It has been suggested that Ba3In2O6might be a high-
Since the discovery of superconductivity [1] there has been a relentless drive to find materials with higher transition temperature (T c ) to broaden technological applications of superconductors. Without a doubt the most significant discovery in this regard is high-T c superconductivity in cuprates [2]. It is no surprise that the desire to find new and better superconductors was accompanied by countless efforts to predict suitable candidate materials. When these efforts first evolved Matthias dismissed them as futile and highlighted the benefits of an empirical approach [3][4][5]. In fact, the discovery of (unconventional) superconductors remains highly empirical to this day. This is despite the impressive developments in the prediction of materials properties [6].
Recently, a novel approach to predict superconductors has emerged. Machine learning utilizes huge materials databases to compare known superconducting materials and identify materials with similar structures not yet identified as superconductors [7][8][9]. One of the most exciting materials this approach has predicted is Ba 3 In 2 O 6 . It is not a direct derivative of a known high-T c superconductor and the predicted T c is fairly high at 78.0 K [7]. The suggestion that this material might be a high-temperature superconductor actually dates back to the first report of high-quality single crystals of Ba 3 In 2 O 6 [10]. This supposition elicited from human intelligence through recognition that its structure (see figure 1), which is closely related to Sr 3 Ti 2 O 7 , is isostructural to the known high-T c superconductor La 2 SrCu 2 O 6 [10][11][12].
Previously, the hygroscopic nature of Ba 3 In 2 O 6 and the resulting instability in air prohibited the electrical characterization of Ba 3 In 2 O 6 powders and small single crystals that were about 0.1 mm in size [10,13,14]. The synthesis of epitaxial thin films of Ba 3 In 2 O 6 has obvious advantages for testing the electrical transport properties of Ba 3 In 2 O 6 but faces additional challenges. To start with, the large a-axis lattice constant (0.419 nm) of Ba 3 In 2 O 6 suggests a limited choice of substrates and its high formation temperature pushes the limits of conventional heaters [13][14][15][16]. Recently, we developed a means to grow single-phase films of Ba 3 In 2 O 6 utilizing suboxide molecular-beam epitaxy (s-MBE) [14,17]. The large a-axis lattice constant of Ba 3 In 2 O 6 is not far from that of (001) MgO, a substrate of industrial relevance and commercial availability [18][19][20][21][22]. While a perovskite substrate with a large lattice constant would provide a more suitable epitaxial template, there are none commercially available close in size. Nonetheless, epitaxial films of reasonable quality were grown on MgO [14]. We further showed that these epitaxial layers can be stabilized by capping with amorphous SiO 2 [14]. This development opens the door to, in this work, finally characterize the electronic properties of Ba 3 In 2 O 6 and answer the question whether it is a high-T c superconductor.
All epitaxial films were grown in a Veeco Gen10 MBE. Epitaxial Ba 3 In 2 O 6 films were grown with a Ba-flux of ≈5.1 × 10 13 Ba/(cm 2 s), and an In 2 O-flux of ≈2.2 × 10 13 In 2 O/(cm 2 s) resulting in a growth rate of 2 nm min -1 . The films were capped with amorphous SiO 2 . Details of epitaxial Ba 3 In 2 O 6 film growth and capping are described in [14]. In brief, the amorphous SiO 2 capping layers were deposited from a molecular beam of SiO (flux of 1 × 10 13 SiO/(cm 2 s)) emanating from an effusion cell containing chunks of amorphous SiO in a background pressure of 5 × 10 -7 Torr of a mixture of ∼10% ozone and 90% oxygen with the substrate temperature at ⩽350 • C. Some samples were prepared on underlying epitaxial SrRuO 3 electrode layers, grown by the means described in [23]. Ce, La, and Sb were evaporated from elemental sources. The SnO, and W 3 O 9 suboxide molecular beams were obtained from heating SnO 2 and WO 3 , respectively [17,24]. All fluxes were roughly estimated by a quartz-crystal microbalance and refined by the subsequent growth of binary oxide calibration layers [25]. The respective flux ranges Φ were: Φ Ce ⩽ 2.5 × 10 12 Ce/(cm 2 s), Φ La ⩽ 1.1 × 10 13 La/(cm 2 s), Φ Sb ⩽ 2.2 × 10 12 Sb/(cm 2 s), Φ SnO ⩽ 1.1 × 10 13 SnO/(cm 2 s), Φ W3O9 ⩽ 0.7 × 10 12 W 3 O 9 /(cm 2 s). (001) MgO substrates were supplied by CrysTec GmbH, and (001) SrTiO 3 substrates were supplied by Shinkosha Co. Ltd and prepared as described by Koster et al [26,27]. Film growth was monitored in situ by reflection high-energy electron diffraction (RHEED). Unless stated otherwise, films were capped by amorphous SiO 2 and grown on (001) MgO substrates.
