Orbital-selective Mott and Peierls transition in H_xVO₂

Abstract

Materials displaying metal-insulator transitions (MITs) as a function of external parameters such as temperature, pressure, or composition are most intriguing from the fundamental point of view and also hold high promise for applications. Vanadium dioxide (VO₂) is one of the most prominent examples of MIT having prospective applications ranging from intelligent coatings, infrared sensing, or imaging, to Mott memory and neuromorphic devices. The key aspects conditioning possible applications are the controllability and reversibility of the transition. Here we present an intriguing MIT in hydrogenated vanadium dioxide, H_xVO₂. The transition relies on an increase of the electron occupancy through hydrogenation on the transition metal vanadium, driving the system insulating by a hybrid of two distinct MIT mechanisms. The insulating phase observed in HVO₂ with a nominal d² electronic configuration contrasts with other rutile d² systems, most of which are metallic. Using spectroscopic tools and state-of-the-art many-body electronic structure calculations, our investigation reveals a correlation-enhanced Peierls and a Mott transition taking place in an orbital-selective manner cooperate to stabilize an insulating phase. The identification of the hybrid mechanism for MIT controlled by hydrogenation opens the way to radically design strategies for future correlated oxide devices by controlling phase reversibly while maintaining high crystallinity.

Introduction

Identifying low energy degrees of freedom and their intricate interplay in correlated electron materials is essential to understanding their physical properties. For metal-to-insulator-transitions (MIT) in particular, strong electronic correlations often play a crucial role in the charge localization of systems with non-trivial band fillings. In these systems, the MIT often occurs with either formation of orderings or enhancement of the pre-existing ones, resulting from an intricate interrelationship of lattice, charge, orbital, and spin degrees of freedom. The MITs accompanied by such an emergence or enhancement of orderings have been reported in many transition metal oxides^1,2.

Vanadium dioxide (VO₂) is one of the most prominent examples of the correlation-driven MIT that has excited the solid-state community for decades^3,4,5,6. VO₂ undergoes MIT around T_MIT ~ 340 K⁷ with a structural transition from a rutile to a monoclinic phase (M1), involving the formation of V–V dimers. The insulating state can be understood as a combined effect of V–V dimerization and the on-site Coulomb interaction. The former induces a bonding-antibonding splitting within the a_1g orbitals with a strong bonding along the dimer direction⁸. The latter opens a gap by enhancing the bonding-antibonding splitting, resulting in a spin-singlet state in the filled bonding band^9,10,11,12.

Recently, the electronic transport and lattice structure of hydrogenated VO₂ (H_xVO₂) have been investigated^{13,14,15,16,17,18}. H_xVO₂ shows successive phase transitions as a function of hydrogen content x at room temperature: an insulator to metal transition followed by the reentrance of the insulating phase. At low H-content, it shows a bad metallic behavior with a resistivity exceeding the Mott–Ioffe–Regel limit^19,20, implying strong electron–electron interactions²¹. Electronic and optical properties in the metallic phase at low hydrogenation are similar to the oxygen vacant VO_2−δ²². As H-doping increases, a structural transition involving dimerization of V-cations occurs¹⁸ [Fig. 1a], accompanied by a MIT in the electronic transport. The insulating phase is maintained up to the fully hydrogenated limit (HVO₂)^23,24. Since the inserted hydrogen is attached to oxygen atoms and hybridizes mainly with O-p states away from the Fermi energy, the primary role of the hydrogenation is changing the V-d occupancy, consistent with density functional theory (DFT) calculations^23,24. Thus, the doping-induced change in the valence suggests the presence of a filling-controlled MIT around the V-d²-filling, which is in clear contrast to other d²-filling rutile-based compounds such as CrO₂, MoO₂, and WO₂ showing a low-T metallic phase^25,26,27.

