Resonant tunneling driven metal-insulator transition in double quantum-well structures of strongly correlated oxide

The metal-insulator transition (MIT), a fascinating phenomenon occurring in some strongly correlated materials, is of central interest in modern condensed-matter physics. Controlling the MIT by external stimuli is a key technological goal for applications in future electronic devices. However, the standard control by means of the field effect, which works extremely well for semiconductor transistors, faces severe difficulties when applied to the MIT. Hence, a radically different approach is needed. Here, we report an MIT induced by resonant tunneling (RT) in double quantum well (QW) structures of strongly correlated oxides. In our structures, two layers of the strongly correlated conductive oxide SrVO3 (SVO) sandwich a barrier layer of the band insulator SrTiO3. The top QW is a marginal Mott-insulating SVO layer, while the bottom QW is a metallic SVO layer. Angle-resolved photoemission spectroscopy experiments reveal that the top QW layer becomes metallized when the thickness of the tunneling barrier layer is reduced. An analysis based on band structure calculations indicates that RT between the quantized states of the double QW induces the MIT. Our work opens avenues for realizing the Mott-transistor based on the wave-function engineering of strongly correlated electrons.


Supplementary Note 3. Structure plot of dzx states for SrVO3 QW structures for designing resonant tunneling in double QW structures
To design double quantum well (QW) structures for resonant tunneling (RT), we utilized the structure plot (the plot of quantization energies as a function of SrVO3 layer thickness) of dzx states for SrVO3 QW structures, as shown in Supplementary Fig. 1. Results with quantum numbers n = 1-4 are shown in red, orange, green, and blue, respectively [3][4][5][6] . The solid lines are predictions for the QW states from the tight-binding (TB) calculation in the renormalized scheme 7 . The TB results reproduce the experimental results, although there are discrepancies between the experiment and the calculation. The discrepancies seem to become larger by approaching the quantization energies to the Fermi level (EF), probably reflecting the unusual band renormalization of the subbands near EF (Supplementary Refs. [3][4][5][6]. By extrapolating the data, the original quantized energy of n = 1 states for a 2-ML SrVO3 QW structure is expected to be in the range of 200-300 meV (hatched green region), although the 2-ML SrVO3 QW is a Mott insulator and its original QW state is localized as the lower Hubbard band (see Fig. 2 in the main text and Supplementary Fig. 18). Judging from the structure plot, we concluded that a 6-ML SrVO3 QW structure is an optimal counterpart in the double QW structure to induce the RT effect between two energetically close QW states: the quantization energy of n = 2 states for the 6-ML SrVO3 QW structure is close to the original quantized energy of n = 1 states for a 2-ML SrVO3 QW structure. The existence of the energetically close QW states in both the top and bottom QW structures suggests the hybridized nature of the envelope wavefunctions of the two subbands, leading to the RT effect between the two QWs. Based on the structure plot, we employed the V2TLV6 double QW structures in the present study.