X-ray diffraction (XRD) measurements were obtained with a Panalytical Empyrean with Cu-K α1 radiation. Cross-sectional scanning transmission electron microscopy (STEM) specimens were prepared using a Thermo Fisher Scientific Helios G4UX focused ion beam (FIB) using standard liftout and thinning methods. High-angle annular dark-field (HAADF) and annular bright field (ABF)-STEM data were acquired using a Thermo Fisher Scientific Spectra 300 X-CFEG operating at 300 kV with a convergence angle of 30 mrad. Inner and outer collection angles for HAADF and ABF imaging were approximately 60 and 200 mrad and 15 and 30 mrad, respectively. Energy dispersive x-ray spectroscopy (EDX) maps were acquired with a Super-X EDX detector, and electron energy loss spectroscopy (EELS) maps were acquired with a Gatan Continuum system equipped with a scintillator CMOS camera. STEM specimens were stored in a vacuum chamber between FIB preparation and imaging to minimize air exposure.
Spectroscopic ellipsometry was performed at room temperature using a single rotating compensator multichannel ellipsometer (M-2000 FI, J.A Woolam, Co. Inc.) [28,29]. Ellipsometric spectra were collected at 50 • and 60 • angles of incidence over a photon energy range of 0.735-5.887 eV and fit via iterative least-square regression using a structural and optical model, which minimizes the unweighted error function or mean square error [30] to extract the complex dielectric function (ε = ε 1 + iε 2 ) spectra and structural properties such as layer thicknesses. Spectra in ε of MgO and amorphous SiO 2 layers were obtained from parametric models fitted to ellipsometric spectra obtained from a bare (001) MgO substrate and a separate amorphous SiO 2 film directly deposited on a (001) MgO substrate, respectively. Spectra in ε of the bare MgO substrate were described with a Sellmeier expression [31] and a constant additive term to ε 1 (ε ∞ ) with a structural model consisting of semi-infinite MgO surface roughness. A surface roughness layer 2.13 ± 0.05 nm thick was obtained from the fit using the Bruggeman effective medium approximation (EMA) [32] consisting of equal fractions of MgO and void to describe spectra in ε for surface roughness. This surface roughness layer thickness was fixed to represent that of the physically mixed interfacial layer for all films deposited on MgO, and spectra in ε for the respective physically mixed layers consist of equal material fractions of MgO and the film. The spectra in ε of the amorphous SiO 2 layer were obtained from a model consisting of the semiinfinite MgO substrate, a 0.5 MgO + 0.5 amorphous SiO 2 EMA layer, the amorphous SiO 2 film, and surface roughness. Spectra in ε of amorphous SiO 2 are represented by a Tauc-Lorentz oscillator [33], Sellmeier expression, and ε ∞ . The amorphous SiO 2 thickness is 54.0 ± 0.3 nm and surface roughness consisting of equal parts amorphous SiO 2 and void is 5.3 ± 0.1 nm thick. A distinct interface layer with a unique set of optical properties common in all samples was also observed between epitaxial thin films and amorphous SiO 2 . The spectra in ε and thickness of this layer were initially obtained using a parametric expression consisting a Lorentz oscillator [31] and ε ∞ , incorporated between the epitaxial thin film and amorphous SiO 2 layer of the undoped Ba 3 In 2 O 6 sample. This spectrum in ε was then used to obtain the thickness of this interfacial layer in the doped epitaxial thin film samples.
