows a suggests that a further increase in O results in a thermo- O ST O c ¼ 22 2% ΔE ¼ dynamically unstable situation, and this leads the system to distinct jump at the critical VO . [ ST E ð22 2%Þ − E ð16 7%Þ¼65 the (1 × 2) reconstruction. This behavior is borne out of our ST . ST . meV]. The isosurfaces ab initio calculations, but only if the polaron states are plotted in Fig. 2 are helpful to understand this trend. At c ¼ 16 7% allowed to form [62]: We computed the surface free energy low concentrations, up to VO . , the polarons reside ΔG Δμ A as a function of the oxygen chemical potential O for preferentially along the TiS1 [001] row. Once the lattice in 1 1 c ¼ 5 6% S0 S1 each system [i.e., the ( × ) surface with VO . , the S1 layer is distorted (as well as the - interlayer 11.1%, 16.7%, 22.2%, 33.3%, 38.9%, 50.0% and the distance), it is increasingly easier to form more polarons. 1 2 S0 c ¼ ( × ) reconstruction]. This computation was done both The layer is kept essentially unperturbed. At VO for the unrealistic case of excess electrons delocalized in 22.2%, however, the polarons also start to populate the S0 the conduction band and for the polarons localized in their layer, and the breaking of the symmetry of the top layer

031053-6 POLARON-DRIVEN SURFACE RECONSTRUCTIONS PHYS. REV. X 7, 031053 (2017)

FIG. 4. TiO2ð110Þ surface phase diagram. Surface free energy (ΔG) for the most stable configurations obtained from the MD for the 1 1 V 1 2 reduced ( × ) structures at different O concentrations (all lines except pink) and for the ( × )Ti2O3 reconstruction (pink line) as a Δμ 1 1 function of the chemical potential O with respect to the stoichiometric ( × ) phase. (a) Delocalized solution: Excess electrons are c ¼ 50 0% 1 1 spread across all lattice sites and delocalized at the bottom of the conduction band. At VO . , the ( × ) structure is degenerate with the (1 × 2)Ti2O3 reconstruction (Ti2O4 with 50% of VO). (b) Localized solution: The excess electrons are trapped in distinct Ti sites, mostly located in S0. The insets show the distribution of excess electrons in the (1 × 2) structure. The localized polaron picture is capable of predicting the (1 × 1)to(1 × 2) transition, manifested by the increased stability of the reconstructed Ti2O3 phase at low oxygen chemical potential compared to the highly reduced (1 × 1) phases. results in an additional energy cost. As pointed out above, overtakes the electrostatic instability from the trapped S0 α;β increased jumping to happens in order to preserve the charges near the (1 × 1) surface. Moreover, the TiS0 sites 3 1 S1 c ¼ 16 7% optimum × pattern in (reached at VO . ), as a in the (1 × 2) reconstructed surface are easily reducible and larger polaron density in S1 would result in the overlap of can conveniently host polarons [see the advantageous E 1 2 the extended polaronic cloud, as well as in a strong formation energy POL in Fig. 5(a)]. The ( × ) phase Coulomb repulsion. While hosting polarons in both layers c ¼ 50% 1 1 is more stable than the highly reduced ( VO )( × ) S1 and S0 reduces this overlap, it requires a distortion of the surface by about ΔE ¼84 meV (ΔE ¼E1×1 −E1×2 ), A A POL POL POL POL lattice around both the TiS1 and TiS0 sites. Apparently, a and this energy gain arises predominantly from the 1 2 E structural switch to a local ( × ) structure happens difference in EL between the two phases, 64 meV ΔE ð50%Þ¼20 instead. The Ti2O3 reconstruction exhibits a high degree [ ST meV]. of structural flexibility, expressed in terms of a low energy E cost ST [Fig. 5(b)] needed to accommodate a large A. Summary and conclusion concentration of polarons (i.e., as large as in the cV ¼ O In conclusion, the present study shows that polarons 50% case). E (charges trapped at Ti lattice sites) play an important role Finally, in Fig. 5(c), we show the evolution of EL as a for the stability of titania surfaces. At slightly reducing function of cV . First, we note that E is about twice as 3þ O EL conditions, Ti polarons are trapped in the subsurface sites larger as E , and it leads to a large polaron energy at any ST of the (1 × 1) TiO2 surface, with the optimal polaron- V E O concentration. To understand the trend of EL,itis polaron distance being three lattice sites. As the polaron E useful to correlate EL with the change in the polaron DOS density increases, Ti3þ polarons are pushed to the less with cV [Figs. 1(d) and 1(e), and Fig. S9 in Ref. [36]). At O favorable Ti surface sites as well. This process, however, low cV , the polarons form a well-localized peak below the O costs energy, so ultimately a transition to a (1 × 2) cV ¼ 22 2% E Fermi energy [Fig. 1(d)]. At O . , EL decreases reconstruction with the formal stoichiometry of Ti2O3 by 100 meV because the additional polarons start to occurs. If we neglect charge trapping and relaxation around populate levels at lower energies (Fig. S9). For larger the polaron, the reconstructed phase does not appear in the c VO , the peak exhibits a progressive broadening towards theoretical phase diagram. E higher energies, which leads to an increase of EL. Our results for the rutile TiO2 (1 × 1)to(1 × 2) E The combined action of both the low strain cost ST and transition could present a new paradigm for surface E the favorable electronic localization energy EL determines reconstructions that involve trapped charges and the the thermodynamic stability of the (1 × 2) phase, which interaction among them. Polaron formation is ubiquitous

