Introduction

Since the level of correlation effects between neighbouring electrons in the outermost 3d orbitals of vanadium ions differs depending on the crystal structure, the polymorphs of vanadium dioxide (VO2) show a wide range of electrical properties, acting as an insulator in monoclinic VO2(M1) and tetragonal VO2(A), a semiconductor in monoclinic VO2(B), and a conductor in tetragonal VO2(R)1,2,3. Therefore, VO2 polymorphs have been extensively studied for a range of interesting applications. VO2(M1) and VO2(R) have attracted wide interest for electronic devices since they show heat-, light-, electric field-, and chemical-induced reversible metal-insulator transitions near room temperature (TMI = 340 K in bulk)4,5,6,7. On the other hand, VO2(A) and VO2(B) have been mainly used for energy applications, including redox-flow batteries, ion batteries, solid oxide fuel cells, hydrogen storage devices, and catalysts8. Compared to the many studies on electronic devices using VO2(M1) and VO2(R), however, the scarcity of published methods to tune the electrical properties of correlated VO2(A) and VO2(B) has limited their potential applications in electrical devices.

Several methods have been suggested for tailoring the correlation effects of VO2(M1) since broad tunability of electrical properties is valuable for electrical devices. In addition to metallization induced by pressure application9, hydrogen doping10,11, or ionic liquid gating12,13, cation doping has been widely used as a method with high efficacy. Chromium doping can result in transition of the dimerization of V−V chains in the VO2(M1) phase into partial dimerization in the VO2(M2) phase14. Substituting a small amount of tungsten for vanadium in VO2(M1) causes notable changes in its electrical property15. For convenience, V1−xWxO2 will be used herein to denote VO2 with tungsten doping of x × 100%. As x increases, the resistivity of V1−xWxO2 films decreases by several orders of magnitude, and TMI also rapidly decreases at a rate of dTMI/dx = 2,100–2,800 K. For 0.08 < x < 0.09, the V1−xWxO2 epitaxial films have a metallic ground state for a wide temperature range of 50–400 K. When x is increased beyond this range, V1−xWxO2 reenters its insulating state.

Exploring tuning knobs of the electrical properties of VO2(A) and VO2(B) would not only enable their usage in electrical devices but also promote rich functionalities for energy devices. Motivated by research on correlated VO2(M1), here, we investigate the effects of tungsten doping on the resistivity of correlated VO2(A) and VO2(B). We organize this paper as follows: first, we describe how, as the tungsten concentration increases, chemical strain increases the lattice parameters of both VO2(A) and VO2(B). Next, we find that tungsten doping is effective for tuning the resistivity of correlated VO2(A) and VO2(B) over a broad range. For x < 0.1–0.15, VO2(A), an insulator in the pure phase, exhibits a monotonic decrease in resistivity of four orders of magnitude with increasing x. VO2(B), a semiconductor in the pure phase, shows a monotonic increase in the resistivity of two orders of magnitude. Finally, to understand these opposite dependences, we explore the systematic evolution of the electronic structures and vanadium oxidation states by performing spectroscopic ellipsometry and X-ray photoemission spectroscopy (XPS), respectively.

Chemical tensile strain in VO2(A) and VO2(B) induced by tungsten doping

Using pulsed laser epitaxy, we grew (100)-oriented V1−xWxO2(A) and (001)-oriented V1−xWxO2(B) epitaxial films on (011)SrTiO3 and (001)LaAlO3, respectively, for x from 0 to 0.25. We provided details of the deposition conditions in our previous reports2,3,16,17,18 as well as in the Methods section. Figure 1a,b show the X-ray diffraction (XRD) θ − 2θ scans of V1−xWxO2(A) and V1−xWxO2(B), respectively (see Fig. S1 for XRD θ − 2θ scans in a wider 2θ range). We clearly observed (600)VO2(A) diffraction peaks for x < 0.1 and (002)VO2(B) diffraction peaks for x < 0.15, indicating preservation of the crystal structures for x < xc ≈ 0.1–0.15. However, for x > xc, these XRD intensities significantly decreased, and some peaks disappeared, indicating that heavy doping of tungsten could lower the quality of our epitaxial VO2(A) and VO2(B) films [we ruled out possible effects of film thickness on the reduction of the XRD intensities since the X-ray reflectivity results (Fig. S2) revealed an almost invariant thickness of ~100 nm with tungsten doping.]. This observation is different from the seemingly preserved crystallinity up to x = 0.33 in V1−xWxO2 epitaxial films grown on (001)-oriented TiO215, which might be due to a strong strain effect between isostructural VO2(R) and TiO2. Hereafter, we will mainly focus on the resistivity of V1−xWxO2 (x < xc) to avoid unwanted effects from film deterioration.

