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Yuuki Yasui, Katsuyuki Matsunaga, [Keisuke Sagisaka](https://orcid.org/0000-0002-5089-4271), Yoshiaki Sugimoto

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[Element-selective structural visualization for the oxygen-induced surface of Nb⁡(110)](https://mdr.nims.go.jp/datasets/df12d76c-ef80-4785-aa74-f4c7302f44b4)

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Element-selective structural visualization for the oxygen-induced surface of ${\rm Nb}(110 )$PHYSICAL REVIEW B 109, 195417 (2024)Element-selective structural visualization for the oxygen-induced surface of Nb(110)Yuuki Yasui ,1,* Katsuyuki Matsunaga ,2,3 Keisuke Sagisaka ,4 and Yoshiaki Sugimoto 1,†1Department of Advanced Materials Science, The University of Tokyo, Kashiwa, Chiba 277-8561, Japan2Department of Materials Physics, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan3Nanostructures Research Laboratory, Japan Fine Ceramics Center, 2-4-1 Mutsuno, Atsuta, Nagoya 456-8587, Japan4Center for Basic Research on Materials, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan(Received 7 September 2023; revised 2 February 2024; accepted 9 April 2024; published 8 May 2024)The highest superconducting transition temperature in Nb among elemental materials facilitates applicationsof superconducting junctions. Nonetheless, its surface forms self-organized oxide structures, which hindersthe preparation of well-defined interfaces. We investigated the atomic structure of oxygen-induced Nb(110)surfaces, aiming to define the substrates for such interfaces. The atomic force microscopy and scanning tunnelingmicroscopy measurements visualized two rows of apparently low-lying Nb and three rows of O between Nbchains. An optimized model structure is proposed based on density-functional theory calculations. Analysis ofthe Bader charge and the density of states clarified how the atoms appear in the microscopies.DOI: 10.1103/PhysRevB.109.195417I. INTRODUCTIONNiobium has the highest superconducting transition tem-perature among elemental metals without the application ofhigh pressure, which promotes applications such as tunnelingjunctions between a normal metal and a superconductor [1–3]and Josephson junctions between superconductors [4–8].Though their interfacial conditions are crucial to determinethe junction properties [9,10], the affinity of Nb to oxygenburdens the preparation of well-defined interfaces.The surface of Nb is covered with oxide layers even inultra-high vacuum (UHV) conditions. The oxide layer cannotbe removed with standard cleaning methods [11], because Oatoms segregate from the bulk to the surface at annealing [12].Recently, methods to prepare clean surfaces were reported.Clean surfaces of Nb(110) are achieved by annealing in UHVat 2410 ◦C, that is, only 70 ◦C below its melting point [12].Hydrogen treatments and additional annealing at 1000 ◦C arerequired for clean Nb(111) surfaces [13]. Such sophisticatedpreparation methods, however, may not be preferred for thedevice fabrication process. We could instead make use of theoxidized surface of Nb for more practical applications byresolving its properties in detail.The structure of the oxide surface of Nb(110) has beenintensively studied. When the crystal is annealed below145 ◦C in an UHV condition, Nb2O5 dominates in the sur-face oxide layer, and NbO2 dominates below 300 ◦C [14,15].NbO is formed with annealing at even higher tempera-tures. In the range of 927 ◦C–1927 ◦C, no significant changewas detected in the surface NbO structure [16]. Scan-ning tunneling microscopy (STM) observations reported Nbatoms form a quasiperiodic chain structure and are referred*yasui@k.u-tokyo.ac.jp†ysugimoto@k.u-tokyo.ac.jpto as Nb∗ chains [12,16–23]. Several models have beenproposed so far [16,23,24] based on x-ray photoelectron spec-troscopy (XPS) [21,24–27], x-ray reflectivity [15], low-energyelectron diffraction [11,14,28,29], Auger electron spec-troscopy [14,29], and electron energy loss spectroscopy [14].These models are constructed by combining the bulk Nb(110)and the bulk NbO(111) structures and by putting Nb adatomsto reproduce the Nb∗ chain structure. A