031053-7 MICHELE RETICCIOLI et al. PHYS. REV. X 7, 031053 (2017)

Nb-doped, V-doped, or Cr-doped TiO2 samples form the (1 × 2)reconstructionmucheasier,evenwhenthe 1 1 V surrounding ( × ) phase has much lower O concen- trations [70–72]. Finally, the control of charge trapping could provide a way to optimize the functionality of TiO2-based memristors [73] and to facilitate charge transfer in catalytic processes [74].

ACKNOWLEDGMENTS This work was supported by the Austrian Science Fund (FWF) SFB project VICOM (Grant No. F41), by the FWF project POLOX (Grant No. I 2460-N36), by the ERC Advanced Research Grant “OxideSurfaces,” by the FWF Wittgenstein-prize (Z250-N16), and by the National Natural Science Foundation of China (Grants No. 21303156 and No. 21543006). The computational results presented have been achieved using the Vienna Scientific Cluster (VSC). C. F., Ma. S., and U. D. conceived and coordinated the research project. M. R., C. F., P. F., and X. H. performed the DFT calculations. M. R. and P. F. conducted the statistical analysis. Ma. S. performed the experiments. Mi. S. and G. K. contributed to the data analysis. C. F., Ma.S., M. R., and U. D. wrote the manuscript. All authors contributed to the interpretation and discussion of the results.

[1] K. Oura, V. G. Lifshits, A. Saranin, A. V. Zotov, and M. Katayama, Surface Science: An Introduction (Springer-Verlag, Berlin, 2003). [2] C. Noguera, Polar Oxide Surfaces, J. Phys. Condens. Matter 12, R367 (2000). [3] X.-Q. Wang, Phases of the Au(100) Surface Reconstruction, Phys. Rev. Lett. 67, 3547 (1991). [4] H. Onishi and Y. Iwasawa, Reconstruction of TiO2ð110Þ Surface: STM Study with Atomic-Scale Resolution, Surf. FIG. 5. Polaron energies (meV/polaron) as a function of cV . O Sci. 313, L783 (1994). (a) Polaron formation energy E , computed as the difference POL [5] G. Binnig, H. Rohrer, C. Gerber, and E. Weibel, between the ground states of the localized and delocalized 7 × 7 Reconstruction on Si(111) Resolved in Real Space, solutions. (b) Strain energy E , i.e., energy cost to locally ST Phys. Rev. Lett. 50, 120 (1983). distort the lattice in order to accommodate polarons. (c) Electronic [6] K. D. Brommer, M. Needels, B. Larson, and J. D. energy E , i.e., energy gained by localizing the electron in the EL Joannopoulos, Ab initio Theory of the Sið111Þ-ð7 × 7Þ distorted lattice. Surface Reconstruction: A Challenge for Massively Parallel Computation, Phys. Rev. Lett. 68, 1355 (1992). in transition-metal oxides and is typically propelled by [7] J. A. Enterkin, A. K. Subramanian, B. C. Russell, oxygen vacancies and doping [58]. Possible examples of M. R. Castell, K. R. Poeppelmeier, and L. D. Marks, A other materials in which polaron-mediated reconstruc- Homologous Series of Structures on the Surface of tions could be operational are oxide perovskites, in SrTiO3ð110Þ, Nat. Mater. 9, 245 (2010). [8] Z. Wang, A. Loon, A. Subramanian, S. Gerhold, E. particular, SrTiO3 [65–67], as well as popular oxides like ceria and hafnia [68]. Thus, this polaron-mediated McDermott, J. A. Enterkin, M. Hieckel, B. C. Russell, R. J. Green, A. Moewes et al., Transition from Reconstruction mechanism is likely to be a pervasive phenomenon that Toward Thin Film on the (110) Surface of Strontium Titanate, could explain structural, electronic, and magnetic recon- Nano Lett. 16, 2407 (2016). structions at surfaces and interfaces [69] andcouldbe [9] W. Moritz and D. Wolf, Structure Determination of employed to tune surface properties and to control the Reconstructed Au(110) Surface, Surf. Sci. 88, L29 the surface geometry. For instance, it is known that (1979).

