Insulator-to-metal transition in ultrathin rutile VO2/TiO2(001)

An insulator-to-metal transition (IMT) is an emergent characteristic of quantum materials. When the IMT occurs in materials with interacting electronic and lattice degrees of freedom, it is often difficult to determine if the energy gap in the insulating state is formed by Mott electron–electron correlation or by Peierls charge-density wave (CDW) ordering. To solve this problem, we investigate a representative material, vanadium dioxide (VO2), which exhibits both strong electron–electron interaction and CDW ordering. For this research, VO2 films of different thicknesses on rutile (001) TiO2 substrates have been fabricated. X-ray diffraction (XRD) data show that ultrathin VO2 films with thickness below 7.5 nm undergo the IMT between rutile insulator below Tc and rutile metal above Tc, while an ultrathin VO2 film with a thickness of 8 nm experiences the structural phase transition from the monoclinic structure below Tc to the rutile structure above Tc. Infrared and optical measurements on a film of 7.2 nm thickness, below Tc, reveal the energy gap of 0.6 eV in the rutile insulator phase and the absence of the 2.5 eV bonding-antibonding CDW structure. Above Tc, a Drude feature in the optical conductivity reveals the IMT to a metallic phase. These results suggest that for VO2 films below a critical thickness of about 7.5 nm, the IMT occurs in the rutile structure of VO2 without the Peierls lattice distortion.


INTRODUCTION
An insulator-to-metal transition (IMT) leads to dramatic changes in physical properties, and it is induced by variation of control parameters such as temperature, chemical doping, and strain 1 . The underlying mechanism of the IMT is ambiguous in materials in which the IMT is accompanied by a structural phase transition (SPT), such as in bulk vanadium dioxide (VO 2 ) 2-8 . Bulk VO 2 undergoes a thermally induced IMT at the intrinsic critical temperature T c ≈ 340 K accompanied by an SPT between a monoclinic (M 1 ) structure and rutile (tetragonal) structure. The high-temperature metallic phase has rutile structure which is viewed as chains of equidistant vanadium atoms along the rutile c R -axis. The low-temperature insulating phase has monoclinic (M 1 ) structure that consists of twisted V-V dimers with alternating spacing of c R ± 2δ (distortion), i.e. the CDW (Peierls) ordering, which generates bonding-antibonding electronic bands. Given the presence of CDW ordering in the M 1 structure, in early works the IMT was considered a Peierls transition 5,6 . However, subsequent experimental and theoretical works demonstrated the significance of electron-electron correlations to the IMT [2][3][4]9 . Some even posited a new kind of Mott insulator whose ground state is the Peierls ordered phase rather than the antiferromagnetic phase expected in classical Mott insulators 10 . Nevertheless, modern theoretical schemes explain that the IMT and the insulating phase have one aspect in common. Specifically, the calculations in the insulating M 1 phase of VO 2 are based on the Peierls ordered structure and the V-V dimers are considered a necessity for a quantitative description. Indeed, even state-of-the art Dynamical Mean-Field Theory (DMFT) calculations, while emphasizing the significance of electronic correlations, use a cluster-DMFT method based on the primacy of the vanadium pairs 10,11 . This is attributed to the complexity of the electron-electron interactions and the CDW instability in the M 1 structure.