more recent investi-gation raised a question on the Nb∗ adatom structure [30].Here, we performed noncontact atomic force microscopy(AFM) on NbO/Nb(110) surfaces. The AFM technique issuited for structural identification [31–34]. Nb and O atomsare visualized independently by using different tip states, andthe surface atomic arrangements are clarified. A comparisonof AFM and STM shows the relative position of Nb andO atoms. A surface model is proposed based on density-functional-theory (DFT) calculations, which is consistent withthe AFM and STM observations. The Bader charge and thedensity of states (DOS) analysis further explain why AFM andSTM visualize atoms differently and why the apparent heightdoes not necessarily represent the atomic height.II. METHODSNb single crystals with a purity of better than 99.99% werepurchased from MaTecK. Several cycles of Ar+ ion sputtering(1.3 × 10−3 Pa, 4 keV, 20 min) and annealing at 1200 ◦C werecarried out in UHV chambers (∼108 Pa) to get rid of impuri-ties. Annealing at 1200 ◦C for 1 min in UHV conditions makesthe oxygen-induced surface structure.AFM measurements at room temperature were performedwith a Unisoku custom-built AFM/STM system [35]. Si can-tilevers with and without a Pt coating were used after cleaningwith Ar+ ion sputtering. Since the tips often contact withthe sample surfaces, it is assumed that the tips are coveredwith materials from the sample surfaces. The resonance fre-2469-9950/2024/109(19)/195417(8) 195417-1 ©2024 American Physical Societyhttps://orcid.org/0000-0001-5774-0147https://orcid.org/0000-0002-7427-6582https://orcid.org/0000-0002-5089-4271https://orcid.org/0000-0003-3346-1586https://crossmark.crossref.org/dialog/?doi=10.1103/PhysRevB.109.195417&domain=pdf&date_stamp=2024-05-08https://doi.org/10.1103/PhysRevB.109.195417YASUI, MATSUNAGA, SAGISAKA, AND SUGIMOTO PHYSICAL REVIEW B 109, 195417 (2024)quencies of the cantilevers with and without a Pt coating arearound 167 kHz and 157 kHz, and the spring constants arearound 38 N/m and 30 N/m, respectively. The oscillationof the cantilever was monitored with an optical interferom-eter. Measurements at helium temperature were performedwith a Unisoku custom-built scanning probe microscopewith the Kolibri sensor [36]. The resonance frequency isaround 1 MHz, and the effective spring constant is around1.3 MN/m. All the measurements were operated with thefrequency-modulation mode. For the constant-frequency-shifttopographic images, the sample bias voltage was adjusted tocompensate for the contact potential difference between thetip and the sample. The dI/dV conductance was measuredwith a standard lock-in technique.DFT calculations were carried out with the projectoraugmented wave (PAW) method involved in the VASP pro-gram [37,38]. The generalized gradient approximation (GGA)and the exchange-correlation functional parameterized byPerdew, Burke, and Ernzerhof (PBE) [39] were used. In thePAW potentials, 4p, 4d , and 5s orbitals for niobium and 2s and2p orbitals for oxygen were considered as valence electrons.Electronic wave functions were expanded by plane waves upto a cutoff energy of 400 eV. Atomic positions in the bcc-Nb unit cell and surface supercells (described below) wereoptimized until their forces became less than 0.1 eV/nm.For calculations of the Nb(110) surface, periodic super-cells containing atomic Nb(110) slabs with a vacuum layerwere initially constructed. A thickness of the vacuum layerwas set at 1 nm for the structural optimization and the DOScalculation, so as to prevent any spurious interactions be-tween the surfaces at both ends of the slab. In order to obtainstructurally optimized Nb(110) surfaces, Nb(110) slabs wereinitially cut out of bulk Nb. In the structural optimization,Nb atoms in the two atomic layers from one slab surfacewere fixed and all other atoms were relaxed with the sameconvergence criterion as that for bulk, described above. Fromcalculations of the different-sized Nb(110) slabs, the slabthickness was determined to be eleven atomic layers so thatthe Nb(110) interlayer distance between the central Nb layersmatches the bulk value. In this case, Brillouin zone inte-gration was performed with a �-centered 5 × 5 × 1 k-pointmesh [12].As can be seen in the Results section, a periodic Nb∗chain structure was observed. According to the distancebetween the Nb∗ chains (around 1.1 nm), different surfacesupercells were generated by a four-times extension of theminimum unit of Nb(110) toward the [111] direction (seeFig. 