The structural model for each epitaxial thin film sample consists of the semi-infinite MgO substrate, a 0.5 MgO + 0.5 epitaxial thin film EMA layer, the epitaxial thin film layer, the interface layer, the amorphous SiO 2 capping layer, the amorphous SiO 2 surface roughness, and air ambient. The surface roughness here was described by an EMA of amorphous SiO 2 and a variable void fraction. All doped and undoped epitaxial thin films exhibit structural and optical anisotropy with the optic axis perpendicular to the sample surface. Spectra in ε were defined separately for electric fields oscillating normal to (in-plane) and parallel to (out-of-plane) the optic axis for each epitaxial thin film. Spectra in ε 2 in each direction for all For the in-plane direction, the transition strength of the critical points at energies >4.5 eV is substantially suppressed for both doped films. For the out-of-plane direction, the Sn-doped epitaxial film has a slight blue shift of the lowest energy critical point with increased transition strength compared to other epitaxial samples whereas the second-lowest critical point is red shifted. For the La-doped sample, both critical point features are located at approximately the same energies as undoped Ba 3 In 2 O 6 , but with differences in transition strength and broadness of the features at higher photon energies. doped and undoped epitaxial films were described by critical point parabolic band (CPPB) oscillators [32] above the lowest energy critical point to describe above gap electronic transitions and an Urbach tail starting at the lowest energy critical point to describe sub-gap absorption [34]. The fit parameters of the CPPB oscillators are critical point resonance energy (E n ), amplitude (A n ), critical point broadening (Γ n ), and the phase projection factor (φ n ). Critical point dimensionality was fixed at µ = 1 for excitonic transitions for simplicity. Spectra in ε 1 were described by Kramers-Kronig integration [31] of the respective ε 2 spectra along with Sellmeier expressions and ε ∞ . For Sellmeier expressions, fit parameters are a resonance energy (E s ) outside the measured spectral range and an amplitude (A s ). Initially, the parametric model for the undoped Ba 3 In 2 O 6 sample was developed and values for the fit parameters were obtained. φ n values of the CPPB oscillators from undoped Ba 3 In 2 O 6 were taken as reference and fixed for the other doped samples corresponding to the critical points at approximately similar resonance energies along each direction. Any other features present in doped samples were modeled by adding CPPB oscillators, the φ n values of which were also fitted. Fit parameters describing spectra in ε and structural parameters are listed in supplementary tables 1-3. After obtaining layer thicknesses from the parametric fit, numerical inversion [35] was then performed to determine spectra in ε for each direction from the measured ellipsometric spectra using fixed thicknesses and parametric spectra in ε for the orthogonal direction and all other layers. Absorption coefficient (α) spectra of each direction of all epitaxial layers was obtained from
where λ is the photon wavelength and k is the extinction coefficient obtained from numerically inverted
The direct optical bandgap in each direction was calculated using Tauc plots [36] of the respective α 2 as a function of photon energy and extrapolating to the photon energy where α 2 = 0. Bandgap energies, lowest energy critical points, Urbach energies, and the range of α extrapolated for the Tauc plots in each direction of each sample are in supplementary tables 1-4; numerically inverted spectra in ε are in figure 2.
Density functional theory adopting the projector augmented wave method [37], as implemented in the Vienna ab initio simulation package [38,39], was used to calculate the electronic structure and the formation energy of point defects. The wave functions were expanded on a plane-wave basis set employing a cut-off energy of 520 eV. The atomic coordinates and the vector lattice were fully optimized when computing bulk properties including band gap. Point defects were studied using the supercell approach using a fixed volume [40]. The F V E Hensling et al different atomic models were generated utilizing the Python Charge Defects Toolkit (PyCDT) [41] using a supercell of 88 atoms. The Brillouin zone was sampled using a Γ only kpoint grid. The exchange-correlation potential was obtained through adopting the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional with an exact-exchange fraction of 0.25 and a screening length of 0.2 Å [42,43]. Spin-polarized calculations were performed, and all supercells were relaxed at fixed volume until the forces on the ions were smaller than 0.1 eV Å -1 . The occupation of the electronic states was determined through the Gaussian smearing method with a smearing width of 0.05 eV. The formation energy of each chargeddefect state was computed as a function of the Fermi level E f as [44,45]
where E tot [X q ] and E bulk tot are the total energies of the defective supercell (for a given defect X in the charge state q) and the bulk energy, respectively. The third term represents the energy needed to exchange atoms with thermodynamic reservoirs, where n i indicates the number of atoms of the species i removed or added to create the defect, and µ i are the corresponding chemical potentials [46]. We computed the phase diagram of Ba-In-O with different possible dopants at 0 K at the same level of theory and determined the limits of the allowed chemical potential of these species. The fourth term represents the energy to exchange electrons with the host material through the electronic chemical potential which is the Fermi energy level E f . Finally, the last term in the equation is a correction accounting for the finite size of the supercell. Here, we used the extended Freysoldt's (Kumagai's) scheme [40,47].