Figure 1
figure 1

X-ray diffraction (XRD) θ‒2θ scans for (a) V1−xWxO2(A) (x ≤ 0.25) epitaxial films grown on (011)-oriented SrTiO3 and (b) V1−xWxO2(B) epitaxial films grown on (001)-oriented LaAlO3. The diffraction peaks of the films, highlighted by asterisks (*), are preserved for x < xc ≈ 0.1–0.15, but these intensities become weaker for x > xc due to film deterioration. With increasing tungsten concentration, V1−xWxO2(A) and V1−xWxO2(B) show a shift in their diffraction peaks towards lower 2θ values. (c) Tungsten concentration dependence of the lattice parameters of V1‒xWxO2(A) and V1‒xWxO2(B). We compare our results to the lattice parameters of V1‒xWxO2 epitaxial films grown on (001)-oriented TiO2 (light grey15 and grey20 triangles). The lattice parameters show monotonic increases with increasing tungsten concentration. The region in graded yellow indicates preservation of the crystal structures when x < xc.

Substitution with tungsten ions, which are larger (0.60 Å)19 than vanadium ions (0.58 Å), causes chemical tensile strain in V1−xWxO2(A) and V1−xWxO2(B) epitaxial films. As shown by the XRD θ − 2θ scans, the (600)VO2(A) diffraction peak gradually shifts to a lower 2θ angle with increasing tungsten concentration (Fig. 1a), indicating an increase in the a-axis lattice parameter. We observe a similar behaviour for V1−xWxO2(B) films. The observation of the (002)VO2(B) diffraction peak at a lower 2θ angle with tungsten doping (Fig. 1b) indicates an increase in the c-axis lattice parameter. As shown in Fig. 1c, the a- and c-axis lattice parameters of V1−xWxO2(A) and V1−xWxO2(B) increase by 4.8% from 8.52 to 8.91 Å and by 2.4% from 6.17 to 6.32 Å, respectively, for x = 0–0.25. This chemical tensile strain is similar to the increase in the c-axis lattice parameter by 5.7% from 2.83 to 2.99Å for x = 0–0.33 in V1−xWxO2 epitaxial films grown on (001) TiO2 (for convenience of this calculation, we assumed that V1−xWxO2 epitaxial films have a tetragonal structure on (001)TiO2, although R, M1, and the intermediate phases could coexist in one film, as indicated by a broadened TMI)15,20.

Tunable resistivity of VO2(A) and VO2(B) with tungsten doping

With increasing tungsten concentration (x < xc), the resistivity of VO2(A) decreased, while that of VO2(B) increased. Figure 2a shows the temperature dependence of the resistivity of V1−xWxO2(A) for x = 0–0.25. The resistivity of pure VO2(A) was very high, i.e., 4.37 Ω cm at 400 K, and increased with decreasing temperature. Such insulating behaviour is attributed to correlation-induced bandgap opening between unoccupied and occupied t2g orbitals1. It should be noted that the resistivity of V1−xWxO2(A) decreased with x (<xc, solid lines). The V1−xWxO2(A) epitaxial film for x = 0.15 showed a smaller resistivity (by three orders of magnitude) of 0.001 Ω cm at 400 K than that of pure VO2(A). This small resistivity indicated that the film was on the verge of metallicity, in terms of the Mott-Ioffe-Regel limit21 (i.e., the material is regarded as a metal when the resistivity is smaller than 0.001 Ω cm.). The resistivity of V1−xWxO2(A) increased for x > xc (dashed lines), probably due to film deterioration. As shown in Fig. 2b, the resistivity of pure VO2(B) also increased with decreasing temperature, indicating insulating behaviour. However, its resistivity was close to the Mott-Ioffe-Regel limit21 at 400 K and significantly smaller (by three orders of magnitude) than that of pure VO2(A). Such a low resistivity in pure VO2(B) is ascribed to thermal electron jumping across the very narrow bandgap (<25 meV) near room temperature1. The resistivity of V1−xWxO2(B) increased with increasing x by two orders of magnitude. Moreover, the resistivity increased more for x > xc, as observed in V1−xWxO2(A).