4). In this case, a 5 × 1 × 1 mesh was used for k-pointsampling.Additional O atoms in the surface layer were also con-sidered. O atoms were introduced at half of the hollow sitesof Nb atoms just below the topmost Nb layer because thethickness of the surface oxide layer was estimated to be 1.4monolayers [16], 1–2 atomic layers [26], or 500 pm [23,24].From the total energies of the O-induced supercells with dif-ferent O configurations as a function of the oxygen chemicalpotential, the most stable O configuration was determined.Removal of Nb and O atoms from the extended supercellswas also assumed to validate the observations, which will bediscussed later.(a) (b)10 nm -200 200z (pm)-60 60z (pm)2 nmFIG. 1. Constant-current STM topographic images taken at tem-perature T = 5 K. (a) A large field-of-view image. The sample biasvoltage Vs = −10 mV, current setpoint Is = −10 pA, and oscillationamplitude A = 90 pm. (b) A magnified image with resolution of theNb∗ chain atoms. Vs = −10 mV, Is = −100 pA, A = 0 pm.The STM image and conductance spectrum are simulatedbased on the Tersoff-Hamann method [40,41] implemented inthe BSKAN code [42]. The cut-off energy is 400 eV, thicknessof the vacuum in the slab is 1.5 nm, the number of k points is21 × 21 × 1, and the sample bias voltage is −10 mV.III. RESULTSThe surface morphology was checked with STM tocompare the sample with the previous reports. A large field-of-view image shows step and terrace structures [Fig. 1(a)].The angle between the two steps is around 110◦, resultingfrom the 〈111〉 directions of the (110) surface. The Nb∗ chainstructures run almost parallel to the step edges and form do-mains for both directions of the step edges.The Nb∗ chain atoms are resolved in a magnified view asin Fig. 1(b). The chain is constituted of around ten atoms witha chain-to-chain distance of 1.1 nm. In our STM observations,atoms were observed only in the chain structure, and atomswere not clearly observed between the chains. The chainstructure was observed for any bias voltage within ±1 V.These features are consistent with the previously reportedSTM observations [12,16–19,21–23].AFM observations give further information on the sur-face atomic structure. Two modes of atomic resolutions wereobtained depending on the tip conditions. In Fig. 2(a) aquasiperiodic chain structure is observed, which is consti-tuted of around ten atoms. The distance between the chainsis around 1 nm. These values are similar to the Nb∗ chainstructure observed in STM, and thus we consider that Nbatoms are observed in this imaging mode. Furthermore, atomsbetween the chains are resolved as in the magnified view inFig. 2(b). Interestingly, an additional two rows of Nb atomsare located at apparently low positions. These atoms havenot been revealed in the STM measurements. A line profilehighlights its periodicity: one Nb∗ row and two low-lyingNb rows [Fig. 2(c)]. The difference in the apparent heightbetween the Nb∗ chain and the lower Nb is merely 20 pm,which suggests that the lower Nb atoms are not located in the195417-2ELEMENT-SELECTIVE STRUCTURAL VISUALIZATION … PHYSICAL REVIEW B 109, 195417 (2024)-40-2002040Height (pm)3210Distance (nm)-60-3003060Height (pm)3210Distance (nm)(e)(c) (f)(a) (d)(b)Nb modeNb modeO modeO mode-30 30z (pm)1 nm1 nm -30 30z (pm)2 nm -60 60z (pm)-80 80z (pm)0.5 nmFIG. 2. Constant-frequency-shift AFM topographic imagestaken at T ∼ 300 K. (a) Nb∗ chain structure in Nb mode imaging.Vs = 300 mV, the frequency-shift setpoint � fs = −1.7 Hz,A = 20 nm. (b) A magnified view with atomic resolution toapparently low-lying Nb atoms. Vs = 100 mV, � fs = −8.0 Hz,A = 20 nm. (c) A line profile of (b). (d) A quasiperiodic structure inO-mode imaging. Vs = 900 mV, � fs = −217 Hz, A = 5 nm.