Strain-stabilized interfacial polarization tunes work function over 1 eV in RuO_2/TiO_2 heterostructures

Domain: neuroscience
Published: 2026-02-09
Editorial outcome: minor_revision

Abstract
Interfacial polarization–charge accumulation at the heterointerface–is a well-established tool in semiconductors, but its influence in metals remains unexplored. Here, we demonstrate that interfacial polarization can robustly modulate surface work function in metallic rutile RuO2 layers in epitaxial RuO2/TiO2 heterostructures grown by hybrid molecular beam epitaxy. Using multislice electron ptychography, we directly visualize polar displacements of transition metal ions relative to oxygen octahedra near the interface, despite the conductive nature of RuO2. This interfacial polarization enables over 1 eV modulation of the RuO2 work function, controlled by small thickness variations (2-3 nm), as measured by Kelvin probe force microscopy, with a critical thickness of ~4 nm–corresponding to the transition from fully-strained to relaxed film. These results establish interfacial polarization as a powerful route to control electronic properties in metals and have implications for designing tunable electronic, catalytic, and quantum devices through interfacial control in polar metallic systems.

Introduction
Interfacial polarization is a cornerstone of modern oxide electronics, playing a pivotal role in phenomena ranging from two-dimensional electron gases at perovskite interfaces1 to emergent ferroelectricity in confined geometries2. In insulating or semiconducting oxides, such polarization can be engineered via epitaxial strain, chemical modulation, or structural asymmetry, leading to functionalities such as switchable dipoles, band bending, and interface conductivity3–5. In contrast, the extension of these design principles to metallic systems has long been thought untenable due to the strong screening of long-range Coulomb interactions by free carriers6. This view has been upended by the emerging class of polar metals7,8, in which metallic conductivity and non-centrosymmetric, polar structures coexist—a concept once considered incompatible. Experimental and theoretical studies have shown that polar distortions can persist in metals under specific symmetry, bonding, and lattice-dynamical conditions9–12. Notably, chemically doped ferroelectrics4,13, strain-tuned perovskites14, and symmetry-driven design strategies15 have yielded polar metals exhibiting phenomena such as enhanced thermoelectricity10,16,17, non-trivial band topology18,19, spin-polarized transport20,21, and ferroelectric-like superconductivity22,23. These discoveries challenge long-standing assumptions and suggest a broader design space for materials that harness both conductivity and polarity.

Several 3d perovskite-based systems have demonstrated coexisting polar displacements, metallicity, and even magnetism24–26. However, exploration beyond perovskites remains limited, and interfacial polarization in metallic rutile oxides—a structurally distinct family—has not been previously demonstrated. Furthermore, direct, spatially resolved identification of such polarization in metallic systems has not been possible thus far, hindering our understanding of its microscopic origin and macroscopic impact.

In this article, we investigate epitaxial heterostructures of RuO2 on TiO2 (110) to reveal the existence and consequences of interfacial polarization in a rutile-based metallic system. RuO2 is a chemically stable, highly conductive oxide with a tetragonal rutile structure, widely studied for its catalytic properties but not known to exhibit polar distortions. Using hybrid molecular beam epitaxy (MBE), we synthesize atomically smooth, single-crystalline RuO2 films and examine their interfacial structure and electronic properties through multislice electron ptychography, Kelvin probe force microscopy (KPFM), and electrical transport. We uncover a robust, strain-induced interfacial polarization at the buried interface, which induces a compensated interfacial layer and enables modulation of the surface work function by over 1 eV—an extraordinary large effect in a metallic system. The work function, defined as the energy barrier for an electron to escape from a material surface, is a fundamental materials parameter that governs charge injection, carrier transport, and interfacial energetics, and thus plays a central role in applications ranging from energy harvesting to solid-state electronics27. Our findings establish a new paradigm that goes beyond the mere observation of interface dipoles in metals: (1) interfacial polarization in metallic layers can be stabilized and controlled via epitaxial strain and heterostructure, and (2) this polarization can significantly modulate the work function and electronic transport properties of the metallic layers. Together, these insights provide a powerful platform for designing functional materials in which electric fields, mechanical strain, or thickness serve as tunable parameters to control both structural and electronic responses. This work opens new frontiers in polar metals and interface-driven functionalities, with implications for oxide electronics, spintronics, and energy applications.