On the other hand, VO 2 films grown on rutile (001) TiO 2 substrates in previous experimental works [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] provide an opportunity to consider the IMT in a simpler structure. For thicker VO 2 films grown on rutile (001) TiO 2 substrates, the T c is close to the intrinsic value of ≈340 K and decreases as the film thickness is reduced. Much of the previous literature has focused on films of thickness equal to or larger than 10 nm and in these films the IMT is accompanied by the SPT 13,16,20 . The electronic IMT in about 4 nm-thick VO 2 films was measured by hard X-ray photoelectron spectroscopy (HAXPES) and X-ray absorption spectroscopy (XAS) but the SPT was not directly measured 28 . A few recent papers have provided evidence in films of reduced thicknesses that the IMT is not accompanied by the SPT 18,22,24 . However, it has been reported that the SPT and the IMT in about 15 nm thick VO 2 film on (001) TiO 2 could occur simultaneously within ±1 K, on the ground that the intensity of the X-ray standing wave sensitively responds to a structural change 26 . In VO 2 films of about 10 nm deposited on (110) and (001) rutile MgF 2 substrates similar to the TiO 2 structure, the SPT between monoclinic and rutile was confirmed by observing Raman scattering 30 . Moreover, in a VO 2 film (thickness of 10 nm) on TiO 2 (001) substrate which can show the SPT between monoclinic and rutile near room temperature, only the IMT was measured, while a VO 2 film (thickness of 5 nm) on TiO 2 (100) substrate did not display the IMT and the SPT near room temperature 31 . Moreover, the orbital assisted metal-insulator transition was suggested in a VO 2 single crystal of much bigger than 7.5 nm thickness, by observing the change of orbital occupation in a manner that charge fluctuations and effective bandwidths are reduced 32 . However, these papers did not directly measure the broadband optical characteristics such as the energy gap which is a defining characteristic of the insulating phase below T c . Nor did they measure the Drude behavior describing the metallic phase above T c . Hence, the electronic structure of the ultrathin films of thickness below 10 nm remains unknown.
To address the question about the origin of the energy gap in insulating VO 2 , we have grown films of different thicknesses on rutile (001) TiO 2 substrates. We found that films with thicknesses below 7.5 nm are in the rutile structure and the monoclinic distortion induced by CDW (Peierls) ordering is absent 25 . This simplifies the problem because what remains to be confirmed is the lattice structure through X-ray diffraction (XRD) below and above T c , the energy gap of the insulating phase, and the Drude behavior in the metallic phase following the IMT.
In this paper, we demonstrate a rutile Mott insulator below T c ≈ 306 K (Fig. 1a) by observing the absence of a structural change, the energy gap of 0.6 eV, and the absence of the CDW bonding-antibonding optical transition. Furthermore, we observe the IMT via the emergence of the Drude feature above T c . These observations were enabled by XRD measurements and broadband infrared and optical spectroscopy in a 7.2 nm thick VO 2 film grown on rutile (001) TiO 2 substrate prepared by pulsed laser deposition (see Methods for details). Moreover, we compare the optical conductivity spectra of ultrathin VO 2 films with that of thicker, bulk-like VO 2 films 33 . Synchrotron XRD data reveal that a 6 nm thick VO 2 film has the same rutile structure above and below T c , and that an 8 nm thick VO 2 film has the M 1 CDW phase below T c . Figure 1a shows the resistance-temperature (R-T) curves measured on a 7.2 nm thick VO 2 film on rutile (001) TiO 2 substrate. The inset in Fig. 1a shows X-ray-diffraction (XRD) patterns of the film measured above and below T c with λ Cu = 1.54056 Å using commercial, table-top X-ray equipment (see "Methods" for details). Apart from the obvious feature from the rutile (001) TiO 2 substrate, there is a broad feature centered at 2θ ≈ 66°. The important point is this broad feature shows no temperature dependence at all and is attributed to rutile VO 2 (see Supplementary Note 2 for more detailed data).

Structural and transport properties
Furthermore, an ultrathin VO 2 film of about 5 nm thickness grown on rutile (001) TiO 2 substrate was imaged by transmission electron microscopy (TEM). Figure 1b shows that the crystalline pattern of the film in real space is the same as that of the substrate demonstrating epitaxial film growth. The reciprocal space selected area electron diffraction (SAED) patterns from a region in the TiO 2 substrate and a region in the VO 2 film are compared in Fig. 1c, d; the patterns are the same. These data are consistent with a previous observation that in a thick VO 2 film grown on rutile (001) TiO 2 , the first 7.5 nm thickness above the film-substrate interface is in the rutile structure 25 . Moreover, ultrathin VO 2 films grown on rutile (001) TiO 2 exist in the rutile structure 18,22,24,29,34,35 . Thus, the VO 2 film in the insulating phase below T c has the rutile structure, as shown in the inset of Fig. 1a, and the complexity in the electronic structure due to the CDW is reduced.