Fig. 1: Atomic structure and frontier orbitals of HVO₂.

a The primitive unit cell of insulating HVO₂ in orthorhombic structure (space group Fdd2). Similar to VO₆, the octahedra are edge-sharing in the (001)_R direction and corner-sharing in (100)_R/(010)_R directions, forming chain-like structures with small octahedral rotations. Two inequivalent V sites with four and two hydrogen atoms attached to the VO₆ octahedron are defined as V1 and V2, respectively. The V–V bond lengths are 2.98 and 2.78 Å, which are comparable to experimental values of monoclinic VO₂ 3.10 and 2.77 Å^9,42. b Definition of vanadium ${d}_{{x}^{2}-{y}^{2}}$ (a_1g-like) and d_xz/d_yz (${e}_{g}^{\pi }$-like) orbitals in this work. The y-axis is set parallel to V-chain direction (001)_R.

Identification of this newly discovered MIT mechanism requires orbital-sensitive measurements to probe the orbital reconstructions associated with the MIT. Moreover, computational methods incorporating both intra- and inter-site correlations need to be employed to correctly capture the essential many-body effects, such as cluster dynamical mean-field theory (CDMFT), which successfully captures the MIT in VO₂¹¹. We investigate the mechanism of the MIT by polarization-dependent spectroscopic ellipsometry and X-ray absorption (XAS) measurements, elucidating the orbital-dependent spectral modifications in the insulating phase. The orbital reconstructions accompanied by the MIT are theoretically investigated considering both on-site and inter-site correlation using Δ+DMFT scheme, which successfully capture the orbital structures observed in the experiments. From our analysis, we will show that the MIT is driven by a simultaneous Mott and Peierls transition depending on the orbital character. Our experimental data provides the spectral information of H_xVO₂ essential for the characterization of electronic structures across the MIT and to the best of our knowledge this is the first proposal of the MIT mechanism involving Mott and Peierls physics with orbital-dependent way, which has not been reported in rutile systems. We expect that the hybrid mechanism along with the continuous control of hydrogenation can provide ways control phase of the matter, which is important to utilize the vanadium-based oxides as various applications^{27,28,29,30,31} such as hydrogen storage and high-performance smart windows^24,32,33,34.

Results and discussion

Effects of the hydrogenation

Figure 2a summarizes our main findings by comparing schematic orbital structures of undoped, partially hydrogenated, and fully hydrogenated H_xVO₂. Since the average occupancy of V-d orbitals is expected to be in between one and two electrons per V, the low-lying frontier orbitals of H_xVO₂ are a_1g- and ${e}_{g}^{\pi }$-like orbitals, with lobes extended along and perpendicular to the dimer direction, respectively, as presented in Fig. 1b. Starting from the insulating VO₂ system involving the correlation-enhanced bonding-antibonding splitting of ${d}_{{x}^{2}-{y}^{2}}$ (a_1g) (left panel), the introduction of a small amount of hydrogen leads to an insulator to metal transition as the added electrons occupy the partially occupied ${e}_{g}^{\pi }$ orbitals (middle panel), consistent with other electron-doped VO₂ systems^17,27,35.

Fig. 2: Orbital structures and optical conductivity of H_xVO₂.

a Schematic energy band diagrams for the insulating VO₂, metallic H_xVO₂, and insulating HVO₂ near Fermi level. b Real part of the optical conductivity of H_xVO₂ thin film on Al₂O₃ (0001) substrate measured at room temperature. CT, charge transfer; B, bonding; AB, antibonding; UHB, upper-Hubbard band; LHB, lower-Hubbard band.

As the electron occupancy reaches 2 electrons per vanadium in the fully hydrogenated HVO₂, a MIT occurs with a structural transition involving the dimerization of V atoms [Fig. 1a]. Just as the filling the bonding state of ${d}_{{x}^{2}-{y}^{2}}$ opens a gap in dimerized VO₂ (left panel), it is strongly suggested that the similar splitting of a_1g orbitals is also present in HVO₂ as the dimerization occurs simultaneously with the MIT^36,37. With a d-occupancy of 2 electrons per V around x = 100%, an additional orbital splitting is expected to induce the band gap. As in Fig. 2, the MIT occurs in which d_yz orbitals split to the lower and upper Hubbard bands by a Mott-transition with an orbital ordering between d_xz and d_yz orbitals, pushing up the energy of d_xz orbital relative to d_yz. Here, the role of electron correlations is essential, which boosts the orbital ordering and, at the same time, opens a gap by splitting the d_yz bands.