Results
Epitaxial, atomically precise RuO2 heterostructures via hybrid MBE
To probe the presence of interfacial polarization in metallic RuO2, we synthesized high-quality TiO2/RuO2/TiO2 (110) heterostructures using hybrid MBE. For RuO2/TiO2 (110), the lattice mismatches between RuO2 and TiO2 are −4.7% along the [001] and +2.3% along the [1\bar{1}0]. Specifically, a 2.5 nm TiO2 buffer layer, a 3.8 nm thick RuO2 film, and a 2.5 nm TiO2 capping layer were sequentially grown on a TiO2 (110) single-crystalline substrate. The symmetric architecture—with identical buffer and cap layers—was designed to eliminate surface- and substrate-induced variations, thereby isolating interfacial effects intrinsic to the RuO2/TiO2 interfaces. X-ray reflectivity (XRR) measurements (Fig. 1a, scattered symbols) show pronounced Kiessig fringes, indicating well-defined layer thicknesses and interfaces. The excellent agreement between the experimental data and the fitting model (solid line in Fig. 1a) confirms the precise control of the RuO2 thickness, tRuO2=3.8 nm. Complementary structural characterization using X-ray diffraction (XRD) θ−2θ scans (Fig. 1b) shows strong (110) Bragg reflections consistent with the rutile phase, accompanied by Laue oscillations near the TiO2 (110) peak. These features signify a high-quality heteroepitaxy. An atomic force microscopy (AFM) image (inset, Fig. 1b) further verifies an atomically flat surface morphology, with well-defined step-terrace structures and a root mean square roughness (Sq) of 155 pm.

Atomic-scale visualization of polar displacements via electron ptychography
The presence of polar displacements at the RuO2/TiO2 interfaces was directly visualized using cross-sectional multislice electron ptychography (Fig. 1c–e and Supplementary Figs. S1–S3), which revealed the emergence of out-of-plane electrical dipoles. Multislice electron ptychography28,29 is a computational phase retrieval technique that uses coherent interference in four-dimensional scanning transmission electron microscopy (4D-STEM) to iteratively reconstruct the incident electron probe and the phase shifts introduced by electrons scattering within the object, which scales with the projected potential. The result is to largely remove the effects of dynamical scattering and the deconvolved object with 3D information29. The greatly improved resolution and linear atomic number dependence allow for precise measurement of both oxygen and cation atom column positions, and thus polar displacements, within the electron microscopy sample.

To ensure accurate measurement of interfacial polar distortions, we focused on the TiO2/RuO2/TiO2 heterostructure, which symmetrically preserves the ultrathin RuO2 layer. In contrast, samples RuO2 as the topmost layer–such as those in RuO2/TiO2 stacks without a TiO2 capping layer – are susceptible to surface damage during sample preparation for electron microscopy. Our analysis specifically focused on fully strained RuO2 films with thicknesses below 4 nm, where the polar phase was confirmed by optical second harmonic generation (SHG) measurements (Supplementary Fig. S4)30.

The left panel of Fig. 1c displays a high-resolution ptychographic reconstruction of the TiO2/RuO2/TiO2 (110) heterostructure. The reconstructed object consisted of 20 slices, each 1 nm thick. The average of only the middle three slices (the 9th-11th slice) is displayed and analyzed. This removes the electron beam-induced damage and amorphous sample contamination on the surface, and also reduces the effect of tilt and surface relaxation of the thin sample. The Ru, Ti, and O atom columns in the rutile structure are clearly resolved in the averaged reconstructed phase. Since the reconstructed phase scales with atomic number (Z0.67)29, RuO2/TiO2 interfaces were identified by analyzing the relative cation peak phase (Supplementary Fig. S2), marked by horizontal lines. These interfaces are atomically abrupt, consistent with XRR results. Based on the boundaries obtained from the ptychographic reconstruction, tRuO2 is determined to be 3.9 nm, in excellent agreement with the XRR analysis (3.8 nm). With precise measurement of the Ru, Ti, and O atom column positions, we extracted displacement vectors of Ru and Ti cations relative to their surrounding anion framework of four oxygens, shown as yellow arrows in the right panel of Fig. 1c. These displacements indicate the presence of polar distortions across both interfaces. Notably, the polarization vectors at the upper and lower interfaces point in opposite directions, each oriented from the TiO2 into the RuO2, consistent with mirror-symmetric interfacial polar fields.