The thermodynamic transition state of defect X from state q 1 to q 2, which corresponds to the energetic level at which a defect captures (or emits) a free carrier, is defined as the position of the Fermi level at which the defect formation energy of both states q 1 and q 2 are equal
The transition level, ϵ (q 1 /q 2 ), relative to the VBM (
Probing an as-grown Ba 3 In 2 O 6 film by a simple four-point measurement quickly reveals its insulating behavior. To understand how insulating Ba 3 In 2 O 6 is, we determine its bandgap by spectroscopic ellipsometry. Supplementary figure 1 shows the spectra in ε of the (a) amorphous SiO 2 capping layer, (b) interface layer, and (c) semi-infinite MgO substrate. Comparison of ε 1 obtained here for MgO matches well with that previously reported [48] with slightly higher values of ε 1 at low photon energies and slightly lower values at high photon energies when compared to the reference spectra. For amorphous SiO 2 , the Tauc-gap is obtained at 2.40 ± 0.02 eV which is lower than the bandgap energies reported for material closer to stoichiometric amorphous SiO 2 [49]. This difference for the molecular-beam deposited amorphous SiO 2 is attributed to oxygen vacancies forming electron trap states which lead to absorption peaks in the 5-7 eV region depending on the extent of oxygen vacancies present in the amorphous film [50].
The direct optical bandgaps obtained for the undoped Ba 3 In 2 O 6 are 2.990 ± 0.006 eV for in-plane and 2.826 ± 0.005 eV for out-of-plane directions as shown in figure 2 (extrapolation in supplementary figure 2). The optical bandgap can be considered the lowest value observed. Hence, the direct optical bandgap of undoped Ba 3 In 2 O 6 is 2.826 ± 0.005 eV. From first-principles defect computations using the HSE functional we determine a direct gap of 2.8 eV and an indirect gap of 2.15 eV (see figure 5(a)). The computed bandgap, thus, agrees well with the experimental value and is within the typical errors between HSE and the experiment [51]. This precision shows that HSE hybrid computations are well suited for studying dopant levels in Ba 3 In 2 O 6 .
Given the insulating behavior in undoped epitaxial Ba 3 In 2 O 6 , the obvious next step in trying to induce (super-) conductivity is to dope the system. A substitution of the A-site cation with La was previously successful for the structural equivalent homologous Sr n+1 Ti n O 3n+1 RP series and for BaSnO 3 [52][53][54]. It, thus, constitutes a reasonable starting point.
We achieve this by successively decreasing the Ba flux and applying a La flux to compensate that decrease. The doping concentrations given in the following, thus, refer to the percentage of flux that was substituted. Figure 3(a) shows the evolution of the (Ba 1-x La x ) 3 In 2 O 6 θ-2θ diffraction pattern with an increase of the La-doping concentration. For 10% La-doping (teal) no secondary phases are notable but a shift of the peaks to higher 2θ values is observed. Increasing the La-concentration further to 20% (purple) results in a further shift of the diffraction angles of the film to higher 2θ values and the formation of a Ba-poor secondary phase becomes barely visible [14]. We, thus, conclude the solubility limit of La in Ba 3 In 2 O 6 to be approximately 20%. The maintenance of excellent structural quality is corroborated by the HAADF STEM image in figure 3(b) of the 20% La-doped epitaxial Ba 3 In 2 O 6 . It is of comparable quality to previously reported undoped films [14]. The shift of the diffraction peaks to higher 2θ values with increasing La-concentration is in good agreement with the substitution of Ba 2+ by La 3+ . As given in table 1, the ionic radius of La 3+ is smaller than that of Ba 2+ [55] resulting in a lattice compression and, thus, a shift of the diffraction peaks to higher 2θ values.
The EELS spectra in figures 4(b) and (c), which correspond to the ADF image in (a), reveal that: (1) As indicated by the θ-2θ diffraction patterns, La substitutes Ba. (2) La solely substitutes for the Ba located on the single layer. This is schematically depicted in figure 4(d).
Despite the ability to substitute significant amounts of Ba 2+ by La 3+ a simple four-point measurement still reveals highly insulating behavior. We, thus, next probe the bandgap for a 20% La-doped epitaxial Ba 3 In 2 O 6 film by spectroscopic ellipsometry. Figure 2 shows the measured bandgap (a) inplane and (b) out-of-plane. The bandgap in the in-plane direction is insignificantly increased when compared to that of the undoped film (3.057 ± 0.005 eV). The out-of-plane bandgap is slightly decreased (2.614 ± 0.006 eV). The extrapolation can be found in supplementary figure 3. As the bandgap is considered the lowest value observed, 20% La-doping results in a lowering of the bandgap by ≈0.21 eV.