In order to improve signal-to-noise in the XRD measurements, we performed XRD measurements on ultrathin VO 2 films at the Canadian Light Source. Figure 2 shows R-T curves and structural characterization of an ultrathin VO 2 film on the rutile (001) TiO 2 substrate. This film is 6 nm thick. The XRD measurements were performed using X-ray energy of 15.120 keV (a wavelength of λ Synchrotron ≈ 0.82 Å) and an exposure time of 600 s. One dimensional detector (Mythen2 1 K from Dectris), able to measure a wide range of two theta angles with one exposure, was used for data collection. Figure 2a shows R-T curves of the 6 nm thick VO 2 film on (001)TiO 2 . Thickness of the film has been determined by the film deposition rate. Figure 2b shows the XRD patterns obtained from the 6 nm VO 2 film below (279 K, blue curve) and above (338 K, red curve) the IMT T c . Here, a large peak 1 (2θ ≈ 32.2°) comes from the rutile TiO 2 substrate. A broad peak 2 (33.5°-33.7°depicted by a red arrow in Fig. 2b) corresponds to the rutile (002) VO 2 peak confirmed by the fitting (Fig. 2c, d). Importantly, peak 2 does not shift its position across the IMT demonstrating the absence of the SPT. The possible increase of the VO 2 peak intensity at 338 K may be due to thermal broadening of the large TiO 2 peak 36 . A remarkable fact in Fig. 2b is the absence of the monoclinic (M 1 ) VO 2 peak near 2θ = 33°at 279 K, as displayed by a blue diamond in Fig. 2b. The synchrotron XRD data conclusively shows that the 6 nm VO 2 film is in the rutile phase at 279 K (below IMT T c ) and remains in the rutile phase at 338 K (above IMT T c ). Therefore, the IMT in Fig. 2a is not accompanied by the SPT. This is direct evidence of the Mott transition from the rutile insulator phase to the rutile metal phase.
We also performed XRD measurements at the Canadian Light Source on an 8 nm thick VO 2 film on rutile (001) TiO 2 substrate. Thickness of the film has been determined by the film deposition rate. The R-T and XRD data on the 8 nm thick film are shown in Fig. 3a, b respectively. The XRD data reveals a shift of the VO 2 peak upon increasing the temperature across the IMT. This shows that the top few surface layers of the film undergo a SPT between the monoclinic (M 1 ) structure and the rutile structure. The SPT is displayed as a shift from 2θ ≈ 33.0°the monoclinic (-402) VO 2 peak, observed below IMT (277 K, blue curve), to 33.4°, designating the rutile (002) VO 2 peak above IMT (319 K, red curve). Note that the 8 nm thick film exceeds the critical film thickness of 7.5 nm 25 , above which the rutile lattice of the insulating phase relaxes to monoclinic (M 1 ) lattice.

Infrared and optical properties
Broadband infrared and optical spectroscopy was employed to determine the real and imaginary parts of the frequencydependent dielectric function in the metallic and insulating phases of the 7.2, 55, and 90 nm thick VO 2 films grown on rutile (001) TiO 2 (see Fig. 4a-c). From the dielectric function, we obtain the optical conductivity. The real part of the optical conductivity (σ 1 ) is related to the imaginary part of the dielectric function by the equation: σ 1 = ωε 2 /(4π) in CGS units 37 . We plot σ 1 in SI units (Ω −1 cm −1 ) in the insulating and metallic phases of the 7.2 nm thick rutile VO 2 film in Fig. 4a. Peaks in optical conductivity can be attributed to direct optical transitions from a filled band to an empty band. The spectrum below T c in the insulating phase of the ultrathin VO 2 film shows the energy band feature β centered at 1.3 eV and an energy gap (E g ) of 0.6 eV disappearing during the IMT. The feature β is due to the optical interband transition between the filled, lower a 1g band to the empty e π g band 33 . We also observe a feature ξ with band center 3.2 eV and a feature κ with a band center of 4.4 eV in the optical conductivity of the insulating phase 33 .