To quantify this effect, Fig. 1d plots the average out-of-plane polar displacement component along a selected atom plane (marked in Fig. 1c). A significant out-of-plane polar displacement – up to ~9 pm (17.4 pm locally) – is observed in the TiO2 layers and propagates into the adjacent RuO2 regions, indicating a breakdown of inversion symmetry within the metallic RuO2 at the interfaces. In contrast, in-plane displacements (Supplementary Fig. S3) are relatively small, emphasizing the anisotropic nature of the polar distortion. We also performed two additional ptychography reconstructions that captured most of the TiO2 capping layer and TiO2 substrate (Supplementary Fig. S5), revealing that the polarization approaches nearly zero at both the top surface and the substrate regions. Additionally, cation-only displacement analysis showed no measurable distortion (Supplementary Fig. S6), excluding oxygen-vacancy-driven effects as the source of the interfacial polarization suggested in previous studies31.

This observation aligns with first-principles predictions: although strained RuO2 shows lattice instabilities at the Brillouin zone boundary32, it lacks zone-center soft modes, suggesting strain alone cannot stabilize a polar ground state. We hypothesize that the spontaneous polarization arises from the coherently strained TiO2 layer at the RuO2/TiO2 interface and extends into the RuO2 layer, causing local symmetry breaking along the out-of-plane [110] direction. Although bulk TiO2 is nominally non-polar, interfacial effects in the fully strained RuO2/TiO2 system – such as inversion symmetry breaking and the continuity of octahedral networks across the interface – can induce polar behavior near the interfaces. Our first-principles calculation suggests the lattice mismatch between RuO2 and TiO2 can induce the [110] polarization in the TiO2 layer (Supplementary Fig. S7). We also confirmed that the strain effect can modify density of states (DOS) near the Fermi level in the metallic RuO2 layer (Supplementary Fig. S8). This coupling between polar TiO2 and metallic RuO2 layers underpins the emergence of interfacial polarization in this system. To examine possible cation intermixing effects on the observed polarization, we synthesized TixRu1-xO2/TiO2 (110) epitaxial films with varying x and found that increasing Ti content substantially suppresses the SHG response (Supplementary Fig. S9), ruling out intermixing layers as the origin of the polar behavior.

Thickness- and strain-modulation of work-function on metal surface
It is conceivable that the observed interfacial polarization, oriented from the TiO2 substrate toward the RuO2 film as revealed by electron ptychography (Fig. 1), should enhance the surface work function (Φ) of RuO2 by contributing an additional internal electric field at the interface. To test this hypothesis, we performed KPFM measurements on uncapped RuO2/TiO2 (110) thin films with varying tRuO2 (see Supplementary Fig. S10 for sample details). The KPFM setup, illustrated in Fig. 2a, measures the local contact potential difference (VCPD) between the conductive tip and the sample surface, from which Φ is determined using Φ = Φtip − qVCPD, where Φtip is the work function of the tip (calibrated by Ultraviolet Photoelectron Spectroscopy (UPS), see Methods for details) and q is the elementary charge. Surface potential mapping for samples with tRuO2 = 3.1, 3.9, and 5.2 nm (Supplementary Figs. S11 and S12) revealed consistent topography with Sq values around 200 pm and uniform VCPD across the scanned area. The small standard deviation in VCPD (~1.6 mV) ensured high precision, while the mean VCPD values showed significant dependence on tRuO2.

Notably, Φ exhibited a non-monotonic trend with a peak at a critical thickness (tc) of ~4 nm, implying additional polarization-related effects. As shown in Fig. 2b, Φ increases from 4.25 eV at tRuO2 = 1.5 nm – close to the bulk TiO2 value of 4.1 eV (Supplementary Fig. S13)33 – to a maximum of 5.40 eV at tRuO2 = 3.5 nm. It then decreases up to tRuO2 ≈ 7 nm, indicating the suppression of the strain-induced interfacial polarization at the surface, and subsequently follows a gradual linear increase, reaching 5.05 eV at 17.2 nm – consistent with previously reported values for (110)-oriented RuO2 surfaces34,35. This non-monotonic behavior deviates from the monotonic Φ vs. thickness trends observed in conventional heterostructures36–38, and suggests the presence of an additional internal electric field, directed from RuO2 surface toward the TiO2 substrate. This electric field, originating from the polarization within TiO2 and oriented toward RuO2, effectively increases Φ, consistent with the direction of polar displacements observed at the RuO2/TiO2 interface via electron ptychography (Fig. 1).