To understand the evolution of the electronic structure in HVO₂, we examine the structural changes developed by hydrogenation. X-ray and neutron diffraction studies verified the lattice structure of H_xVO₂ and identified orthorhombic structure (space group Fdd2(43)) for highly hydrogenated and insulating phase¹⁸. The structural characterization of our epitaxial films is published elsewhere³⁷. As illustrated in Fig. 1a, it has four V atoms in the primitive unit cell. We note that HVO₂ has substantial dimerization along the V-chain with long (short) bonds between vanadium sites with (without) H attached to the bridging oxygens.

Electronic structures and optical conductivity

A pronounced insulator-to-metal transition and reentrance to the insulating phase of H_xVO₂ at room temperature are well-exhibited in the real part of the optical conductivity σ₁(ω) in Fig. 2b. The subsequent transitions observed by increasing x are consistent with transport measurements^23,24. At x = 0%, the overall peak structure of our film is in good agreement with previous reports on monoclinic VO₂³⁸. We can observe an optical gap between filled a_1g and ${e}_{g}^{\pi }$ orbitals. The low-intensity peaks near 1.2 and 3 eV are mainly attributed to transitions within V-d orbitals, shown schematically in Fig. 2a. A peak near 3.5 eV marked as CT-1 is the charge transfer peak and corresponds to the excitation from O-p to V-d derived bands^39,40.

At x = 3%, the optical gap is closed, while the charge transfer peak is almost fully maintained except for a decrease in peak height. We find the gap reopening at x = 100%, reentering the insulating phase. We note here that the composition x is estimated by optical and diffraction characteristics of H_xVO₂ (see “Methods” and Fig. S2 in the Supplementary Information), which may deviate from exact chemical stoichiometry. The charge transfer peak is shifted higher in energy by 1.3 eV (marked as CT-2) with largely reduced spectral weight over the measured frequency range. At intermediate H-content of x = 46%, σ₁(ω) shows two charge transfer peaks. At the same doping, the coexistence of two XRD peaks that correspond to the (100)_R lattice of low and high H-compositions (x = 3% and 100%) are observed (see Fig. S2b in the Supplementary Information for details).

We now investigate the electronic structure of the insulating O2 phase in the fully hydrogenated limit (HVO₂), including the effect of strong local Coulomb interactions on the V-d orbitals. For this, we employ a Δ+DMFT approach, where we project the DFT Hamiltonian onto localized a_1g- and ${e}_{g}^{\pi }$-like Wannier orbitals for the two inequivalent V atoms in the unit cell as in Fig. 1b. In the reduced model, the on-site correlations of d_xz and d_yz orbitals are treated by DMFT utilizing a continuous-time Quantum Monte Carlo impurity solver. Our approximation properly respects the fact that the intra- and inter-dimer hopping energies of d_xz and d_yz orbitals are similar in magnitude and can be considered a local problem, adequately described in a DMFT approach. On the other hand, the inter-site correlations originating from the dimer-forming ${d}_{{x}^{2}-{y}^{2}}$ orbitals are approximated by a static (frequency-independent) dimer-like self-energy of the form of an inter-site orbital-dependent potential Δ as described in ref. ⁴¹. This approach effectively captures the correlation-enhanced bonding-antibonding splitting of ${e}_{g}^{\pi }$ orbitals. Such a static treatment of the inter-site correlations has been previously employed in pure VO₂ by a LDA+Δ correction⁴¹.

Figure 3a presents the orbital-projected spectral function for HVO₂ calculated within the Δ+DMFT method. We find a Mott-insulating phase with a gap at the Fermi energy (E_F), consistent with our optical spectra [Fig. 2b] and previous transport experiments^23,36,42. The O-p derived bands are −4 eV below the E_F which is roughly 1.5 eV lower than those of metallic H_xVO₂ and of pure VO₂²⁶, which is consistent with the blue shift of the charge transfer peak observed in our optical spectra [CT-2 in Fig. 2b]. The change arises from the formation of O–H bonding during hydrogenation, supposing that the attachment of H⁺ ion to oxygen lowers the energy of O-p bands (Fig. S4 in the Supplementary Information).