To shed light on the lack of conductivity despite the lowered bandgap and the significant incorporation of La 3+ on the Ba 2+ -site, we utilize first-principles defect computations using the HSE functional. Figure 5 shows the formation energy of different neutral (horizontal lines) and charged (positive slope for a positive charge and negative slope for a negative charge with respect to the regular charge of the site) defects in La-doped Ba 3 In 2 O 6 for cation-rich and oxygen-poor conditions (other conditions found in supplementary figure 4). Cation-rich and oxygen-poor conditions should favor n-type doping. We first consider the defect formation energies for different substitution sites for La. Two different formation energies for La 3+ are observed for the two different Ba 2+ -sites to be occupied. A substitution on the rock salt site (brown) shows a higher formation energy than on the single layer site (olive) and is even higher than the substitution of La 3+ for In 3+ (grey). This is in good agreement with the experimental observations. The transition state between the neutral 2+ state and the 3+ state of La on the single layer site is located 0.11 eV below the bandgap. It is thus shallow enough to potentially bring carriers especially when high levels of La substitute to Ba.
The reason for the lack of conductivity can nevertheless be elucidated with these defect computations-through a compensation effect. The fivefold coordination of In leaves an easy interstitial site to fill (see figure 1 black arrows). An oxygen occupation of this interstitial is represented in light blue in figure 5. It is apparent that an occupation of the interstitial with oxygen in the 2-state is energetically favorable in the presence of La 3+ , even for the oxygen-poor conditions assumed. Any potential electron doping is, thus, compensated by the oppositely charged oxygen interstitials. Astonishingly, these oxygen interstitials can be experimentally observed. The ABF in figure 3(c) reveals additional oxygen at the expected positions marked by the blue arrows.
In addition to La, Ce was attempted as a dopant due to its successful utilization in high-T c superconducting cuprates [56]. The behavior of Ce-doped Ba 3 In 2 O 6 was, as far as tested, identical to that of La-doped Ba 3 In 2 O 6 . While La doping of Ba 3 In 2 O 6 did not result in the desired (super-) conductivity, the excellent agreement between first-principles defect computations and experimental observations are notable, especially the observation of oxygen interstitials compensating the La-doping.
While B-site doping in cuprate high-T c superconductors typically rapidly destroys the superconductivity due to the 2D oxygen-copper plane-based conduction mechanism, B-site doping is what led to the discovery of superconductivity in bismuth oxide-based superconductors in the first place [57][58][59]. We can draw inspiration for a promising dopant for the Insite from one of the most relevant oxide conductors, Sn-doped In 2 O 3 (ITO) [60].
We achieve Sn-doping by successively decreasing the In 2 O flux and increasing the SnO flux accordingly. Figure 6(a) shows the θ-2θ-scan of a 20% Sn-doped sample (green) in comparison to the same stoichiometric sample (red) as shown in figure 3(a). 20% Sn-doping results in no additional peaks and the sharp peaks of the undoped sample are preserved. Zooming in on the 0016 peak (figure 6(b)) reveals a peak shift to lower 2θ angles. The maintenance of high structural quality is also confirmed by the HAADF image in figure 6(c). There is no notable difference between the image of 20% Sn-doped Ba 3 In 2 O 6 in figure 6(c) and undoped epitaxial Ba 3 In 2 O 6 films in the literature [14]. Attempting higher percentages of Sn incorporation results in phase separation, while lower percentages are possible, the results from such films are comparable. Here, we focus on 20% Sn-doped samples because the effects described are most apparent for these films.
The peak shift to lower angles observable for 20% Sndoping in figure 6(b) is surprising as we expect Sn to be in its more stable 4+ oxidation state. Considering table 1, Sn 4+ has a smaller ionic radius than In 3+ [55]. Thus, a peak shift in the opposite direction, i.e. to higher angles is expected.
To ensure the incorporation of Sn on the In-site we utilize EDX as Sn and In cannot be distinguished by EELS. Figure 7(a) shows a wider field of view of figure 6(c). Figures 7(b) and (c) show EDX elemental maps with atomic resolution of that same section for In and Ba, respectively. The signal-to-noise ratio in the Sn map in figure 7(d) is too small to draw any conclusions. Nonetheless, a line profile along the blue line in figure 7(a) reveals the Sn substitution site. Figures 7(e) and (f) clearly show that the Snsignal follows that of the In-signal and is opposite to that of the Ba-signal.