To understand the origin of the peak in Φ at tc of ~ 4 nm, we performed X-ray diffraction reciprocal space maps (RSMs) of RuO2/TiO2 (110) films, indicating that strain relaxation begins between 4 and 6.5 nm, aligning with the critical thickness observed in KPFM. RSMs around the TiO2 (332) and (301) Bragg peaks (Fig. 2c, d, and Supplementary Fig. S10d) show that at tRuO2 = 4 nm, RuO2 remains fully strained along [001], while partial relaxation appears at 6.5 nm as Q001 shifts toward bulk RuO2. We also confirmed the fully strained state of ultrathin 2 nm RuO2 layers along [001] and [1\bar{1}0] both in-plane using two-dimensional materials40,44 – obtained via diverse methodologies in previous studies. Our films exhibit an exceptionally large work function modulation of ~1.15 eV (red line), far exceeding the typical variation (<0.5 eV) achieved via thickness control of the metallic thin films (Supplementary Fig. S16) or external strain45. This variation is comparable to leading examples – such as the ∼1.2 eV shifts observed in molecule-adsorption studies on metal surfaces40 – yet is achieved here without any surface modification.

Interfacial polarization effects on electrical transport
To investigate the relationship between interfacial polarization and charge transport, we performed electrical transport measurements on RuO2/TiO2 heterostructures, as shown in Fig. 4, Supplementary Figs. S17 and S18. Figures 4a, b display the room-temperature 2D conductivity (σ2D) for RuO2/TiO2 and TiO2/RuO2/TiO2 heterostructures as a function of tRuO2. Given the presence of interfacial polar displacements at the RuO2/TiO2 interface (Fig. 1) and the non-monotonic dependence of the work function on tRuO2 (Fig. 2b), it is plausible that the interfacial regions exhibit distinct transport behavior compared to the intrinsic bulk of RuO2. Therefore, the measured σ2D arises from parallel conduction channels, as illustrated schematically in the insets of Fig. 4a, b. For the RuO2/TiO2 structure, σ2D can be modeled as a parallel sum of bulk conductivity (σb) and interfacial conductivity (σi1), expressed as: σ2D = (tRuO2 − ti1)·σb + ti1·σi1 = tRuO2·σb − ti1·(σb − σi1), where ti1 is the effective thickness of the interface. Assuming σi1 ≪ σb – consistent with prior reports of reduced conductivity in polar metals8, this simplifies to: σ2D = tRuO2·σb − ti1·σb. In this linear form, the slope corresponds to σb, the x-intercept yields the effective interfacial thickness ti1. Fitting the experimental data in Fig. 4a yields σb = 15,875 S/cm – of the same order of magnitude as the bulk RuO2 value of 28,400 S/cm46 – and ti1 = 1.59 nm. Using these results and a representative data point at tRuO2 = 2.1 nm, we estimate σi1 = 4,117 S/cm, supporting the self-consistency of the model and validating the assumption that σi1 ≪ σb. The estimated σi1 values is of the same order of magnitude as that of known polar metals (e.g., La-doped BaTiO3), consistent with the reduced conductivity characteristic of polar metals8. For TiO2/RuO2/TiO2 heterostructures, the total σ2D includes contributions from both the lower and upper interfaces, expressed as: σ2D = tRuO2·σb – (ti1 + ti2)·{σb − (σi1 + σi2)}, where ti2 and σi2 are effective thickness and conductivity at upper RuO2/TiO2 interface, respectively. Assuming σi1 + σi2 ≪ σb, the simplified linear fit (Fig. 4b) gives σb = 11,700 S/cm and a combined interfacial thickness ti1 + ti2 = 0.71 nm. These linear trends persist at low temperatures (1.8 K and 100 K), as confirmed in Supplementary Fig. S18, with fitting results summarized therein. Interestingly, both σb and the effective interfacial thicknesses (ti1 or ti1 + ti2) increase as temperature decreases. The rise in σb is indicative of metallic behavior, while the expansion of the interfacial thickness may reflect a broader interfacial region with suppressed conductivity. This temperature dependence supports the coexistence of polar and metallic phases within the RuO2 layer.