Fig. 3: Δ+DMFT calculation of the insulating HVO₂.

a The spectral function A(ω) of O-p (red), V-da_1g/${e}_{g}^{\pi }$-like (blue), and V-d ${e}_{g}^{\sigma }$-like (green) orbital dominated states. b–d Orbital decomposed A(ω) of b ${d}_{{x}^{2}-{y}^{2}}$, c d_xz, and d d_yz orbitals. The inequivalent V1 and V2 atoms are indicated by solid and dashed lines, respectively. e Experimental optical conductivity σ₁(ω) of VO₂ measured at 180 K (empty circles) and HVO₂ at 300 K (filled squares) grown on Al₂O₃ (0001) substrate. As the in-plane lattice directions of the sample are not aligned within the beam spot, the optical anisotropy was undetected. f Calculated σ₁(ω) of the Δ+DMFT method for insulating VO₂ (dotted line) and HVO₂ (solid line). The spectra for the two polarizations, E ∥(001)_R and E ∥(010)_R, is averaged for direct comparison to the experiment.

The orbital-resolved spectral functions clearly demonstrate an orbital-selective mechanism that induces a MIT, as shown in Fig. 3b–d. The spectral function A(ω) of the a_1g-like orbital (panel b) exhibits a gap resulting from the enhancement of the bonding-antibonding splitting by the Δ-potential from inter-site correlations. This mechanism corresponds to a correlation-assisted Peierls transition from dimerization, as discussed in VO₂^11,12. The ${e}_{g}^{\pi }$-like orbitals exhibit an orbital ordering with the d_xz orbital shifted above the Fermi energy (panel c) and a Mott gap formed in the d_yz orbital (panel d), driven by local correlations. In essence, the pronounced difference in the hopping anisotropy between a_1g- and ${e}_{g}^{\pi }$ orbitals leads to two distinct mechanisms: a correlation-assisted Peierls and Mott transition for a_1g and ${e}_{g}^{\pi }$ orbitals, respectively, which we define as an orbital-selective Mott and Peierls transition.

We note that there is no qualitative difference between the inequivalent V1 and V2 sites defined in Fig. 1a. The major features of the orbital orderings without correlations (defined with non-magnetic Wannier Hamiltonian), such as bonding-antibonding splitting of ${d}_{{x}^{2}-{y}^{2}}$ orbitals and energy of d_xz orbital higher than d_yz orbitals are the same for both sites with the octahedral distortions and attached hydrogen ion. Given the non-interacting orbital structure with the bonding-antibonding splitting of ${d}_{{x}^{2}-{y}^{2}}$ orbitals and the energy difference between d_xz/d_yz orbitals, the Mott and Peierls and Mott transition occurring by the inclusion of the inter-site and on-site correlations enhances the orbital splitting. The resulting orbital splitting is much larger (in the order of U) than that from structural effects (<0.4 eV), and the enhanced splittings dominate the orbital structures. The orbital energies from the non-magnetic Wannier tight-binding Hamiltonian are discussed in Sec. VII in the Supplementary Information.

The calculated optical conductivity matches with the important characteristics of the spectral transfer observed in the experiment, which strongly supports the orbital selective phase transition in HVO₂. Figure 3e shows the experimental σ₁(ω) of the VO₂ extracted from thin film grown on an Al₂O₃ substrate before and after hydrogenation. The σ₁(ω) of VO₂ calculated by using Δ-potential to include inter-site correlations [Fig. 3f] is consistent with that calculated by CDMFT⁴³ and also with the experimental data; this supports the validity of employing a static intra-dimer Δ-potential in our approach. Moreover, we find that the calculated optical conductivity of HVO₂ from Δ+DMFT successfully reproduces the essential features such as the optical gap, suppression of the spectral weight, and the blue shift of the charge transfer peak about 1.5 eV coming from the down-shift of O-p states (for details see Fig. S4 in the Supplementary Information). These results provide a strong support to the Mott and Peierls insulating phase as the ground state of HVO₂.