(e) A magnified view, where three O rows are resolved.Vs = 900 mV, � fs = −227 Hz, A = 5 nm. (f) A line profile of(e). The bias voltages are adjusted to compensate for the contactpotential difference between the tips and the samples.underlying layer. We refer to these apparently low-lying Nbatoms as Nb-1 and Nb-2.For a different imaging mode, another structure was visual-ized at a different area of the sample as in Figs. 2(d)–2(f). Weconsider that the other elements, namely, O atoms, are visu-alized. In this visualization mode, the quasiperiodicity is con-sistent with that for the Nb mode: around 10 atoms in lengthand 1 nm in width. Importantly, three rows of O form a unit ofquasi-repetition, and each row has nearly the same numberof atoms. The height in these rows appears within 30 pm,suggesting these rows are located nearly in the same plane.O mode Nb sensitiveNb mode Nb sensitive(a)(e) (f)(b)O mode Nb sensitive(c) (d)3 nm -20 20z (pm)-8.5 -6.5Δf (Hz)2 nm 2 nm 0 18I (pA)1 nm -18.5 -14.5Δf (Hz)0 70I (pA)1 nm3 nm -150 150z (pm)FIG. 3. Correspondence of AFM and STM visualized atomicpositions. (a) A frequency-shift image during a constant-height scan.The image is low-pass Fourier filtered. (b) Simultaneously obtainedcurrent image with Fourier low-pass filter. (c) A raw frequency-shift image at a constant-height scan. (d) Simultaneously obtainedcurrent image with low-pass Fourier filter. Yellow lines highlightthe positions of Nb∗ chains in current images, and the same pixelsare also marked in the frequency-shift images. For (a)–(d), Vs ∼1 µV, A = 90 pm, T = 5 K. (e) Constant-frequency-shift AFM to-pographic image. Vs = −200 mV, � fs = −5.1 Hz, A = 20 nm, T ∼300 K. (f) Constant-current topographic image in the same field ofview. Vs = −2000 mV, Is = −30 pA, A = 20 nm, T ∼ 300 K. Impu-rities are marked with yellow arrows for references to the position.Such element-selective imaging is reported in other mate-rials such as CaF2 [43–45], TiO2 [46–48], MgAl2O4 [49,50],oxygen-terminated Cu [51], and SrTiO3 [52]. This is inter-195417-3YASUI, MATSUNAGA, SAGISAKA, AND SUGIMOTO PHYSICAL REVIEW B 109, 195417 (2024)preted as follows. The constant-frequency-shift feedback ismaintained in the attractive force region. Each element in thesample is charged in opposite polarity due to the difference inthe electronegativity. When the electrostatic force dominatesthe tip-sample interaction, one of the elements can providean attractive force depending on the charge state of the tip.Therefore, the tip termination polarity determines which ele-ment is to be detected. We consider that a similar mechanismis applied to the NbO/Nb(110) surfaces.Relative positions of Nb and O atoms are determinedby simultaneous measurements of AFM and STM. Thefrequency-shift images visualize the O atoms [Figs. 3(a)and 3(c)], while the current images represent the positionof Nb∗ chain atoms [Figs. 3(b) and 3(d)]. Positions of Nb∗chains are marked with yellow lines in Figs. 3(b) and 3(d).Corresponding pixels are also marked to compare in Figs. 3(a)and 3(c). The Nb∗ chains appear in the valley between thebunches of three O rows. There is a slight shift (∼70 pm) awayfrom the center of the valley.Comparison in the Nb mode is shown in Figs. 3(e) and 3(f).These images are taken separately in the same field of view.The positions can be compared by referring to impuritiesmarked with arrows. These impurities are located in betweenthe chains for both AFM and STM images. Thus, the chainstructure in Nb-mode AFM detects the same Nb∗ chains seenin STM.To summarize the AFM observations, two rows of appar-ently low-lying Nb atoms and three rows of O atoms are foundbetween the Nb∗ chains. In previous studies, the surface oxidestructure had been constructed by a combination of the bulkNb(110) and the bulk NbO(111). However, the ideal surfaceof NbO(111) cannot explain the present AFM observationsfor the following reasons. Firstly, the bulk NbO(111) structureexpects three Nb rows between Nb∗ chains. Secondly, thenumber of O atoms in each row is not uniform due to thekagome structure of NbO(111). Thirdly, the Nb∗ chains wereplaced on top of the NbO layer as adatoms, but the protrusionmay be too high to explain the observation.IV. DISCUSSIONA simple combination of the bulk Nb(110) and the