Moreover, across all temperatures, σb in TiO2/RuO2/TiO2 heterostructures is consistently lower than in RuO2/TiO2 films, and ti1 + ti2 is smaller than ti1 alone. The extracted value of ti1 + ti2 = 0.71 nm at 300 K, or roughly two unit cells of RuO2, agrees well with the polar interfacial region observed via ptychography (Fig. 1c). This reduction in effective interfacial region suggests that the opposing interfacial polarizations at the top and bottom interfaces of the TiO2/RuO2/TiO2 stack—confirmed by Fig. 1c—partially cancel each other, reducing the net interfacial region. Interfacial polarization effects are further reflected in the 2D carrier density (n2D) and mobility (μ) as functions of tRuO2, shown in Fig. 4c–f. These quantities were extracted from magnetic (H)-field-dependent Hall measurements at room temperature, using linear fits between ±9 T (Fig. 3d inset and Supplementary Fig. S17). For RuO2/TiO2 films, n2D shows a dip, while μ exhibits a peak near tRuO2 ≈ 3.5 nm – closely matching the tc observed in KPFM measurements. We attribute qualitatively this behavior to an additional interfacial contribution arising from polarization-induced carrier localization, which leads to the dip in n2D. For thicker films (t > 4 nm), n2D increases almost linearly with thickness, suggesting a nearly constant 3D carrier density (n3D = n2D/t). In contrast, the reduction in μ above tc is likely due to enhanced carrier scattering associated with structural defects generated during strain relaxation. In TiO2/RuO2/TiO2 films, although n2D remains relatively featureless (Fig. 4d), μ shows a peak at tRuO2 ≈ 1.9 nm, aligning with the smaller interfacial thickness (ti1 + ti2) compared to RuO2/TiO2 films. While these measurements reveal a clear “anomaly” in both n2D and μ as a function of tRuO2, they are based on a simplified model that assumes single-channel conduction and neutral interfaces. This assumption overlooks the presence of an electric field in the interfacial region, which is expected to influence the charge conduction profile across the film thickness. A detailed treatment of these interfacial effects should be the focus of future investigations.

In summary, our study demonstrates the coexistence of interfacial polarization and metallicity in epitaxial RuO2/TiO2 heterostructures and their controllability via epitaxial design. Cross-sectional multislice electron ptychography reveals atomic-scale polar displacements directed from TiO2 to RuO2 at interfaces. Complementary KPFM measurements show a non-monotonic thickness dependence of the surface work function, which increases by more than 1 eV for RuO2 thicknesses below ~4 nm – coinciding with the regime where epitaxial strain is preserved. Notably, the emergence of electrical polarization is intimately linked to the transport properties of ultrathin, metallic RuO2. By accounting for interfacial contributions, we extract the intrinsic conductivity of RuO2 layers in the heterostructure, finding values comparable to bulk RuO2. This analysis further reveals that the thickness of a compensated interfacial layer is ~1.6 nm in RuO2/TiO2 structures, while it is reduced to ~0.7 nm in TiO2/RuO2/TiO2 heterostructures, consistent with the opposing interfacial polarization observed via electron ptychography. These findings establish a pathway for realizing interfacial polar metallic states via interfacial design, offering new opportunities to simultaneously engineer polarization and conductivity in rutile oxide systems.

Methods
Hybrid MBE and structural characterizations
Epitaxial RuO2 heterostructure films were grown on TiO2 (110) single-crystal substrates (Crystec) using an oxide hybrid molecular beam epitaxy (hMBE) system (Scienta Omicron). The substrate preparation involved sequential cleaning with acetone, methanol, and isopropanol, followed by a 2-h bake at 200°C in a load-lock chamber. Prior to film growth, the substrates underwent a 20-min annealing in oxygen plasma at 300°C. For RuO2 layer growth, a metal-organic precursor, Ru(acac)3, was thermally evaporated using a low-temperature effusion cell (MBE Komponenten) operated between 170 and 180°C. For TiO2 layer growth, titanium was supplied using a liquid precursor, titanium tetraisopropoxide (TTIP, 99.999%, Sigma-Aldrich), which was injected into the MBE system via a line-of-sight gas injector (E-Science Inc.). The injection process was controlled using a customized gas-inlet system with a linear-leak valve and a Baratron capacitance manometer (MKS Instruments Inc.). The growth was carried out under a radio-frequency oxygen plasma at an oxygen pressure of 5 × 10−6 Torr. To minimize the formation of oxygen vacancies, the sample was cooled to 120°C in the presence of oxygen plasma after growth. The film surface evolution was monitored in situ using reflection high-energy electron diffraction (Staib Instruments) before, during, and after growth. Structural characterization—including crystallinity, film thickness, roughness, and strain state—was conducted using X-ray diffraction (Rigaku SmartLab XE) with reciprocal space mapping (RSM), X-ray reflectivity, and θ−2θ measurements. In addition, surface morphology was analyzed using atomic force microscopy (Bruker Nanoscope V Multimode 8) in peak-force tapping mode.