Polarization-dependent optical responses

An interesting feature resulting from the orbital-selective Mott and Peierls transition is orbital ordering, by which polarization-dependent responses are expected. We employ two different measurements, polarization-dependent X-ray absorption and ellipsometry, to further confirm the proposed Mott-Peierls insulating phase. We prepare an additional set of VO₂ films of 10-nm thickness grown epitaxially on TiO₂ (100) substrate, which allows measuring the polarization-dependent responses³⁶.

To obtain the orbital-dependent responses using polarized light, alignment of the VO₂ on the substrate is crucial³⁷. The VO₂ films epitaxially grown on Al₂O₃ have a significant advantage due to the large band gap (~7 eV), allowing for the optical measurements up to the visible/UV ranges, but the VO₂ films have domains oriented in different directions inhibiting the polarization-dependent experiments. In contrast, the VO₂ films grown in TiO₂ are oriented in either (100)_R or (001)_R^36,37, making it possible to perform polarization-dependent measurements up to the visible ranges.

Figure 4a presents the measurement geometry where the s- and p-polarized light is mainly parallel and perpendicular to (001)_R (or y-axis) in Fig. 1, respectively. We find that the linear dichroism of O K-edge (O 1s → 2p transition) of VO₂ (Fig. S3) before hydrogenation is in good agreement with that of single crystal VO₂^44,45,46. This shows that our film on TiO₂ is oriented well-enough to detect the dichroism signal.

Fig. 4: Orbital-dependent optical properties of HVO₂.

a Hydrogenated 10-nm-thickness VO₂/TiO₂ (100)_R thin film and measurement geometry in XAS and ellipsometry. The (001)_R direction is parallel to the y-axis defined for the calculations in Fig. 1b. b O K-edge XAS spectra with E ∥(001)_R (filled circles) and E ⊥(001)_R (empty circles) for HVO₂ taken at 250 K. c–e Decomposed A(ω) calculated for c d_xz and d_yz, d ${d}_{{x}^{2}-{y}^{2}}$, and e d_xz and ${d}_{{z}^{2}}$ orbitals. The intensity for inequivalent V1 and V2 atoms, total 4 atoms in unit cell, are summed up. f, g Optical conductivity σ₁(ω) spectra from (f) experiment and (g) Δ+DMFT. h The deviation of σ₁(ω) in E ∥(001)_R, σ_∥(ω), and E ⊥(001)_R, σ_⊥(ω). The experimental spectrum in symbols is multiplied by 6. Pol., polarization.

The X-ray absorption of fully hydrogenated HVO₂ in Fig. 4b confirms the calculated orbital polarization of an orbital selective Mott and Peierls insulator. We define the case of an intensity of E ∥(001)_R greater (less) than E ⊥(001)_R as positive (negative) dichroism. There are three characteristic features in the XAS: (1) a peak at 528.5 eV with negative dichroism, (2) a small peak at 529.5 eV with positive dichroism (marked with a star), and (3) peak around 532 eV with positive dichroism. The dichroism can be understood from the orbital-projected spectral function of each d-orbitals summed over all V-atoms in the unit cell presented in Fig. 4c–e. The negative dichroism of (1) can be understood from the d_xz-derived states located right above the Fermi energy [Fig. 4c], which hybridize mainly with O-p_x/p_z orbitals and thus have large absorption for the polarization in the xz [E ⊥(001)_R] plane. The feature of (2) is associated with the transition to the ${d}_{{x}^{2}-{y}^{2}}$-derived antibonding states [Fig. 4d] in which the ${d}_{{x}^{2}-{y}^{2}}$-p_y hybridization prefers the absorption of E ∥(001)R (parallel to y-axis in Fig. 1b), resulting in overall positive dichroism and the peak position well matches with the transition energy to the antibonding ${d}_{{x}^{2}-{y}^{2}}$ state. We find the positive dichroism of (3) is common for both VO₂ and HVO₂, due to the similar ${e}_{g}^{\sigma }$ orbital structures between them.