Figure 2
figure 2

Tungsten concentration dependence of the resistivity-temperature curves of (a) V1‒xWxO2(A) and (b) V1‒xWxO2(B). The resistivity of the insulating VO2(A) phase decreases as the tungsten concentration increases up to xc (solid lines) but increases for x > xc (dashed lines). By contrast, the resistivity of the semimetallic VO2(B) phase increases with increasing tungsten concentration for all x values. Comparison of the tungsten concentration dependences of the resistivity between (c) V1‒xWxO2(A) at 400 K, (d) V1‒xWxO2(B) at 400 K, (e) V1‒xWxO2(M1) at 135 K, and (f) V1‒xWxO2(R) at 400 K. We plotted data for V1‒xWxO2(M1) and V1‒xWxO2(R) from the literature (light grey15, grey20, and black22 triangles). For x < xc, the resistivities of insulating (A and M1) and metallic (B and R) materials decrease and increase, respectively. For x > xc, the resistivities of all films increase. The region in graded yellow for x < xc indicates that the crystal structures are preserved.

We noted interesting features of the tungsten doping effects on the resistivity of V1−xWxO2(A) and V1−xWxO2(B) (x < xc). The dependences were opposite: the resistivity of V1−xWxO2(A) decreased, i.e., 4.37 → 0.01 Ω cm at 400 K for x = 0 → 0.1, while V1−xWxO2(B) showed increasing resistivity, i.e., 0.003 → 0.01 Ω cm. It is surprising that the resistivities of VO2(A) and VO2(B) changed to such an extent, although we doped a relatively small amount (x < 0.1) of tungsten ions. Therefore, our work indicates that tungsten doping is promising for tuning the resistivity of VO2(A) and VO2(B). This extensive tunability is expected to provide many opportunities to realize both electronic and energy devices using correlated VO2(A) and VO2(B).

To obtain more information about these opposing and large dependences, we compared the tungsten-doping dependences of the resistivity in V1−xWxO2(A) and V1−xWxO2(B) to those in previous reports on V1−xWxO2(M1) and V1−xWxO2(R). It was simple to evaluate the resistivities of our V1−xWxO2(A) and V1−xWxO2(B) epitaxial films since, across a wide temperature range, they do not show any phase transitions. However, when we plotted the resistivities of V1−xWxO2(M1) and V1−xWxO2(R), we had to pay attention to the different resistivities of the M1 and R phases due to the TMI variation induced by the tungsten doping. Figure 2c–f show the 400 K resistivities of V1−xWxO2(A) and V1−xWxO2(B), the 135 K resistivity of V1−xWxO2(M1)15,20,22, and the 400 K resistivity of V1−xWxO2(R)15,20,22. We note three features of the tungsten doping effect across the polymorphs. (1) For light doping (x < xc), at which the crystal structures are well preserved (highlighted in yellow), the resistivities of insulating VO2(A) and VO2(M1) decrease by 3–4 orders of magnitude compared to those in the pure phases, while semiconducting VO2(B) and metallic VO2(R) exhibit increases in the resistivity by 1–2 orders of magnitude compared to those in the pure phases. (2) It is quite surprising that the resistivities of V1−xWxO2(A) and V1−xWxO2(M1) can be smaller than those of V1−xWxO2(B) and V1−xWxO2(R) when doped with certain amounts of tungsten (e.g., x ≈ xc in this work). (3) For heavy doping (x > xc), all phases show increased resistivity. We suggest that the increases seen in V1−xWxO2(A) and V1−xWxO2(B) can be attributed to deterioration of the films because we observed suppression of diffraction peaks in the θ−2θ XRD scans (Fig. 1a,b). The similar dependences between VO2(A) and VO2(M1) and between VO2(B) and VO2(R) suggest that the proposed mechanisms underlying the tungsten doping effects in VO2(M1) and VO2(R) may apply to VO2(A) and VO2(B), respectively.