Kelvin probe force microscopy
Kelvin Probe Force Microscopy (KPFM) was performed on an MFP-3D Infinity AFM (Asylum Research, an Oxford Instrument branch, CA) using Pt-coated conductive AFM probes (Multi75E-G, Budget Sensors) in standard amplitude modulation mode. All KPFM measurements were conducted under ambient conditions. The samples were fixed using copper tape connected to ground, and a small amount of silver paste was applied to connect the top surface to the copper tape. Therefore, the RuO2 layer was electrically grounded during KPFM measurements. The KFPM feedback tracks the DC voltage needed to minimize the 2nd harmonic vibration amplitude of the AFM cantilever electrically induced by the applied AC bias (Fig. 2a), which quantifies the contact potential difference (VCPD) between the tip and sample surface. The sample work function Φ = Φtip − qVCPD. The tip work function Φtip is calibrated by measuring the VCPD on a reference sample, 5.2 nm RuO2/TiO2 (110), whose work function is determined by ultraviolet photoelectron spectroscopy (UPS), as shown in Supplementary Fig. S12. Thus, the absolute values of Φ for various samples can be quantitatively determined and compared (standard error propagation were applied).

Ultraviolet photoelectron spectroscopy
Ultraviolet photoelectron spectroscopy (UPS) measurements were conducted using an Omicron XPS/UPS system. A DC bias was applied during the measurements to ensure the spectra would be within the detector range, which has been corrected in the presented data. The work function value (Fermi level is set at zero on the UPS spectra after correction) of the sample was calculated by Φ = hν − Esec, where hν is the photon energy (21.2 eV for the He I ultraviolet source), and Esec is high binding energy cutoff (also known as secondary electron cutoff). The value of Esec was determined by identifying the intersection point between a tangent line fitted to the leading edge of the cutoff and the baseline (Supplementary Figs. S12 and 13).

Electrical transport
Electrical measurements were performed using the Van der Pauw geometry with aluminum wire bonding in a physical property measurement system (PPMS, Dynacool, Quantum Design, USA) with a temperature range between 1.8 K and 300 K, and a magnetic field range of ±9 T.

Scanning transmission electron microscopy imaging and multislice electron ptychography
Cross-sectional samples for electron microscopy were prepared along the [001] direction using a FEI Helios 600i DualBeam SEM/FIB, followed by Ar+ ion milling. A Thermo Fisher Scientific Themis Z aberration-corrected scanning/transmission electron microscope operating at 200 kV was used for scanning transmission electron microscopy (STEM) imaging and collection of ptychographic 4D-STEM datasets. The beam current was set to 10–15 pA to minimize electron beam damage to the sample surface. For high-angle annular dark field (HAADF) STEM imaging, the incident probe had an 18.9 mrad convergence semi-angle, while the detector collection angle was 72–179 mrad. Image distortions from sample drift were corrected using the revolving STEM (revSTEM) method47 on an 8-frame 1024 × 1024 image series, each frame with a 2 μs dwell time.

For acquiring ptychographic 4D-STEM datasets, the incident electron probe was overfocused by 10 nm and had a 26 mrad convergence semi-angle. The 4D-STEM dataset was collected using a 128 × 128 pixel Electron Microscope Pixel Array Detector (EMPAD)48 with a diffraction pixel size of 0.78 mrad/px, a scan step size of 0.0443 nm/px, and a dwell time of 1 ms. Ptychographic reconstructions were performed using a modified version of the fold_slice29 fork of the PtychoShelves49 software package. The multislice reconstruction engine was a GPU-accelerated maximum-likelihood solver that utilized 16 incoherent probe modes50–52. In total, the reconstruction utilized two 300-iteration stages. In both stages, the depth regularization parameter was 0.1, and the probe was allowed to update from the first iteration. In the second stage, the diffraction patterns were zero-padded by a factor of two to double the real space sampling. The reconstructed sample thickness was 20 nm (1 nm slices), determined by adding several extra slices to the actual sample thickness of 12 nm estimated by the position-averaged convergent beam electron diffraction (PACBED)53. This allows the top and bottom slices to reconstruct the amorphous surface contamination and the electron beam-induced structure. The interior of the sample can be isolated from the surface by averaging only the three middle slices. Additionally, the impacts of sample tilt and surface relaxation are eliminated.