For the sake of comparison, we have obtained the optical conductivity of two thicker VO 2 films (55 and 90 nm thicknesses) grown on rutile (001) TiO 2 substrates (Fig. 4b, c). The figures show the Y peak corresponding to the peak measured in bulk-like M 1 insulating phase of thick VO 2 film on Al 2 O 3 (ref. 33 and Supplementary Fig. 4). When the optical conductivity spectrum of the ultrathin film (Fig. 4a) is compared to the optical conductivity spectra of the thicker VO 2 films (Fig. 4b, c), the similarities include the existence of features X and Z which correspond to features β and ξ, respectively. However, the Y feature with band center of about 2.5 eV, existing in Fig. 4b, c and Supplementary Fig. 4, is not seen in Fig. 4a. The feature Y in the optical conductivity spectra of the M 1 insulating phase is known to be due to optical interband transition between the a 1g bonding (d || ) and a 1g anti-bonding (d || * ) bands generated due to the CDW (Peierls) ordering of V-V dimers 38,39 . Its absence indicates that the ultrathin VO 2 film has the rutile structure without CDW ordering, as also proven by the analysis of the TEM image in Fig. 1b, d and the absence of a structural transition in the XRD data (Fig. 1a,  inset). Remarkably, the absence of the Y feature indicates that the formation of both the energy gap of about 0.6 eV and the associated optical interband transition β are independent of the Y feature. This further demonstrates that Peierls ordering is not responsible for the formation of the energy gap of β, leading to the conclusion that the forming mechanism of the energy gap is primarily caused by electron-electron interaction. This is different from the conclusion in ref. 40 that cooperative Mott-Peierls MIT characteristic in bulk VO 2 almost holds down to 2.0 nm thick film grown on Nb-doped (001) TiO 2 although ref. 40 does not include direct measurements of the SPT using XRD and the substrate is different from that used in our work.
The feature κ in the spectrum of rutile insulating VO 2 in Fig. 4a is an optical interband transition, which is not evident in the spectra  of insulating M 1 VO 2 (Fig. 4b, c).The feature κ is also seen in the rutile metallic phase (Fig. 4a) and may arise from strong electronic correlations in the strained rutile structure. The feature ξ (and Z) at about 3.2 eV is attributed to the optical transition from the filled O 2p band to the empty e π g band and from the filled a 1g band to the empty e σ g band 11,33,[41][42][43] . The optical conductivity spectrum of the metallic state shows that the weak Drude conductivity in the dc limit (ω → 0) (Fig. 4a) is about a factor of 5 lower than those obtained in the thick bulk-like VO 2 films (Fig. 4b, c). The effective number of delocalized carriers per vanadium atom, N Drude eff , in the metallic state is about four times lower than the value for bulk-like rutile VO 2 metal (see "Methods"). This is primarily because the spectral weight of the free-carrier Drude mode (feature α) in the metallic state is lower compared to that of bulk-like metallic VO 2 [refs. 3,33 ]. Importantly, we observe an optical interband transition (feature β') in the nearinfrared in the metallic state which is similar to that seen in the optical conductivity of the insulating state (see Fig. 4a). Based on the features α and β' in the optical conductivity of the metallic state of the ultrathin VO 2 film, we propose the following scenario. The weak Drude feature arises from delocalized carriers which appear at the Fermi level as a quasiparticle peak (QP). The e π g conduction band stays above the Fermi level and is therefore empty. This leads to the interband transition β' across the energy gap. This interband energy gap remains in parts of momentum space, which can be considered to be a pseudogap. In contrast, bulk VO 2 is metallic in the rutile structure because the Fermi level crosses partly filled a 1g and e π g bands. We have considered the possibility that part of the ultrathin film undergoes the IMT to a bulk-like rutile metal leading to coexisting metallic and insulating phases at T = 330 K (above the IMT T c ). We performed near-field infrared microscopy experiments that are sensitive to in-plane and out-of-plane inhomogeneity 3,44 . Figure 5 shows scattering-type scanning near-field infrared microscopy (s-SNIM) images taken on the 7.2 nm VO 2 on (001) TiO 2 . It is clear that, in the fully insulating phase (T = 300 K) and fully metallic phase (T = 330 K), the film displays uniform infrared properties and there is no phase coexistence. There is phase coexistence at the intermediate temperatures. Images were obtained using a Neaspec GmbH near-field microscope with an Arrow NCPt (Non-Contact Pt) tip illuminated by~10 μm wavelength from a CO 2 laser. The near-field signal was obtained by operating the microscope in the pseudo-heterodyne detection scheme 45 . The signal was detected by an MCT detector and was demodulated at the third harmonic of the tip tapping frequency.