Considering the perfect structure revealed by XRD and HAADF and the distribution of Sn by EDX, it is clear that Sn is incorporated on the B-site of the epitaxial Ba 3 In 2 O 6 films. The peak shift to lower 2θ values can, thus, only be explained by a substitution of In 3+ by Sn 2+ . In contrast to the smaller ionic radius of Sn 4+ , the ionic radius of Sn 2+ is larger than that of In 3+ (see table 1) and explains a shift to lower angles in 2θ. For obvious reasons we do not expect electron doping when substituting In 3+ by Sn 2+ . However, p-type doping as observed in cuprates is feasible for such a substitution [61]. Nonetheless, a four-point measurement quickly reveals the absence of any conductivity. Spectroscopic ellipsometry further reveals no significant change in the bandgap: 2.900 ± 0.006 eV (supplementary figure 5). Given the precision of first-principles defect computations using the HSE functional and experimental results, thus far, it is intriguing to probe whether light can be shed on the unusual Sn 2+ state in 20% Sn-doped Ba 3 In 2 O 6 . Figure 8 shows the formation energy of different defects in Sn-doped Ba 3 In 2 O 6 for cation-rich and oxygen-poor conditions (other conditions are found in supplementary figure 6). As for the La defect and as expected, the oxygen interstitial site is also compensating ntype doping as observed experimentally in figure 6(d). The Sn on In defect can be low in energy in agreement with the high concentration of Sn incorporated experimentally in Ba 3 In 2 O 6 . The Sn In (+1/0) is, however, slightly deeper than La Ba (+1/0). Interestingly, when the Fermi level is pushed towards the conduction band -1 defect state is favored and will correspond to a +2 oxidation state for Sn in agreement with the experimental evidence. We note that the Sn In (0/-1) is far from the valence band edge making Sn 2+ not an option for p-type doping.
As other potential B-site dopants, W and Sb were attempted as both are well-known dopants for In 2 O 3 [62,63]. However, it was not possible to incorporate either one successfully. In terms of achieving (super-)conductivity Sn-doping proved equally as futile as La-doping. Yet again the underlying defect chemistry turned out to be intriguing. The usually difficult to stabilize Sn 2+ [64] is readily stabilized when doping Ba 3 In 2 O 6 with Sn.
As neither A-site nor B-site doping with the obvious dopants proved successful, the next step was to turn to different approaches to induce superconductivity.
As discussed in section 3.1 the formation of oxygen interstitials is at least one of the reasons why La-doped Ba 3 In 2 O 6 remains insulating. Superconductivity in nickelates, which was recently discovered, is not observed without prior topotactic reduction of the epitaxial films [65,66]. Thus, we assess whether reduction of the films may induce superconductivity in 20% La-doped Ba 3 In 2 O 6 by either decreasing or completely annihilating the oxygen interstitials. To this end, reductions are performed on such a sample without a capping layer using a thermal atomic hydrogen source [67,68] with the same setup described in [69]. Three successive reductions are performed. Reduction 1: nominal atomic H-flux 2.1 × 10 15 at cm -2 s -1 , temperature 300 • C, time 10 min. Reduction 2: nominal atomic H-flux 2.3 × 10 15 at cm -2 s -1 , temperature 500 • C, time 30 min. Reduction 3: 2.3 × 10 15 at cm -2 s -1 , temperature 750 • C, time 20 min. In this experimental setup the structure of the 20% La-doped Ba 3 In 2 O 6 can be measured in situ using RHEED.
However, no substantial changes to the sample surface were apparent following the three reductions and the original structure was maintained throughout the experiment. Following each of the subsequent reduction attempts, the sample is cooled in vacuum (⩽2 × 10 -9 Torr) to well below 100 • C before brief exposure to air and measurement of the sample resistance. However, no measurable conductivity was detected after any of the reductions (R ⩾ 50 MΩ).
In-situ surface alkali doping has previously successfully been applied to induce superconductivity in several different material systems [70][71][72][73][74]. To characterize the electric properties of the film, we perform in-situ resistivity measurements using a custom-built UHV four-point transport probe with a base pressure of 7 × 10 -11 Torr. The uncapped, undoped film expectedly shows highly insulating behavior, exceeding the measurement limit of our electronics for temperatures below 270 K. While being maintained in UHV at 50 K, we sequentially deposit Cs adatoms in steps of 0.1 ML, up to a total nominal coverage of 2 ML. Unfortunately, no deviation from the low temperature insulating behavior is observed, as the film resistance remains consistently above the measurement impedance limit of our electronics.