First-principles calculations
We performed first-principles calculations based on density functional theory (DFT)54 as implemented in the Vienna ab initio simulation package55. The projector augmented wave potentials56,57 were used to describe the valence electrons, and the plane-wave kinetic energy cutoff was chosen to be 500 eV. The exchange-correlation function was treated by the generalized gradient approximation of Perdew–Burke–Ernzerhof58. To describe (110)-oriented rutile structures, we used √2 × √2 × 1 supercell structures with three lattice vectors aligned along [001], [110], and [1\bar{1}0], respectively. The theoretical equilibrium lattice constants along [001] and [110] ([1\bar{1}0]) directions of bulk RuO2 were calculated to be 3.119 Å and 6.394 Å, while that of bulk TiO2 were calculated to be 2.970 Å and 6.588 Å, respectively. In the strained structures, the out-of-plane lattice constants were fully relaxed using DFT calculations. The corresponding Brillouin zones were sampled with a 20 × 10 × 10 k-grid mesh. The methodology and analysis for the strain-dependent density of states (DOS) of RuO2 are described in our previous report59.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors present an intriguing study on the modulation of work function exceeding 1 eV in RuO₂/TiO₂ epitaxial\nheterostructures, controlled by the thickness of the RuO₂ layer. The observed variation is attributed to interfacial polarization\ninduced by cation displacements, as revealed through electron ptychography. The manuscript is well-organized and the\nexperimental findings are of potential interest to researchers in oxide electronics and solid-state physics.\nHowever, I find that the current manuscript remains largely phenomenological. To meet the standards of Nature\nCommunications, I believe a deeper physical understanding is required. Specifically, I recommend the inclusion of\ntheoretical modeling or first-principles calculations to substantiate the proposed mechanisms. For instance, how does the\nelectronic density of states evolve in ultrathin RuO₂/TiO₂ heterostructures? Without such insight, the interpretation of the\nexperimental data remains speculative. Below, I outline several technical concerns that should be addressed:\n1. Oxygen Vacancy Formation at the Interface:\nThe authors attribute the observed interfacial polarization to cation displacements. However, prior studies (e.g., Phys. Rev. B\n86, 140102(R)) suggest that oxygen vacancies can induce similar effects in nominally non-polar oxides. Given the\nsignificant lattice mismatch between RuO₂ and TiO₂, can the authors comment on the possibility of oxygen vacancy\nformation at the interface? While post-annealing may suppress bulk vacancies, interfacial vacancies may persist and play a\ncritical role.\n2. Interpretation of Work Function Modulation (Fig. 2b):\n• Grounding Configuration: Fig. 2a indicates that the sample is grounded via the TiO₂ substrate, not the RuO₂ film.\nConsidering the higher work function of RuO₂ relative to the electron affinity of TiO₂, a Schottky barrier is expected at the\ninterface, especially for thicker RuO₂ films. This could impede electron transfer to ground. Yet, the KPFM data show high\nsignal-to-noise ratio. The authors should clarify the experimental setup and confirm that the measured signals originate from\nRuO₂. Including data for a sample with RuO₂ thickness = 0 nm would be helpful.\n• Thickness Dependence: The abrupt increase in work function is attributed to the emergence of polarity in thin RuO₂ films.\nHowever, the subsequent decrease in work function with increasing thickness—falling below the bulk value—is\ncounterintuitive. If bulk RuO₂ is nonpolar, one would expect the work function to asymptotically approach ~5.1 eV from\nabove. The authors should provide a physical explanation for this trend.\n3. Clarification of Figure 2e:\nThe schematic for tRuO2>tc suggests the presence of an electric field throughout the film and polarization from the interface\nto mid-film, implying surface charge accumulation. The authors should clarify the physical meaning of these illustrations and\ndistinguish between the cases more explicitly.\n4. Carrier Density Trends (Figure 4c):\nThe observed minimum in 2D carrier density (n2D) as a function of RuO₂ thickness is not explained. Furthermore, the\nincrease in n2D from 4 nm to 17 nm suggests that the 3D carrier density (n3D=n2D/tRuO) also increases, without signs of\nsaturation. This implies partial carrier localization even at 17 nm thickness. The authors should discuss the possible origins\nof this behavior and its correlation with the work function trend.", "reviewer_2": "Referee report on Nature Communications manuscript NCOMMS-25-58504-T\nIn this paper, the authors report on the realization of RuO2/TiO2 and TiO2/RuO2/TiO2 structures grown by oxide molecular\nbeam epitaxy, their characterization, and the study of some electronic properties.\nMore precisely, advanced STEM analyses allow the polar displacements in TiO2 and at the TiO2/RuO2 interfaces to be\ndetermined. The work function of RuO2 in RuO2/TiO2 structures is studied as a function of the RuO2 thickness using Kelvin\nprobe microscopy. Finally, transport properties are realized for both RuO2/TiO2 and TiO2/RuO2/TiO2 structures\n(conductivity, mobility and Hall effect).