Electronic structures of tungsten-doped VO2(A) and VO2(B)

To better understand the opposing dependences on tungsten doping, we investigated the electronic structures of V1−xWxO2(A) and V1−xWxO2(B) epitaxial films for various x values. Figure 3a shows the optical conductivity σ1(ω) of V1−xWxO2(A) (x = 0, 0.05, 0.1) as a function of photon energy. Pure VO2(A) (first row) exhibited opening of a correlation-induced bandgap1. For x = 0.05 (second row), a spectral weight distinctly appeared near 0.8 eV. For x = 0.1 (third row), the bandgap might be narrower than 25 meV at room temperature (Figs. S3 and S4), so the electrons in the occupied t2g orbital could thermally jump into the unoccupied t2g orbitals even at room temperature, consistent with the low resistivity shown in Fig. 2a. To examine the variation in optical spectra with x in more detail, we evaluated σ1(ω) using Lorentz oscillators, \({{\rm{\sigma }}}_{1}(\omega )=\frac{{e}^{2}}{{m}^{\ast }}\frac{{N}_{D}{\gamma }_{D}}{{\omega }^{2}+{\gamma }_{D}^{2}}+\frac{{e}^{2}}{{m}^{\ast }}\sum _{j}\frac{{N}_{j}{\gamma }_{j}{\omega }^{2}}{{({\omega }_{j}^{2}-{\omega }^{2})}^{2}+{\gamma }_{j}^{2}{\omega }^{2}}\), where m*, γj, and ωj are the effective mass, damping coefficient, and angular frequency of the jth resonance line, respectively23. The first and second terms in σ1(ω) represent the metallic Drude response and interband transitions, respectively. The β-peak represents an interband transition from occupied t2g to unoccupied t2g orbitals and shifts to a lower photon energy with increasing x. Additionally, a new peak (asterisk) appeared near 0.8 eV, representing the creation of an in-gap state between the occupied t2g and unoccupied t2g orbitals. The spectroscopic findings are consistent with the decrease in resistivity in V1−xWxO2(A). It should be noted that the spectroscopic results for V1−xWxO2(A) are similar to observations for V1−xWxO2(M1)24. Figure 3b shows proposed changes in the electronic structures of VO2(A) with tungsten doping, i.e., a shift of the unoccupied t2g orbital towards the Fermi level and the appearance of a new in-gap state just above the Fermi level.

Figure 3
figure 3

Evolution of the electronic structures of tungsten-doped VO2(A) and VO2(B). (a) Optical conductivity, σ1(ω), of V1−xWxO2(A) (x = 0, 0.05, 0.1). Open circles represent experimentally measured σ1(ω), and solid lines represent Lorentz oscillators. Due to optical transitions from occupied t2g to unoccupied t2g levels, the β-peak moves slightly towards lower photon energy for higher x. A new in-gap state (asterisk) appears near 0.8 eV. (b) Schematics of the electronic bandstructures of pure VO2(A) and V1−xWxO2(A). (c) σ1(ω) of V1−xWxO2(B) (x = 0, 0.05, 0.1). For higher x, the β-peak moves slightly towards higher photon energy, and the Drude response (yellow line) is slightly suppressed. (d) Electronic bandstructure schematics of pure VO2(B) and V1−xWxO2(B).

Different from V1−xWxO2(A), the electronic structure of V1−xWxO2(B) did not show any obvious changes. Figure 3c shows the σ1(ω) of V1−xWxO2(B) (x = 0, 0.05, 0.1) as a function of photon energy. Pure VO2(B) in the first row exhibited a non-negligible spectral weight near zero photon energy1, consistent with its low resistivity near room temperature shown in Fig. 2b. With increasing tungsten concentration, the β-peak moved very slightly towards higher photon energy, and the Drude response (yellow line) was suppressed. Although such a blueshift is very weak, it is somewhat consistent with the more resistive V1−xWxO2(B) with increasing x. Figure 3d shows a very weak change in the electronic structure of VO2(B) with tungsten doping. Therefore, we suggest that the resistivity increase in V1−xWxO2(B) is attributable to mechanisms other than any simple change in the electronic structure.

Mechanisms underlying the tunable resistivity of tungsten-doped VO2(A) and VO2(B)

Taking our experimental results together, we found that the resistivities of VO2(A) and VO2(M1) and those of VO2(B) and VO2(R) have similar dependences on tungsten doping. Numerous studies have attributed the stabilization of metallic V1−xWxO2(M1) to correlation variations, with structural distortion of V−V dimers24,25,26 and band filling by electron doping27, as we will explain in detail in the following paragraphs. In this stage, we aimed to understand the behaviours of V1−xWxO2(A) and V1−xWxO2(B) (x < xc) by adapting and modifying the mechanisms in V1−xWxO2(M1) and V1−xWxO2(R).