Further support for the empty e π g conduction bands in ultrathin rutile metallic VO 2 comes from the relatively small change in feature ξ between the insulating and metallic states (see Fig. 4a). Feature ξ consists of optical interband transitions from the filled O 2p band to the e π g band 33 . However, it is dominated by spectral weight of the interband transitions from the filled O 2p band to the e π g band as the optical selection rule favors optical transition when there is a change of unity in the orbital angular momentum of the electrons like that between p-orbitals and d-orbitals. In bulk-like VO 2 , there is a drastic reduction in the spectral weight of feature ξ because the empty e π g band in the insulating phase becomes partly occupied in the metallic phase (Fig. 4b, c). Clearly, the relatively small change in feature ξ between the insulating and metallic states in the ultrathin VO 2 film suggests that the e π g band is empty in the metallic state and downshifts by about 0.1 eV. Moreover, the spectral weight of feature ξ is shifted to the QP states in the metallic phase.

DISCUSSION
We discuss this research based on rutile insulator showing the absence of d || * states in the VO 2 films of thickness less than the defined critical value of ≈7.5 nm. We note that previous observations of d || * state of V-V dimers, reported and analyzed in ref. 39 , and more recently measured by XAS (X-ray absorption spectroscopy) and HAXPES were done for epitaxial films with larger than 7 nm thickness grown on VO 2 /TiO 2 (001) and VO 2 / TiO 2 (100) (refs. 31 and 46 ) and VO 2 /Nb:TiO 2 (001) (ref. 40 ). Above all, we review XAS in which an electron is promoted from a core-level to an empty orbital, thus, probing the empty levels, and O K-edge XAS that has been used to probe empty d || * state, associated with the V-V dimers formation 39 . However, XAS, as well as HAXPES, are not direct measurements of crystallographic structure. We notice in the published literature that often there is lack of atomic structure characterization of ultrathin VO 2 films by relevant XRD and TEM techniques. We think that our corresponding results (Figs. 1b-d, 2b-d, 3b) fill the void. Moreover, we also performed indirect measurement of the V-V dimer associated interband peaks by broadband infrared and optical spectroscopy (Fig. 4), and obtained results consistent with those acquired by direct tools like XRD and TEM.
In ref. 31 , the results of XAS and HAXPES for epitaxial 10 nmthick (above ≈7.5 nm critical thickness) VO 2 (T c ≈ 0°C or 278 K) on TiO 2 (001) showed d || * indicating the V-V dimer below T c , which is consistent with our results. However, an epitaxial 5 nm-VO 2 (T c ≈ 100°C or 378 K) on TiO 2 (100) also displayed the d || * band. On the basis of different T c 's, we can suggest that the epitaxial film   on TiO 2 (100) has completely different type and level of strain than the epitaxial film on TiO 2 (001). Moreover, the VO 2 /TiO 2 (100) sample is beyond our research scope. Subsequently, VO 2 films below 10 nm thickness on Nb-doped TiO 2 (001) obtained d||* band by XAS experiments 40 . This is a discrepancy with the results of rutile insulator proposed by X-ray and optical measurements in this research, which may be caused by a difference in lattice constants of TiO 2 and Nb-doped TiO 2 substrates, resulting in different strain imposed on the films. Nb with a larger than Ti ionic radius, as a substitute of Ti in TiO 2 lattice, may cause distortions. Moreover, pure TiO 2 is a good insulator, whereas Nb-doped TiO 2 is conducting, and this difference in electrical conductivity of the substrates may affect properties of ultrathin films grown on these two different types of substrates. Also, the difference may be explained by different growth conditions of the films, which can be also confirmed by differences in resistance-temperature curves measured in our work and in ref. 40 . Nevertheless, these differences allowed us to stabilize the rutile insulating phase for up to 7.2 nm-VO 2 film, that is confirmed by direct and indirect measurements of VO 2 lattice and electronic structure.