bulkNbO(111) may not be sufficient for a more realistic model.To get further insight into the O-induced surface structure ofNb(110), we performed DFT calculations of the O-inducedNb(110) supercells extended by four times toward the [111]direction (see Sec. II). The initial states contain O atomsstuffed in the surface layer of Nb(110). Since such a surfaceis subjected to compressive stress due to oxygen inclusion, re-moval of pairs of Nb and O in the surface layer was assumed.All possible combinations of removal were calculated, and themost stable atomic structure obtained after structure optimiza-tion is shown in Fig. 4. The calculated structure captures thebasic periodicity in the AFM observations. The Nb∗ chains(colored in blue) run along the [111] direction, where thedistance between the chains is 1.17 nm. Two Nb rows (coloredin green) and three O rows (colored in red and orange) arelocated between the Nb∗ chains. Nb atoms are aligned almostparallel to the [111] direction, and O atoms are aligned close[-1 1 1][-1 1 -1][1 1 0][1 -1 2]Nb-1 Nb-2Nb* O-1 O-3O-2(a)(b)FIG. 4. A DFT-optimized model structure. (a) Top view. The sec-ond Nb layer is depicted only on the left-hand-side column. (b) Sideview. Blue, Nb∗ chain atoms; green, apparently low-positioned Nbatoms; gray, bulk Nb atoms; red/orange, O atoms. The parallelogramin gray depicts the cell for the calculation.(a)(c)(e)(b)(f)(d)FIG. 5. Comparison of the experimental observations and themodel. (a) STM topographic image [Fig. 1(b)]. (b) Simulated STMimage for Vs = −10 mV. (c) AFM topographic image in Nb mode[Fig. 2(b)]. (d) AFM topographic image in O mode [Fig. 2(e)]. (e),(f) AFM line profiles [Figs. 2(c) and 2(f)]. Images in (c) and (d) areprocessed with Fourier low-pass filters and affine corrections. The zdirection of the AFM line profiles are scaled by factors of (e) 5 and(f) 15.195417-4ELEMENT-SELECTIVE STRUCTURAL VISUALIZATION … PHYSICAL REVIEW B 109, 195417 (2024)TABLE I. Parameters obtained for the present structural model.Nb∗ Nb-1 Nb-2 O-1 O-2 O-3Bader charge +0.54 +1.41 +0.74 –1.22 –1.17 –1.24DOS at EF 0.96 0.56 0.73 0.06 0.07 0.08Relative height (pm) 0 51 35 37 151 –3to the [112] direction. A comparison of the model and AFMimages is illustrated in Figs. 5(c) and 5(d).The height profile of the model can be compared with theline profiles in AFM, as shown in Figs. 5(e) and 5(f). In theAFM observation, three O rows appear in similar heights.In contrast, the model expects that O-2 locates 114 pm and154 pm higher than O-1 and O-3, respectively. AFM to-pographic images detect the charge state, and hence theBader-charge analysis [53], which approximates the chargestate of each atom, helps to interpret the observations. Wefound that O-2 has a smaller charge than O-1 and O-3(Table I). That reduces the height difference in AFM feedback.On the other hand, the value of the Bader charge alone cannotexplain why the Nb∗ atoms appear higher in the AFM. Wespeculate that the Nb∗ atoms are exposed to the vacuum, whileNb-1 and Nb-2 atoms are partly covered with O atoms. Thus,the charge of Nb-1 and Nb-2 is screened with surrounding Oatoms, leaving the unscreened Nb∗ atoms apparently high.Let us compare the model with the STM observations.STM topographic images detect the DOS integrated from theFermi level EF to Vs, on top of atomic corrugations. Hence, theDOS at EF simulates how atoms appear in STM topographicimages. We calculated the DOS for the present structure asshown in Table I. The Nb∗ has larger DOS than those of Nb-1and Nb-2, and thus the Nb∗ chains appear higher in the STMmeasurements. Besides, the low DOS of O atoms explainswhy O atoms are not detected with STM.The present model is further supported by comparing theobserved STM topographic image with a simulated STM im-age as in Figs. 5(a) and 5(b). Nb∗ appears most strongly in thesimulated image, as expected from the large DOS at EF. Nb-2appears very weakly in the simulated image. This rationalizes1050DOS (arb. units)-10 -5 0 5 10E - EF (eV) Nb in surface NbO O in surface NbO(a)1050DOS (arb. units) Nb(110) surface NbO surface(b)FIG. 6. DOS calculated for the present model. (a) Effect of thesurface oxidization. (b) Contribution