V1−xWxO2(A) shows tunable properties due mainly to correlation effects being modulated by chemical-strain-induced redistribution of V−V distances. Goodenough noted that vanadium oxides are metallic when the distance between vanadium ions is less than 2.94 Å28. VO2(M1) is insulating because correlated electrons are localized in V−V dimers, where the asymmetric distances of V−V atoms inside and between dimers are 2.65 and 3.12 Å, respectively. It is widely accepted that the transition from insulating VO2(M1) to metallic VO2(R) is accompanied by a symmetric redistribution of V−V chains, with an even distance of 2.88 Å. When vanadium ions are replaced with tungsten, the X-ray absorption fine structure indicates that the local structure around each tungsten atom is intrinsically symmetric, with a tetragonal-like structure. Therefore, the nearby V−V dimers in a VO2(M1) lattice are rearranged to form rutile-like VO2 nuclei25,26. In VO2(A), vanadium ions along the c-axis have alternating distances of 3.25, 3.11, and 2.77 Å at room temperature (<162 °C)29. Although the XRD results imply that V1−xWxO2(A) mostly has a tetragonal structure similar to pure VO2(A), expansion of the local structure due to tungsten could symmetrize the V−V chains. This rearrangement would weaken the correlation effect in V1−xWxO2(A), leading to lower resistivity.

As an alternative mechanism for V1−xWxO2(A), we also considered electron doping since V4+ ions neighbouring the site of W6+ dopants change to V3+ ions to maintain charge neutrality30. This band filling drastically decreases the Coulomb repulsion energy and accordingly weakens the electron correlation27, metallizing V1−xWxO2(M1). We also found a significant evolution of V3+ oxidation states in V1−xWxO2(A) with tungsten doping (x = 0, 0.05, 0.1). Figure 4 shows XPS V 2p3/2, V 2p1/2, and O 1 s spectra in the binding energy range of 505–535 eV. We fitted the XPS spectra of pure VO2(A) (Fig. 4a) with V4+2p3/2 (red pattern) at 515.84 ± 0.2 eV and V4+2p1/2 (orange pattern) at V4+2p3/2 + 7.33 eV31, indicating that the oxidation state of our non-doped epitaxial films was firmly V4+. Interestingly, V3+ peaks [V3+2p3/2 (blue pattern) at 515.29 ± 0.2 eV and V3+2p1/2 (purple pattern) at V3+2p3/2 + 7.33 eV31] were additionally required to resolve the XPS spectra of V1−xWxO2(A) (x = 0.05, 0.1). It should be noted that the V3+ peaks were stronger with increasing x. This similar observation between V1−xWxO2(A) and V1−xWxO2(M1) indicates that electron-doping-induced band filling also plays an important role in tungsten-doped metallization30.

Figure 4
figure 4

X-ray photoemission spectroscopy (XPS) V 2p3/2, V 2p1/2, and O 1 s spectra of (a) V1−xWxO2(A) and (b) V1−xWxO2(B) in the binding energy range of 505–535 eV. While the XPS spectra of non-doped epitaxial films are fitted by V4+ peaks (red and yellow patterns), V3+ peaks (blue and purple patterns) are additionally required for the XPS spectra of V1−xWxO2 (x = 0.05, 0.1). The intensity of the V3+ peaks increases with increasing x.

Although we also found significant evolution of the V3+ XPS peaks in V1−xWxO2(B) (Fig. 4b), it is quite interesting to note that VO2(B) became more insulating with increasing x. Therefore, we hypothesize that another mechanism, different from those for V1−xWxO2(A) and V1−xWxO2(M1), plays an important role in the tunable properties of V1−xWxO2(B) (x < xc). It should be noted that the correlation effects in VO2(B) and VO2(R) are weaker than those in VO2(A) and VO2(M1), considering their lower resistivities and narrower bandgaps1,2. Therefore, we suggest that the increase in resistivity in V1−xWxO2(B) originates from disorder-induced electron scattering. Since more dopants will scatter more electrons, the resistivity will increase with heavier doping32,33.

Conclusion

Tungsten doping provided an effective way to tune the resistivity of correlated VO2(A) and VO2(B). XRD revealed that the crystal structures of V1−xWxO2(A) and V1−xWxO2(B) expanded and were well preserved for x < 0.1–0.15. At this low doping concentration, the resistivity of V1−xWxO2(A) decreased, similar to that of V1−xWxO2(M1), with increasing tungsten concentration; in contrast, the resistivity of V1−xWxO2(B) increased, similar to that of V1−xWxO2(R). Spectroscopic ellipsometry revealed that tungsten doping resulted in a redshift of the unoccupied t2g orbital, the creation of an in-gap state in V1−xWxO2(A), and a slight blueshift of unoccupied t2g orbitals in V1−xWxO2(B). Both vanadate films showed evolution of the V3+ oxidation states based on the XPS study. Referring to the mechanisms in correlated V1−xWxO2(M1), we proposed that V1−xWxO2(A) and V1−xWxO2(B) showed opposite dependences due to either chemical-strain-induced redistribution of VV distances or electron-doping-induced band filling and disorder-induced electron scattering, respectively. We leave further consideration of the mechanisms for future studies.