Moreover, as for ref. 46 , even though it shows an important scientific result, we note this work is related to VO 2 films with different strain effect grown on TiO 2 (100), while our work focuses on the VO 2 films on TiO 2 (001). These two types of samples are very different due to difference in the in-plane lattice constants of the substrates. Thus, in the case of TiO 2 (100), b-axis (~4.59 Å) and c-axis (~2.96 Å) are in-plane, while in the case of TiO 2 (001), a-axis c Plot of σ 1 in the insulating (black) and metallic (purple) phases of a thick 90 nm VO 2 film grown on rutile (001) TiO 2 . As expected, the Y peak in the thicker 90 nm film is more prominent than in the 55 nm thick film. The Y peak is also slightly red-shifted in the 90 nm thick film due to a higher degree of strain relaxation compared to the 55 nm thick film. (~4.59 Å) and b-axis (~4.59 Å) are in-plane. The different lengths of the a-and c-lattice constants results in a very different tensile/ compressive strain in the VO 2 films grown on TiO 2 (100) and TiO 2 (001), very different T c values (77.6°C vs 19.1°C), and different transition pathway, as described in ref. 31 . We review first-principles DFT/DMFT research on the IMT in rutile VO 2 structure in the presence of strain. The DFT + U (Density Functional Theory with the Hubbard electron-electron correlation parameter U) calculations showed that in the ultrathin VO 2 locked by epitaxial strain in the rutile structure, the change in the electronic state from insulating to metallic can occur by means of changing the U value only from 4.5 to 0.0 eV 22 . Moreover, on the basis of cluster-DMFT (dynamic mean field theory) calculations, it was proposed that under the influence of small external strain, the rutile VO 2 phase can support either metallic or insulating states, or coexistence of both 38 . In particular, it was also shown that the insulating rutile phase can be stabilized in the case of large (about 3.5 eV) values of on-site Hubbard U 38 . We believe our experimental results will further stimulate first-principles theoretical studies.
The Ginzburg-Landau (G-L) calculations of strained VO 2 films in ref. 31 are interesting but provide limited information. The authors of ref. 31 clearly admit that the G-L calculations qualitatively track their experimental results. There are obvious quantitative discrepancies. For example, the experimental T c of the insulatormetal transition (IMT) in VO 2 on (001) TiO 2 is about 20°C lower than the temperature of the structural-phase transition (SPT) between monoclinic and rutile predicted by the G-L theory. The discrepancy between experiment and G-L theory comes from the different mechanisms of the IMT and the SPT. Moreover, it is wellknown that G-L theory is a general, phenomenological theory. The G-L theory may provide a qualitative, macroscopic description of the SPT, but it does not provide insight into the microscopic IMT mechanism.
In conclusion, the rutile insulator and the absence of bondingantibonding CDW gap are discovered in the ultrathin VO 2 films with thickness below 7.5 nm grown by PLD on rutile (001) TiO 2 substrates. This suggests a purely electronic IMT in the rutile structure of VO 2 without the SPT. This result is an important extension of the previously observed IMT without the SPT 4,47 . Moreover, it was suggested that in addition to electron-electron correlations, impurities play a decisive role in the IMT as well [47][48][49][50] . As the surface and interface has many kinds of impurities including oxygen vacancies induced by terraces, facets, and cracks, etc 10,34,35 , and defects induced by shear stress coming from lattice mismatch between substrate and thin film, it follows that impurities may induce the IMT [47][48][49][50] . Moreover, as another evidence of the influence of impurities, it is well known that the resistance jump ratio of 2.5 orders-of-magnitude in VO 2 /TiO 2 films at T c , as shown in Figs. 1a, 2a, and 3a, is smaller than that of about 4 orders-of-magnitude in thick VO 2 /Al 2 O 3 films and a good VO 2 single crystal. This difference results from the exponential characteristic below T c of extrinsic semiconductors (with impurities of 0.018%) that are not able to generate the SPT 47 .

Film growth conditions
The ultrathin VO 2 films were grown on rutile (001) TiO 2 substrates at 500°C via pulsed laser deposition. A KrF excimer laser was used to ablate a metallic vanadium target with a pulse energy of 300 mJ and a repetition rate of 10 Hz. The oxygen pressure was maintained at 20 mTorr while growing and cooling of the sample.