Supplementary Note 4. Sample growth and characterization
The double quantum well (QW) structures of (N-ML SrVO3)/(L-ML SrTiO3)/(M-ML SrVO3) (VNTLVM) were fabricated onto atomically flat TiO2-terminated 0.05 wt% Nb-doped SrTiO3 (Nb:STO) (001) substrates in a laser molecular-beam epitaxy chamber that is connected under ultrahigh vacuum to an angle-resolved photoemission spectroscopy (ARPES) system at BL-2A MUSASHI of Photon Factory, KEK (see Supplementary Note 6). Sintered SrVOy and SrTiO3 pellets were used as ablation targets. An Nd-doped yttrium aluminum garnet laser was used for target ablation in its frequency-tripled mode (l = 355 nm) at a repetition rate of 1 Hz. During the deposition of both layers, the substrate temperature was maintained at 900°C, and the oxygen pressure was maintained at less than 10 -8 Torr (Supplementary Refs. [3][4][5][6]8). Note that each layer of the double QW structures was grown under the same conditions as those of previously reported QW structures, wherein coherent growth on the substrate and the formation of a chemically abrupt SrVO3/ SrTiO3 interface were achieved [3][4][5][6]8 . During the growth of each layer, the thickness was precisely controlled at the atomic scale by monitoring the intensity oscillation of reflection highenergy electron diffraction (RHEED) spots. As a typical example, the RHEED intensity oscillations during the growth of a V6T2V2 heterostructure are shown in Supplementary Fig. 2.
The clear RHEED oscillations during the growth of the SrVO3 and SrTiO3 layers indicate a layerby-layer growth. The period of oscillation corresponds to the deposition of one monolayer (ML) of SrVO3 and SrTiO3, which was also confirmed using the deposition rate estimated from grazingincidence x-ray reflectivity measurements. The high surface quality, surface flatness, and epitaxial growth of each layer are confirmed by the RHEED patterns which show sharp streak patterns and Kikuchi lines at all growth stages. Furthermore, the almost identical RHEED pattern after SrVO3-layer deposition indicates that the top and bottom SrVO3 layers are grown with almost identical crystallinity.
The surface morphologies of the prepared QW structures were analyzed by atomic force microscopy (AFM). Atomically flat surfaces with step-and-terrace structures, which reflected the morphology of the Nb:STO substrate, were clearly observed for all samples, indicating that not only the surface but also the buried interfaces were atomically flat. As a typical example, the AFM image of a double QW structure after fabrication is presented in Supplementary Fig. 3.
A clear step-and-terrace structure is observed even after fabricating the VNTLVM double QW structure. The surface structures and cleanness of the measured double QW structures were also -6 -confirmed via low-energy electron diffraction (LEED) and core-level photoemission measurements, respectively. The LEED patterns exhibited sharp 1 × 1 spots with some superstructure spots of √2×√2-R45° for all samples. The prepared films were transferred to the photoemission (PES) chamber under an ultrahigh vacuum of 10 -10 Torr. The in-vacuum transfer was necessary to avoid degradation of the SrVO3 surfaces upon exposure to air ( Supplementary Fig. 11). The surface cleanness and stoichiometry of the samples were carefully characterized by analyzing the relative intensities of the relevant core levels.

Core-level analysis for SrVO3/SrTiO3 interfaces
We present evidence that the prepared double QW structures have atomically and chemically abrupt SrVO3/SrTiO3 interfaces. This feature is a precondition to the present study on the double QW structures, and the evidence demonstrates that the precondition is fulfilled. Supplementary   Figure 4 shows the Ti 2p core-level spectra of SrVO3/SrTiO3 with varying SrVO3 overlayer thickness t, as well as a SrTiO3 substrate as a reference. The spectra shown in Supplementary core level maintains its original Ti 4+ feature, indicative of the invariance of the chemical environments even at the interface, although slightly asymmetric spectral behavior is observed for thicker SrVO3 films owing to the formation of the Schottky barrier 3,9 . To evaluate the length of the possible interdiffusion, we plot ITi as a function of t in Supplementary

Core-level analysis for digital control of SrTiO3 layers
The excellent agreement between the experiment and calculation presented in Supplementary Fig.   4 also indicates the successful digital control of the SrVO3 layer thickness. We also evaluate the thickness of a SrTiO3 barrier layer sandwiched between SrVO3 layers using core-level spectra.  The line shape of the Ti 2p core level maintains its original Ti 4+ feature, indicative of the invariance of the chemical environments even at the interface. Although the core levels remain almost identical, the width of the main peak at 458.5 eV is slightly broadened with reducing L.
The slight broadening of the main peak may be due to the metallization of the top SrVO3 layer through the resonant tunneling (RT) effects. In addition, an almost exact match between L = 10 and ∞ indicates that there is no fundamental difference between the SrTiO3 barrier layers and SrTiO3 substrates.
In contrast to the Ti 2p core levels, the other ones mainly reflect the chemical states of the top 2-ML SrVO3 layer owing to the probing depth of the XPS measurements. For V 2p core levels, the complicated final-state effects 11 and some contributions from the bottom SrVO3 layers make any quantitative analysis difficult, although the existence of V 5+ states at 517.5-518 eV due to the surface oxidation [12][13][14] is hardly seen in the spectra. For this reason, the V 2p core levels were

Characterization of double QW structures by HAADF-STEM measurements
Supplementary Figure 9 Supplementary Fig. 12b), whereas the dxy-and dyz-derived subbands in the LV mode ( Supplementary Fig. 12d). In other words, the polarization-dependent ARPES enables the determination of the subbands of dzx states and dxy/dyz-states separately.