031053-8 POLARON-DRIVEN SURFACE RECONSTRUCTIONS PHYS. REV. X 7, 031053 (2017)

[10] K. M. Ho and K. P. Bohnen, Stability of the Missing-Row Oxygen-Induced Restructuring of the TiO2ð110Þ Surface: A Reconstruction on fcc (110) Transition-Metal Surfaces, Comprehensive Study, Surf. Sci. 437, 173 (1999). Phys. Rev. Lett. 59, 1833 (1987). [29] M. Li, W. Hebenstreit, and U. Diebold, Morphology [11] P. Heilmann, K. Heinz, and K. Mller, The Superstructures of Change of Oxygen-Restructured TiO2ð110Þ Surfaces by the Clean Pt(100) and Ir(100) Surfaces, Surf. Sci. 83, 487 UHV Annealing: Formation of a Low-Temperature (1 × 2) (1979). Structure, Phys. Rev. B 61, 4926 (2000). [12] G. Profeta and E. Tosatti, Triangular Mott-Hubbard [30] K. F. McCarty and N. C. Bartelt, The 1 × 1=1 × 2 Phase Insulator Phases of Sn=Sið111Þ and Sn=Geð111Þ Surfaces, Transition of the TiO2ð110Þ Surface-Variation of Transition Phys. Rev. Lett. 98, 086401 (2007). Temperature with Crystal Composition, Surf. Sci. 527, [13] H. Fröhlich, Electrons in Lattice Fields, Adv. Phys. 3, 325 L203 (2003). (1954). [31] K. F. McCarty and N. C. Bartelt, Role of Bulk Thermal [14] A. S. Alexandrov and J. T. Devreese, Advances in Polaron Defects in the Reconstruction Dynamics of the TiO2ð110Þ Physics (Springer-Verlag, New York, 2010). Surface, Phys. Rev. Lett. 90, 046104 (2003). [15] A. L. Shluger and A. M. Stoneham, Small Polarons in Real [32] G. Kresse and J. Hafner, Ab Initio Molecular Dynamics for Crystals: Concepts and Problems, J. Phys. Condens. Matter Liquid Metals, Phys. Rev. B 47, 558 (1993). 5, 3049 (1993). [33] G. Kresse and J. Furthmüller, Efficient Iterative Schemes for [16] P. Deák, B. Aradi, and T. Frauenheim, Quantitative Theory Ab Initio Total-Energy Calculations Using a Plane-Wave of the Oxygen Vacancy and Carrier Self-Trapping in Bulk Basis Set, Phys. Rev. B 54, 11169 (1996). TiO2, Phys. Rev. B 86, 195206 (2012). [34] J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized [17] M. Setvin, C. Franchini, X. Hao, M. Schmid, A. Janotti, M. Gradient Approximation Made Simple, Phys. Rev. Lett. 77, Kaltak, C. G. Van de Walle, G. Kresse, and U. Diebold, 3865 (1996). Direct View at Excess Electrons in TiO2 Rutile and Anatase, [35] F. Aryasetiawan, K. Karlsson, O. Jepsen, and U. Schönberger, Phys. Rev. Lett. 113, 086402 (2014). Calculations of Hubbard U from First-Principles, Phys. [18] E. Salje, A. S. Alexandrov, and W. Y. Liang, Polarons Rev. B 74, 125106 (2006). and Bipolarons in High-Tc Superconductors and Related [36] See Supplemental Material at http://link.aps.org/ Materials (Cambridge University Press, Cambridge, supplemental/10.1103/PhysRevX.7.031053 for further England, 2005). details. [19] J. M. De Teresa, M. R. Ibarra, P. A. Algarabel, C. Ritter, C. [37] Q. Wang, A. R. Oganov, Q. Zhu, and X.