X-ray diffraction measurements
To highlight the growth quality of VO 2 , as well as evolution of its properties across the phase transition, both electrical and structural measurements were performed as a function of temperature. The electrical resistance of the films was acquired using a conventional four-probe system (JANIS CCS-450) equipped with a resistive heater to provide the sample heating up to 350 K. The temperature values were measured by two silicon diode thermometers integrated with an automatic temperature controller. The crystalline structure of the 7.2 nm thick VO 2 film was evaluated by variable temperature X-ray diffractometer (RIGAKU, D/MAX-2500) using Cu Kα radiation with an operating voltage of 40 kV and current of 300 mA. The sample was heated up with a rate 1°C/min and stabilized for 3 min at a particular temperature prior to performing the continuous theta-2theta scans with a 0.01°step. Temperature dependent XRD measurements on the 7.2 nm thick VO 2 film on rutile (001) TiO 2 substrate are shown in Supplementary Fig. 2a. An obvious feature from the rutile (001) TiO 2 substrate is seen in the data. There is also a broad VO 2 feature centered at 2θ ≈ 66°that is independent of temperature indicating that the ultrathin VO 2 film maintains the rutile structure across the IMT.

TEM measurements
The ultrathin VO 2 film used for optical measurements is 7.2 nm thick as determined by grazing-angle X-ray reflectivity (XRR) measurement (see Supplementary Fig. 2b). Grazing-angle XRR measurements were obtained with a Panalytical Empyrean X-ray diffractometer. Atomic Force Microscopy (AFM) scans reveal the film's surface to be very smooth with an rms roughness of 0.2 nm. Epitaxial growth was confirmed by TEM (Fig. 1). For TEM experiments, thin samples that are transparent to electrons were prepared by a focused-ion beam technique using Ga ions as a polisher. The microstructural characterizations were done via cross-sectional observations of VO 2 /TiO 2 with High-Resolution TEM operated at 300 kV. The obtained images were analyzed with DigitalMicrograph software (Gatan Inc.).

XRD measurements using a synchrotron light source
Synchrotron XRD measurements were conducted at the BXDS-WLE beamline in the Canadian Light Source. X-ray energy of 15.120 keV was selected by Si(111) monochromator. Samples were mounted on the heating-cooling stage of HFS350-GI (Linkam Scientific Instruments Inc.) by using a silver epoxy. A K-type thermocouple was attached on the sample stage also by using the silver epoxy. During a low temperature measurement a dry nitrogen gas was blown over the sample to prevent condensation of water moisture. Mythen2 1K, a one dimensional detector from Dectris, was mounted on a detector arm and placed at desired twotheta angles. The sample-to-detector distance was 1128 mm.

Optical measurements and analysis
Spectroscopic ellipsometry at 70°and 75°angles of incidence was performed on the 7.2 nm thick VO 2 film on rutile (001) TiO 2 substrate and on the pristine rutile (001) TiO 2 substrate for photon energies 0.6-6.5 eV (4800 to 52,000 cm −1 ) using the Variable-Angle Spectroscopic Ellipsometer (VASE) from J. A. Woollam Co., Inc. The ellipsometry data was complemented by mid-and far-infrared spectroscopy measurements performed in normal incidence transmission and near-normal incidence reflectance geometries from photon energies 50-740 meV (400-6000 cm −1 ) in a Bruker Vertex 80v Fourier Transform Infrared (FTIR) spectrometer. For all spectroscopy measurements, the sample temperature was varied and monitored using a Lakeshore temperature controller, resistive heaters, silicon diode thermometer, and home-built heating stages to take data above and below T c .
Kramers-Kronig consistent oscillators were employed in the substrate model to fit the ellipsometry, transmission, and reflectance data on the pristine TiO 2 substrate using W-VASE software from J. A. Woollam Co., Inc. Next, the ellipsometry, transmission and reflectance data from the VO 2 films on the substrate was modeled by adding a VO 2 layer to the TiO 2 substrate model. The thickness of the VO 2 layer was equal to the VO 2 film thickness. The data was fit using Kramers-Kronig consistent oscillators in the VO 2 layer. Thus, we obtain the broadband dielectric function of the VO 2 film above and below the IMT temperature (see Supplementary Fig. 3). The real and imaginary parts of the dielectric function are used respectively to obtain the imaginary and real parts of the optical conductivity. Due to the ultrathin nature of the film, we do not observe VO 2 phonon features in the mid-and far-infrared reflectance spectrum which is dominated by the phonons of the TiO 2 substrate.
The effective number of delocalized carriers per vanadium atom, N Drude eff , in the metallic state can be calculated from the conductivity σ Drude 1 ω ð Þ of the Drude oscillator used in the fits to the infrared and optical D.J. Lahneman et al.