from the surface Nb and Oatoms.150100500dI/dV (pS)-1 0 1V (V)420Conductance(arb. units)-1 0 1Sample bias (V)(a) (b)FIG. 7. (a) A measured dI/dV curve. Vs = −1 V, Is = −100 pA,bias modulation amplitude Vmod = 25 mV, bias modulation fre-quency fbias = 617.3 Hz, A = 0 pm, and T = 5 K. (b) A simulatedconductance curve at 400 pm above Nb∗.the weak signal between Nb∗ chains. Nb-1 hardly appears inthe simulation, as its low DOS implies.We calculated the DOS for the present oxide surface model(Fig. 6). The peak structure at −450 mV in the clean Nb(110)surface originates from the Nb 4dz2 orbital. The peak is sup-pressed in the oxide surface. Figure 6(b) shows the projectedDOS for each element at the surface. The DOS near EFis mostly contributed from Nb 4d orbitals. O 2p orbitalsappear mainly from −7 eV to − 4 eV. Figure 7(a) shows ameasured tunneling conductance spectrum, which is approxi-mately proportional to the DOS. The observed dI/dV curvereproduces the previous report [30], where a characteristicpeak is obtained at −450 mV. The peak is reproduced with asimulation of tunneling conductance at 400 pm above the Nb∗atom [Fig. 7(b)]. The consistency further supports the presentmodel.In the present model, the quasiperiodic structure includingthe finite length of Nb∗ chains is not obtained because ofthe limitation in the cell size for the calculation. We considerthat the relaxation from the compressive strain coming fromextra O inclusion causes the quasiperiodic structure, similarto the case in N-adsorbed Cu(001) surfaces [54]. This mayalso cause the rotation of Nb∗ chains by 5◦ with respect tothe [111] direction as reported in Ref. [23]. This also limitsthe discussion of the global symmetry of the surface, andhence we cannot make a conclusion about the Nishiyama-Wasserman epitaxial relationship proposed in previousreports [18,22].We also discuss the present model by referring to previousreports. Photoelectron spectroscopy studies estimate the ratioof Nb and O is close to 1:1 in the topmost layer [16,19]. Thepresent model holds this condition. An XPS experiment con-cluded that there are two oxygen chemical states, chemisorbedoxygen and oxygen entering into NbOx clusters, with the ratioof 2 : 1 [21]. We speculate that the O atoms observed in AFMbelong to the chemisorbed state and that sparse O inclusionsnear the surface might belong to the other oxygen state.V. CONCLUSIONUsing the noncontact AFM technique, elements were se-lectively imaged in atomic resolution in the oxygen-inducedsurface structure of Nb(110). This suggests that two rows ofNb atoms and three rows of O atoms are located between the195417-5YASUI, MATSUNAGA, SAGISAKA, AND SUGIMOTO PHYSICAL REVIEW B 109, 195417 (2024)(a) (b) (c)FIG. 8. DFT-optimized structural models from different initial states. The total energy for the model in Fig. 4 is −458.19 eV. The totalenergies are (a) −458.07 eV, (b) −458.16 eV, and (c) −458.11 eV.Nb∗ chains. Based on DFT calculations, a surface model isproposed. The Bader-charge and the DOS calculations sim-ulate why the apparent height in AFM and STM does notnecessarily represent the atomic height. The present resultsmay pave a way for using the self-organized oxide surface ofNb as well-defined substrates for superconducting junctions.ACKNOWLEDGMENTSThe authors acknowledge D. Katsube and Y. Adachifor discussion. This work was supported by Grant-in-AidJSPS KAKENHI Grants No. 22H04496, No. 20H05849, No.21K18867, No. 22H05448, and No. 22H01950, by the JSTFOREST Program (Grant No. JPMJFR203J, Japan), by theAsahi Glass Foundation, and by the Murata Science Founda-tion.APPENDIXFigure 8 gives references for higher energy states obtainedfrom different initial states. Figure 9 presents a conductancecurve representing the superconducting gap observed on theoxide surface.2001000dI/dV (nS)-10 0 10V (mV)FIG. 9. A dI/dV spectrum showing the superconducting gapobserved on the oxide surface. Vs = −10 mV, Is = −1 nA, Vmod =0.1 mV, fbias = 617.3 Hz, A = 0 pm, T = 5 K, and external mag-netic field μ0H = 50 mT.[1] I. Giaever, Energy gap in superconductors measured by electrontunneling, Phys. Rev. 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