-F. Zhou, New Marquina, J. Blasco, J. Garcia, A. del Moral, and Z. Arnold, Reconstructions of the (110) Surface of Rutile TiO2 Pre- Evidence for Magnetic Polarons in the Magnetoresistive dicted by an Evolutionary Method, Phys. Rev. Lett. 113, Perovskites, Nature (London) 386, 256 (1997). 266101 (2014). [20] H. M. Rønnow, C. Renner, G. Aeppli, T. Kimura, and Y. [38] I. Mochizuki, H. Ariga, Y. Fukaya, K. Wada, M. Maekawa, Tokura, Polarons and Confinement of Electronic Motion to A. Kawasuso, T. Shidara, K. Asakura, and T. Hyodo, Two Dimensions in a Layered Manganite, Nature (London) Structure Determination of the Rutile-TiO2ð110Þ-ð1 × 2Þ 440, 1025 (2006). Surface Using Total-Reflection High-Energy Positron [21] M. Wang, C. Bi, L. Li, S. Long, Q. Liu, H. Lv, N. Lu, Diffraction (TRHEPD), Phys. Chem. Chem. Phys. 18, P. Sun, and M. Liu, Thermoelectric Seebeck Effect in 7085 (2016). Oxide-Based Resistive Switching Memory, Nat. Commun. [39] J. Tersoff and D. R. Hamann, Theory of the Scanning 5, 4598 (2014). Tunneling Microscope, Phys. Rev. B 31, 805 (1985). [22] A. L. Linsebigler, G. Lu, and J. T. Yates, Photocatalysis [40] K. Reuter and M. Scheffler, Composition, Structure, and on TiO2 Surfaces: Principles, Mechanisms, and Selected Stability of RuO2ð110Þ as a Function of Oxygen Pressure, Results, Chem. Rev. 95, 735 (1995). Phys. Rev. B 65, 035406 (2001). [23] N. A. Deskins, R. Rousseau, and M. Dupuis, Localized [41] Z. Majzik, M. Setvín, A. Bettac, A. Feltz, V. Cháb, and Electronic States from Surface Hydroxyls and Polarons in P. Jelnek, Simultaneous Current, Force and Dissipation TiO2ð110Þ, J. Phys. Chem. C 113, 14583 (2009). Measurements on the Si(111) 7 × 7 Surface with an [24] P. M. Kowalski, M. Farnesi Camellone, N. N. Nair, B. Optimized qPlus AFM/STM Technique, Beilstein J. Nano- Meyer, and D. Marx, Charge Localization Dynamics technol. 3, 249 (2012). Induced by Oxygen Vacancies on the TiO2ð110Þ Surface, [42] M. Setvín, J. Javorský, D. Turčinková, I. Matolínová, P. Phys. Rev. Lett. 105, 146405 (2010). Sobotík, P. Kocán, and I. Ošt’ádal, Ultrasharp Tungsten [25] N. A. Deskins, R. Rousseau, and M. Dupuis, Distribution of Tips—Characterization and Nondestructive Cleaning, 3þ Ti Surface Sites in Reduced TiO2, J. Phys. Chem. C 115, Ultramicroscopy 113, 152 (2012). 7562 (2011). [43] A. Yurtsever, D. Fernandez-Torre, C. Gonzalez, P. Jelinek, [26] U. Diebold, The Surface Science of Titanium Dioxide, P. Pou, Y. Sugimoto, M. Abe, R. Perez, and S. Morita, Surf. Sci. Rep. 48, 53 (2003). NC-AFM Imaging of the TiO2ð110Þ-ð1 × 1Þ Surface at Low [27] C. Di Valentin, G. Pacchioni, and A. Selloni, Reduced and Temperature, Phys. Rev. B 85, 125416 (2012). 3þ N-Type Doped TiO2: Nature of Ti Species, J. Phys. [44] R. Bechstein, C. González, J. Schütte, P. Jelínek, R. Pérez, Chem. C 113, 20543 (2009). and A. Kühnle, All-Inclusive Imaging of the Rutile [28] M. Li, W. Hebenstreit, L. Gross, U. Diebold, M. A. TiO2ð110Þ Surface Using NC-AFM, Nanotechnology 20, Henderson, D. R. Jennison, P. A. Schultz, and M. P. Sears, 505703 (2009).