The polarization-dependent optical conductivity σ₁(ω) provides further evidence of the proposed orbital structures of HVO₂. In both experiment and calculation, we find that the difference in σ₁(ω) between E ∥(001)_R and E ⊥(001)_R gradually increases up to 3 eV [Fig. 4f, g). We note that σ₁(ω) above 3 eV becomes unreliable due to a strong TiO₂ signal and thus not shown. Below 1 eV, the optical response is contributed mainly from the transitions from occupied d_yz and ${d}_{{x}^{2}-{y}^{2}}$ states to unoccupied d_xz states, having small matrix elements and dichroism. Above 1 eV, the transitions between bonding and antibonding ${d}_{{x}^{2}-{y}^{2}}$ start to be significant, having large matrix elements for E ∥(001)_R compared with E ⊥(001)_R. This, in turn, results in a significant increase of the dichroism [Fig. 4h] at around 2.5 eV corresponding to the bonding-antibonding splitting of ${d}_{{x}^{2}-{y}^{2}}$ bands. We find that the measured dichorism in the experiment is roughly 6 times smaller than in the calculation. This is partially from the magnitude of the experimental optical conductivity being about half of the calculated one, resulting in about 50% reduction of the dichroism signal. The non-ideal sample may be another reason, such as oxygen vacancies formation on the surface during annealing or the coexistence of other remnant phases (e.g., mixed domains). Overall, the consistent trend of the experimental and theoretical dichroism in the optical conductivity further supports the orbital structures resulting from a Mott and Peierls transition.

We note that the inter-site correlations included with the Δ+DMFT approach are crucial for predicting the correct orbital reconstructions across the MIT. To confirm the role of the inter-site correlations, we have additionally performed single-site DMFT calculations that neglect these nonlocal effects (see Fig. S6 in the Supplementary Information). In this case we find that the orbital ordering pattern is not consistent with the polarization-dependent XAS. Moreover, the optical conductivity and its polarization show marked differences around the low-frequency region (see Supplementary Information for further discussion).

Outlook and conclusion

Several properties of the MIT in H_xVO₂ need further investigation. For example, since two different mechanisms are involved in the MIT, it is an essential question whether the two transitions occur synchronously or asynchronously, and how the hydrogens percolate into the films. Unveiling the dynamics of the intermediate state can answer such questions. Theoretically, a temperature-dependent self-energy calculated for the O1 and O2 structures by DFT plus cellular DMFT methods including both a_1g and ${e}_{g}^{\pi }$ orbitals could predict whether two transitions occur simultaneously. This would be an important future direction to pursue in the future. Experimentally, systematic temperature-dependent measurements of the orbital polarization by polarized X-ray absorption, dimerization by X-ray diffraction, and conductivity by transport or optical absorption measurements can be used. These experiments would allow investigating the orbital occupation, structural parameters, and band gap as the function of temperature. A key to achieving systematic results here is to maintain the hydrogen content at different temperatures, which is challenging because the x of the H_xVO₂ films changes at a different rate at different temperatures and chamber pressure. Therefore, systematic studies and surrounding hydrogen gas pressure conditions need to be preceded in H_xVO₂.

To conclude, we have investigated the electronic and optical properties of H_xVO₂ across the MIT occurring in the highly hydrogenated limit. Our main finding is that the insulating phase is induced in an orbital selective way, in which the a_1g-like orbital undergoes a correlation-assisted Peierls transition due to the relatively large dimer hopping, in a similar fashion as in pure VO₂. On the other hand, the ${e}_{g}^{\pi }$-like orbitals undergo a Mott-insulator transition after orbital ordering. We identify this scenario as an orbital-selective hybrid Mott and Peierls transition. The resulting orbital structure from the MIT is supported by polarization-dependent XAS and ellipsometry, showing energy-dependent dichroism, as well as Δ+DMFT calculations which successfully reproduce the experimental data. To the best of our knowledge, this is the first study uncovering the nature of the insulating phase under hydrogenation by providing solid evidence of orbital reconstructions across the MIT.