Photo-induced superconductivity is a relative new development enabled by advances in laser technology allowing for the generation of precisely shaped strong-field pulses at THz frequencies [75]. Thus far the technique has proven especially successful for superconductivity in cuprates [76,77]. To attempt photo-induced superconductivity in Ba 3 In 2 O 6 the sample is bonded and its resistivity is measured in van-der-Pauw geometry. As expected, the initial resistance is large (⩾100 GΩ). Nevertheless, resonantly pumping the sample with 405 nm 50 mW laser, and an incident diameter of 1.4 mm is attempted. No change of resistance independent of the beam position on the sample is observed (figure 9(a)). We further optically monitored the resistance change by measuring the transient reflectivity. If resonantly pumping changes the electronic occupation, the reflectivity of the sample is expected to change. To this end a 1 kHz, 800 nm, 35 fs pulsed laser is utilized with a β-BaB 2 O 4 crystal to convert the 800 nm pump pulses to 400 nm pulses. We chopped the pump at 500 Hz and use a synchronized lock-in amplifier to measure the change in reflectivity of the sample induced by the pump pulses. The setup is depicted in figure 9(b). Temporal overlap is guaranteed on a highly reactive test sample before probing the Ba 3 In 2 O 6 sample. Using fluences up to 10 mJ cm -2 , no substantial change in reflectivity at or after the temporal overlap is observed. This indicates that the system is not responsive to pumping with 400 nm light.
Liquid ion gating has proven to be a valuable tool for achieving or enhancing superconductivity in various oxides [78][79][80]. Applying it successfully, however, requires a conducting backside electrode. Thus far the epitaxial growth of Ba 3 In 2 O 6 has solely been demonstrated on insulating substrates, i.e. (001) MgO and (001) SrTiO 3 [14]. We, thus, attempt an epitaxial growth of Ba 3 In 2 O 6 on a 30 nm epitaxial film of SrRuO 3 on (001) SrTiO 3 [23]. Attempts to grow epitaxial SrRuO 3 on (001) MgO were unsuccessful. Figure 10 shows the θ-2θ-scan of a 120 nm Ba 3 In 2 O 6 / 30 nm SrRuO 3 / (001) SrTiO 3 sample. The diffraction pattern shows that the bilayer consists of the intended epitaxial phases with no detected impurity phases. The crystalline quality is similar to Ba 3 In 2 O 6 films grown on (001) SrTiO 3, which is impressive considering the high temperatures needed for the growth of the Ba 3 In 2 O 6 layer [14]. Epitaxial Ba 3 In 2 O 6 with a conducting SrRuO 3 backside electrode allows us to probe for superconductivity by liquid-ion gating. For that the films are patterned into 900 × 100 µm 2 Hall bar devices. Hydrated polyethylene glycol and N,N-diethyl-N-methyl-N-(2methoxyethyl)ammoniumbis(trifluoromethylesulfonyl)imide are tried as electrolytes over a wide temperature range with gate voltages of up to ±3 V. In this parameter space no signs of superconductivity were detectable (supplementary figure 7).
In this paper we want to answer two questions. The main question is if Ba 3 In 2 O 6 is a high-T c superconductor. Additionally, as this prediction was made recently by machine learning [7], we also consider this an initial trial of whether the prediction of superconductivity by this new approach is more successful in comparison to more traditional means of predicting materials properties. To this end we probed the material by various experimental and theoretical methods and tried various strategies to induce superconductivity, the results of which were presented in section 3. Here these results are discussed comprehensively.
While we attempted to induce superconductivity through various strategies, the failure of each of them is linked to the same fundamental issue of Ba 3 In 2 O 6 . Ba 3 In 2 O 6 has a comparably wide bandgap of ≈2.8 eV, which is in stark contrast to what is desired for superconductivity [81]. Additionally a wide bandgap makes in general electronic doping more difficult as it increases the chance of deep dopants (>0.2 eV below the conduction band), which do not contribute significant amounts of electrons. However, In-based oxide with large band gaps such as In 2 O 3 can be highly doped. Interestingly, finding a shallow donor is not the central issue for the two dopants discussed in depth here. The issue for both is linked to the crystal structure of Ba 3 In 2 O 6 and to the 5-fold coordination of In (see figure 1). This leaves a site that can be readily filled by oxygen interstitials, which compensate electron doping. 5-fold coordinated In 3+ is rare in oxides and In 3+ favors in the vast majority of the case an octahedral 6-fold coordination [82]. We observe these oxygen interstitials experimentally. Likely, oxygen interstitials will be equally problematic for other electron doping attempts. The 5-fold coordination of In is also a probable explanation for the stabilization of the lower and less stable 2+ oxidation state of Sn through the lone-pair effect [83]. This potentially rules out doping by other elements, for which the lower oxidation state can be stabilized in the same manner [84], and for which the lower oxidation state is not a suitable electron donor. They may constitute a promising approach for p-type doping if the resulting defect states are less deep.