Supplementary Note 8. Analysis of ARPES spectra 8.1 ARPES images
Supplementary Figure 13 shows the ARPES intensity plots in the energy-momentum (E-k) space of V6T2V2 and V2T2V6 double QW structures, together with their curvature intensity plots 18 . The intensity modulation of the ARPES images between the left and right sides with respect to the centerline (kx = 0 Å -1 ) is due to pronounced matrix-element effects. In order to show the band structure more clearly, we display the images enclosed by the dotted squares in the main text (Fig.   3). Note that we carefully checked that the band dispersion itself is almost the same between the ARPES intensity plots and the curvature plots by picking up the peak position from the raw data ( Supplementary Fig. 14). The solid lines show the DFT results for the dzx quantization states (Fig. 3 in the main text and Supplementary Fig. 26). Error bars reflect the uncertainties originating from the energy resolution and the standard deviation in the peak positions of MDCs and EDCs.

Momentum distribution curves for a series of V2TLV6 double QW structures
Supplementary Figure 15 shows the ARPES images of a series of V2TLV6 double QW structures.
The data are the same as those in Fig. 2

Momentum distribution curves for band crossing EF
Supplementary Figure 17 shows the MDCs in the energy range from 0.1 eV to -0.04 eV for a series of V2TLV6 double QW structures to confirm the emergence of the subband crossing over EF. For V2T2V6, it is clearly observed that the MDC peaks, which correspond to the band dispersion in the rightmost panel of Fig. 2 in the main text ( Supplementary Figs. 13b, 14b, and the rightmost panel of Supplementary Fig. 15

ARPES images for a series of V2TLV5 double QW structures
Supplementary Figure 21 shows the ARPES images for a series of V2TLV5 double QW structures, together with an ARPES image of V2T2V6 (the same as that in Fig. 2  Interestingly, a closer look reveals that the intensity of the coherent band in V2T2V5 is much weaker than that in V2T2V6. This intensity reduction in the metallic band may be attributable to the energy offset of the corresponding QW states (between n = 2 in the bottom QW structure and n = 1 in the top one, as shown in the structure plot in Supplementary Fig. 1), suggesting that the MIT is derived from the resonant tunneling in the double QW structures. images. Note that the series of ARPES spectra are normalized to the incident photon flux, and the normalized intensity is given by a color scale shown on the right-hand side.

ARPES images for V2T2V5 and V5T2V2
Supplementary Figure 22 shows the ARPES intensity plots and their corresponding curvature intensity plots in the energy-momentum (E-k) space of V5T2V2 and V2T2V5 double QW structures in the same manner as in Supplementary Fig. 13. It should be noted that there is no detectable difference in the dispersion of the metallic band appearing at the top 2-ML QW between V2T2V5 and V2T2V6 ( Supplementary Fig. 13), reflecting the resonant tunneling nature of the metallization.

Supplementary Note 12. Contributions from bottom QW states in ARPES images
Supplementary Figure  This value is in line with the experimental results shown in Supplementary Fig. 20.
black lines) correspond to the quantization energies (subband minimum energies). Note that the DFT results are presented in the same manner as in Fig. 3 in the main text, while the result for V2TLV6 with L = 2 is the same as that in Fig. 3.

Termination-layer dependence
Supplementary Figure 29 shows the DFT calculations for VO2-terminated (the same as those in Fig. 3 in the main text) and SrO-terminated V2T2V6 structures. At first glance, there is no significant difference between the two. However, a closer look reveals that the QW states in the SrO-terminated 2-ML SrVO3 QW (n2ML) rigidly shift toward lower binding energies, resulting in a resonant tunneling (RT) effect between n2ML = 1 and n6ML = 3 (n2ML = 2 and n6ML = 5), owing to the proximity of the respective quantization energy levels. Although the weak but distinct hybridization effect in the SrO termination is also confirmed by the existence probability shown in Supplementary Fig. 30, the RT effect in the SrO termination is much weaker than that in the VO2 termination, reflecting the larger difference in the quantization energies of the original QW states.
It should be noted that the termination layer of the fabricated double QW structure is a VO2 atomic layer, since we used TiO2-terminated SrTiO3 substrates 19 . Thus, we compared the ARPES results with the DFT calculations for the VO2-terminated V2T2V6 structure. Indeed, as can be seen in Fig. 3 in the main text, the experimental data show much better agreement with the VO2terminated V2T2V6 structure.