031053-9 MICHELE RETICCIOLI et al. PHYS. REV. X 7, 031053 (2017)

[45] L. Gross, F. Mohn, N. Moll, P. Liljeroth, and G. Meyer, The Reduced TiO2 (110) Surfaces, J. Phys. Chem. C 121, 11325 Chemical Structure of a Molecule Resolved by Atomic (2017). Force Microscopy, Science 325, 1110 (2009). [61] P. Deák, B. Aradi, and T. Frauenheim, Oxygen Deficiency [46] A. Janotti, C. Franchini, J. B. Varley, G. Kresse, and C. G. in TiO2: Similarities and Differences Between the Ti Van de Walle, Dual Behavior of Excess Electrons in Rutile Self-Interstitial and the O Vacancy in Bulk Rutile and TiO2, Phys. Status Solidi RRL 7, 199 (2013). Anatase, Phys. Rev. B 92, 045204 (2015). [47] C. L. Pang, S. A. Haycock, H. Raza, P. W. Murray, G. [62] X. Hao, Z. Wang, M. Schmid, U. Diebold, and C. Franchini, Thornton, O. Gülseren, R. James, and D. W. Bullett, Added Coexistence of Trapped and Free Excess Electrons in Row Model of TiO2ð110Þ1 × 2, Phys. Rev. B 58, 1586 SrTiO3, Phys. Rev. B 91, 085204 (2015). (1998). [63] T. Shibuya, K. Yasuoka, S. Mirbt, and B. Sanyal, A [48] K. T. Park, M. Pan, V. Meunier, and E. W. Plummer, Systematic Study of Polarons Due to Oxygen Vacancy Reoxidation of TiO2ð110Þ via Ti Interstitials and Line Formation at the Rutile TiO2ð110Þ Surface by GGA þ U Defects, Phys. Rev. B 75, 245415 (2007). and HSE06 Methods, J. Phys. Condens. Matter 24, 435504 [49] N. Shibata, A. Goto, S.-Y. Choi, T. Mizoguchi, S. D. (2012). Findlay, T. Yamamoto, and Y. Ikuhara, Direct Imaging of [64] For the (1 × 2) phase, we also call localization energy 322 E Reconstructed Atoms on TiO2 (110) Surfaces, Science , POL for simplicity, though the underlying physics of 570 (2008). localization may also involve effects other than polaronic [50] K.-O. Ng and D. Vanderbilt, Structure and Apparent distortions. Topography of TiO2ð110Þ Surfaces, Phys. Rev. B 56, [65] Z. Wang, A. Loon, A. Subramanian, S. Gerhold, E. 10544 (1997). McDermott, J. A. Enterkin, M. Hieckel, B. C. Russell, [51] M. Batzill, K. Katsiev, D. J. Gaspar, and U. Diebold, R. J. Green, A. Moewes et al., Transition from Reconstruction Variations of the Local Electronic Surface Properties of Toward Thin Film on the (110) Surface of Strontium Titanate, TiO2ð110Þ Induced by Intrinsic and Extrinsic Defects, Phys. Nano Lett. 16, 2407 (2016). Rev. B 66, 235401 (2002). [66] N. Erdman, K. R. Poeppelmeier, M. Asta, O. Warschkow, [52] C. Sànchez-Sànchez, M. G. Garnier, P. Aebi, M. Blanco- D. E. Ellis, and L. D. Marks, The Structure and Chemistry of Rey, P. L. de Andres, J. A. Martín-Gago, and M. F. López, the TiO2-Rich Surface of SrTiO3ð001Þ, Nature (London) Valence Band Electronic Structure Characterization of the 419, 55 (2002). Rutile TiO2 ð110Þ-ð1 × 2Þ Reconstructed Surface, Surf. Sci. [67] X. Hao, Z. Wang, M. Schmid, U. Diebold, and C. Franchini, 608, 92 (2013). Coexistence of Trapped and Free Excess Electrons in [53] C. M. Yim, C. L. Pang, and G. F. Thornton, Probing the SrTiO3, Phys. Rev. B 91, 085204 (2015). Local Electronic Structure of the Cross-Linked (1 × 2) [68] A. M. Stoneham, J. Gavartin, A. L. Shluger, A. V. Kimmel, Reconstruction of Rutile TiO2ð110Þ, Surf. Sci. 650,71 D. Muoz Ramo, H. M. Rnnow, G. Aeppli, and C. Renner, (2016), The Surface Science of Heterogeneous Catalysis: In Trapping, Self-Trapping and the Polaron Family, J. Phys. Honor of Robert J. Madix. Condens. Matter 19, 255208 (2007). [54] S. Wendt, P. T. Sprunger, E. Lira et al., The Role of [69] C. Cancellieri, A. S. Mishchenko, U. Aschauer, A. Interstitial Sites in the Ti3d Defect State in the Band Gap Filippetti, C. Faber, O. S. Barisic, V. A. Rogalev, T. Schmitt, of Titania, Science 320, 1755 (2008). N. Nagaosa, and V. N. Strocov, Polaronic Metal State at [55] S. Livraghi, S. Maurelli, M. C. Paganini, M. Chiesa, and E. the LaAlO3=SrTiO3 Interface, Nat. Commun. 7, 10386 Giamello, Probing the Local Environment of Ti3þ Ions in (2016). 17 TiO2 (Rutile) by O HYSCORE, Angew. Chem., Int. Ed. 50, [70] R. Shimizu, K. Iwaya, T. Ohsawa, T. Hasegawa, T. 8038 (2011). Hashizume, and T. Hitosugi, Simplified Method to Prepare [56] V. E. Henrich, G. Dresselhaus, and H. J. Zeiger, Observation Atomically-Ordered TiO2ð110Þ-(1 × 1) Surfaces with Steps of Two-Dimensional Phases Associated with Defect States and Terraces, Appl. Surf. Sci. 257, 4867 (2011). on the Surface of TiO2, Phys. Rev. Lett. 36, 1335 (1976). [71] X. Song, E. Primorac, H. Kughlenbeck, and H.-J. Freund, [57] A. C. Papageorgiou, N. S. Beglitis, C. L. Pang, G. Teobaldi, Effect of Vanadium Admixing on the Surface Structure of G. Cabailh, Q. Chen, A. J. Fisher, W. A. Hofer, and G. TiO2 (110) under Non-oxidizing Conditions, Surf. Sci. 653, Thornton, Electron Traps and Their Effect on the Surface 181 (2016). Chemistry of TiO2ð110Þ, Proc. Natl. Acad. Sci. U.S.A. 107, [72] R. Bechstein, M. Kitta, J. Schutte, A. Kuhnle, and H. 2391 (2010). Onishi, Evidence for Vacancy Creation by Chromium [58] P. G. Moses, A. Janotti, C. Franchini, G. Kresse, and C. G. Doping of Rutile Titanium Dioxide (110), J. Phys. Chem. Van de Walle, Donor Defects and Small Polarons on the C 113, 3277 (2009). TiO2ð110Þ Surface, J. Appl. Phys. 119, 181503 (2016). [73] E. Gale, TiO2-Based Memristors and ReRAM: Materials, [59] S. Yang, A. T. Brant, N. C. Giles, and L. E. Halliburton, Mechanisms and Models (A Review), Semicond. Sci. Intrinsic Small Polarons in Rutile TiO2, Phys. Rev. B 87, Technol. 29, 104004 (2014). 125201 (2013). [74] M. A. Henderson, A Surface Science Perspective on [60] T. Shibuya, K. Yasuoka, S. Mirbt, and B. Sanyal, Subsur- Photocatalysis, Surf. Sci. Rep. 66, 185 (2011). face Polaron Concentration as a Factor in the Chemistry of

031053-10