Considering these findings, inducing superconductivity in Ba 3 In 2 O 6 seems unlikely as the formation of the oxygen interstitial will always compensate the donated electrons. A few more dopants explored computationally: F O and Zr In show respectively a shallow donor and a deep donor (as shown in supplementary figure 8). F O appears, however, not more shallow than La Ba or In Sn . The oxygen interstitial compensation problem will only be addressed if very reducing conditions are applied which might be difficult while keeping the Ba 3 In 2 O 6 phase. Our computations indicate that this could be achieved only if going to non-equilibrium conditions.
The most promising route may be to induce p-type conductivity even though our results indicate that it will be difficult to find a shallow defect state. The isostructural known high-T c superconductor La 2 SrCu 2 O 6 is also based on p-type conductivity and here oxygen interstitials add holes. Unfortunately, the large bandgap of Ba 3 In 2 O 6 makes it an insulator and the energy level of oxygen interstitials are too deep to induce ptype conductivity. Ba 3 In 2 O 6 is, of course, a very isolated case to consider for a superconductor predicted by machine learning. For this specific case our verdict is that machine learning is not more successful than the traditional means of predicting materials properties for identifying new superconductors. Nonetheless, utilizing machine learning to predict high-T c superconductors is still a comparably new approach and is constantly being improved [8,[85][86][87]. Our work indicates that bringing factors that are readily computable with first-principles computations such as band gap and the energetics of doping into these superconductor predictions would be helpful in the selection of the most promising systems in which high T c superconductivity might be experimentally realized. It may well be that Ba 3 In 2 O 6 is a potential theoretical superconductor but that the carrier level needed can never be achieved. At this point novel superconducting materials (and other materials of interest) are being suggested at a speed greatly exceeding the ability of experimentalists to synthesize and thoroughly probe these materials. It will be exciting to see if novel trends in the epitaxial deposition of materials will help close this speed gap between theoretical prediction and experimental validation (or refutation) to some extent [16].
Already in the 1980s Ba 3 In 2 O 6 was suspected of being a high-T c superconductor due to its structure [2]. More recently this suspicion was raised again by machine learning predictions [7]. Unfortunately, the hygroscopic behavior of Ba 3 In 2 O 6 previously impeded its thorough characterization. Utilizing the recent progress in epitaxially growing and stabilizing Ba 3 In 2 O 6 [14] we are able to probe the electronic structure of Ba 3 In 2 O 6 and compare it to first principles calculations.
We find Ba 3 In 2 O 6 to be highly insulating, which is not surprising given that we determine its bandgap to be relatively wide (experimentally ≈ 2.8 eV, first principles ≈ 2.15 eV).
The wide bandgap makes doping difficult due to the increased probability of deep defects. Additionally, we find the 5-fold coordination of In to result in interesting effects that regrettably also counter electron dopability. The In 5-fold coordination leaves an easy site for oxygen interstitials to form, which are also observed experimentally by ABF-STEM. Oxygen interstitials compensate the electron doping by, e.g. La. The 5-fold coordinated In site also stabilizes the lower 2+ oxidation state of Sn as a dopant through the lone pair effect. Other strategies of inducing superconductivity such as alkali surface doping, optical pumping, and liquid ion gating prove equally futile. At this point we conclude that it is highly unlikely, but not necessarily impossible, to induce superconductivity in Ba 3 In 2 O 6 .
The ability of Ba 3 In 2 O 6 to accommodate significant concentrations of oxygen interstitials, however, makes it an interesting material for catalysis applications. In fact, it was recently predicted as a promising photocatalyst for solar-tohydrogen conversion [88].
This case study also provides valuable feedback for new machine learning strategies. Combining machine learning results with easily computable properties such as band gap and doping may yield more reliable results-making the prediction of high-T c superconductors tangible.