Our results provide a potential pathway to stabilize an insulating phase by combining Peierls and Mott physics coexisting in orbital space. This is in close analogy to the M2 phase in VO₂ having alternating antiferromagnetic and dimerized edge-sharing chains⁴⁷. The present compound, HVO₂, is the first example of a compound displaying coexistence of Mott and Peierls behavior without spatial separation, differentiated only in orbital space. The proposed hybrid mechanism for a MIT provides a route for devising functionalities of correlated oxides from the two main aspects. The broken orbital symmetry with large energy separation in the presence of the two distinct ordering gives polarization-dependent responses varying with light frequencies and the lowered crystalline symmetry can be utilized for the optical control of the MIT by exciting the dimer oscillation allowed by the distinct V1 and V2 sites. Moreover, we expect that the transition temperature of the MIT could be controlled by the uniaxial strain along the chain direction. Utilizing hydrogenation, we expect to control the MIT with a small electric field, which could be achieved by tuning the hydrogen doping to the MIT boundary such that modulating the orbital occupation by small applied electric fields could induce the MIT.

Methods

Sample preparation

We prepared 30-nm-thick VO₂ films epitaxially grown on the Al₂O₃ (0001) substrate, and 10-nm-thick VO₂ on the TiO₂ substrate (100)_R and (001)_R using pulsed laser deposition. The top surface of the films was then deposited with nano-sized Pt-islands to implement hydrogen spillover method as described in refs. ^23,36,37.

Spectroscopic ellipsometry

For the optical conductivity measurements, we used spectroscopic ellipsometry (M-2000) and implemented fitting program (V-VASE) of J. A. Woollam Co. The hydrogenation was controlled on a hot plate (annealing T ~ 400 K) under the flow of H₂ (5%)/Ar (95%) in air. Each measurement was immediately followed by the XRD to characterize the lattice constant, from which we applied the linear relation between hydrogenation and lattice constants^18,23 to obtain doping content x.

To obtain the anisotropic optical conductivity, we scanned the VO₂/TiO₂ (100)_R and the TiO₂ (100)_R substrate twice for each sample, with s-polarized light parallel to (010)_R and (001)_R by rotating the film in 90^∘ in-plane. After fitting the substrate with experimental data, we modeled the anisotropic film on the anisotropic substrate and fitted the optical conductivity with experimental film data. The photon energy ranges of the thin film spectra are limited by the band gap of the substrates, which is around 3 eV for TiO₂ and 7 eV for Al₂O₃ (see Fig. S4).

NEXAFS

NEXAFS data were obtained at the beamline 2A of Pohang Accelerator Laboratory (PAL). The incident angle [θ_i in Fig. 4a] was about 67.5^∘. To compare the XAS data with different light polarization, a constant offset below 510 eV has been subtracted. The resulting dichroism signal of VO₂ at the V L₃-edge are consistent with previous reports^46,48.

DFT+DMFT calculations

We performed first-principles DFT calculations within the generalized gradient approximation (GGA) using the Vienna ab-initio simulation package^49,50. We used the projector augmented wave method⁵¹ and Perdew–Becke–Erzenhof parametrization⁵² for the exchange-correlation functional. The experimental lattice parameters¹⁸ have been used for the O1 and O2 structures in which the 8 × 8 × 16 and 8 × 8 × 8k-point grids are used, respectively. The energy cut-off of 500 eV is used. For the insulating O2 phase, the effective tight-binding Hamiltonian consisting of the V-d-derived frontier orbitals (${d}_{{x}^{2}-{y}^{2}},{d}_{xz},{d}_{yz}$) is obtained for four V-sites of the primitive unit cell of HVO₂ using the Wannier90 package⁵³, based on the non-magnetic DFT-GGA calculation. To this Hamiltonian a local Coulomb interaction term is added with interaction parameters similar to those of the undoped parent compound with U = 3.5 eV and J = 0.7 eV and solved by Δ+DMFT method in which ${d}_{{x}^{2}-{y}^{2}}$ orbitals have been treated with static inter-site correlations Δ of −1.0 eV within the Hubbard dimer approximation (for detail see the Supplementary Information). For d_xz and d_yz orbitals, we have used a continuous-time quantum Monte-Carlo impurity solver in the hybridization expansion with a density–density form of the interaction as implemented in the ALPS package⁵⁴. The optical conductivity is calculated by upfolding the band structures⁴³. The spectral functions from DMFT are upfolded to the p-d energy window. The optical matrix elements are calculated in the energy range containing O-p and V-d bands by upfolding the band structure⁴³. The matrix elements were evaluated using the real space position operators in the Wannier basis.