The extreme tunability of correlated VO2(A) and VO2(B) enables their use in next-generation electronic devices, as well as energy devices. As we mentioned in the Introduction section, VO2(M1) has shown a reversible resistivity change due to intercalation of hydrogen10,11 and ionic liquid gating12,13. The similar doping dependence between VO2(A) and VO2(M1) suggests that these dynamic control methods would enable application of correlated VO2(A) [also VO2(B)] in memories, transistors, and gas sensors, as has been extensively studied for VO2(M1).

Methods

Epitaxial film growth of tungsten-doped VO2(A) and VO2(B)

We recently optimized the growth conditions for epitaxial films of VO2(A) and VO2(B) on either perovskite oxides or Y-stabilized ZrO22,3,16,17,18. Using pulsed laser epitaxy, we deposited VO2(A) and VO2(B) epitaxial films on (011)-oriented SrTiO3 and (001)-oriented LaAlO3 substrates, respectively. We ablated a tungsten-doped V2O5 target with a KrF (248 nm wavelength) pulsed laser at a rate of 10 Hz and an intensity of 1 J cm−2. For the targets, we mixed WO3 and V2O5 powders in the desired molar ratio and sintered pellets at 650 °C for 12 hours in air. We used this low sintering temperature due to the low melting point (690 °C) of V2O5. We fixed the substrate temperature at 420 °C since VO2(A) and VO2(B) are thermodynamically unstable above 430 °C and transition into VO2(R) above 470 °C2,29. We used a flow of oxygen gas with a partial pressure, \({P}_{{{\rm{O}}}_{2}}\), of 8 mTorr for VO2(A) and 15 mTorr for VO2(B) since VO2 stably forms in only a narrow range of 5 mTorr <\({P}_{{{\rm{O}}}_{2}}\) < 30 mTorr16,34.

Measurement of electrical and optical properties

To investigate the electrical transport properties, we used a physical property measurement system (Quantum Design Inc.). We used the four-point probe method, which is the most common method for measuring the resistivity35. We deposited evenly spaced Pt contacts on the middle of the film surface. We applied a small constant current through the outer two contacts and measured the voltage between the inner two contacts. We swept the temperature in the range of 10–400 K. We measured the reflectance, R(ω), spectra in a photon energy range of 0.1–1 eV via a Fourier transform-type infrared spectrometer (model VERTEX 70 v; Bruker). We employed an in situ gold overcoating technique to obtain an accurate absolute value of R(ω). We obtained the optical conductivity of the VO2 film via a two-layer model fit of the measured R(ω) with Drude-Lorentz oscillators23,36. We used spectroscopic ellipsometers (models V-VASE and M-2000; J. A. Woollam Co.) to obtain the complex dielectric constants, \(\epsilon (\omega )={\epsilon }_{1}(\omega )+i{\epsilon }_{2}(\omega )\), in the energy region between 1 and 5 eV. The optical conductivity, σ1(ω), in this energy range can be calculated by \({\sigma }_{1}(\omega )={\epsilon }_{0}\omega {\epsilon }_{2}(\omega )\)23, where \({\epsilon }_{0}\) is the vacuum permittivity.

Characterization of structural properties and oxidation states

We investigated the crystal structures via a four-circle high-resolution X-ray diffractometer (model Empyrean; PANalytical) using Cu radiation with a wavelength of 1.5406 Å. Using the fringe patterns obtained in X-ray reflectivity measurements, we confirmed that the films had an ~100-nm thickness (Fig. S2). To determine the oxidation states of vanadium, we carried out XPS (model ESCALAB 250Xi; Thermo Scientific) using a monochromatic Al source with a photon energy of 1486.6 eV under an environmental pressure of 10−8 Torr. To remove contamination, the film surface was sputtered with argon ions for 10 seconds16. We used the O 1 s peak at 530.0 eV as the energy reference. We supplied electrons using an electron gun to avoid any charging effect.