\nThe important finding is that the work function is found to depend on the thickness of the RuO2 layer in a non-monotonic\nway. It increases a lot (>1eV) between 2 and 5nm before to decrease abruptly. The maximum work function is found to\ncorrelate with the thickness at which the RuO2 layer relaxes. The STEM analyses show that a polarity is found in TiO2\nlayers and in the metallic RuO2 layer at the interfaces. This polar region does not extend over more than a few unit cells –\nthe electric field in this region is thought to modify the work function.\nThis is a nice paper, interesting and well-written. The results are clearly presented and broadly interesting. I think the paper\ncan be published in Nature communications if the authors convincingly answer the comments and questions listed below.\nComments and questions:\n-A TiO2 buffer layer is used on a TiO2 substrate. Is this necessary because of the unknown state of the substrate “polar”\nsurface?\n-STEM analyses. Can the authors provide the method used to measure the atom displacements in Figure 2c? Also, it seems\nthat the polarization at the bottom buffer TiO2 layer extends to the bottom edge of the reconstructed image. Does the\npolarization also extends to the surface of the capping TiO2 layer? Furthermore, do the authors have information on what\nis happening at the TiO2 buffer layer and TiO2 substrate interface?\n-The TiO2 layers are polar. I am not sure to understand the origin of this polarity. Is a single TiO2 layer on TiO2 found to be\npolar or is this linked to the TiO2/RuO2 interface (although there is no polar discontinuity at the interface).\n-The authors talk about metallic RuO2 and metallic polar RuO2 regions (main text and conclusions). At the same time, the\ntransport analyses reveal the presence of dead layers (precisely the layer region that is polar). Should the phrasing be\nmodified?\n-The KPFM measurements reveal a linear increase of the work function and an anomalous enhancement between 2 and\n5nm. What is the physical reason for the linear enhancement with RuO2 thickness?\n-In line with this question, the data demonstrate that the RuO2 films relax above 5-6nm. However, there is no marked change\nin the work function linear increase with thickness (not taking into account the anomalous enhancement) – and no clear\nchange on the sheet conductance versus thickness – both seem unaffected by the strain relaxation. Is this understood?\n-One is also tempted to conclude from the data that the work function value can simply be tuned by thickness control of the\nRuO2 layer.\n-A very important point that should be clarified. At 4-5nm thickness, there is an abrupt decrease of the work function. As I\nunderstand, the authors propose that this abrupt decrease is linked to strain relaxation. But what is the reason for the\ndecrease? What is physically happening? Looking at Fig. 2e, for thick layers, the dipoles are still there – so what is affecting\nthe work function when strain is released? What is the explanation for the drop in the work function?\n-Following on this, do the authors have STEM and polar displacements profiles for “thick films” – something must be different\nand this information ideally should allow the work function abrupt change to be understood.\n-The authors mention SHG measurements and conclude from a change in SHG intensity as a function of RuO2 thickness\nthat RuO2 becomes non-polar. I am not sure to understand this sinceTiO2 and the TiO2/RuO2 interface remain polar (Fig.\n2e) – why would the SHG signal disappear?\n-In the conclusion the authors claimed that the intrinsic conductivity of the RuO2 layers in the heterostructure has\ncomparable value to bulk RuO2. Can the authors provide an explanation on why can the values of 15875 and 11700 be\ncomparable with 28400 (lines 218 and 225)? It seems like the values extracted are around half of the bulk value.\n-Finally, on Fig. 2c and 2d, the RuO2 film peaks are very difficult to spot – the Figure should be improved.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Responses to the reviewers’ comments\nBlack font: Referee’s comments\nBlue font: Our response\nWe sincerely thank the reviewers for their thorough and insightful evaluation of our manuscript.\nThe comments provided were thoughtful and constructive, and they have significantly helped\nus improve the clarity, depth, and overall quality of our work. We have carefully addressed all\npoints and revised the manuscript accordingly, and we believe the resulting version is much\nstrengthened thanks to their valuable input. A detailed, point-by-point response is provided\nbelow.\nReviewer 1\nComment#1: The authors present an intriguing study on the modulation of work function\nexceeding 1 eV in RuO2/TiO2 epitaxial heterostructures, controlled by the thickness of the\nRuO2 layer. The observed variation is attributed to interfacial polarization induced by cation\ndisplacements, as revealed through electron ptychography. The manuscript is well-organized\nand the experimental findings are of potential interest to researchers in oxide electronics and\nsolid-state physics.\nResponse: We thank the reviewer for the positive remarks.\nComment#2: However, I find that the current manuscript remains largely phenomenological.\nTo meet the standards of Nature Communications, I believe a deeper physical understanding\nis required. Specifically, I recommend the inclusion of theoretical modeling or first-principles\ncalculations to substantiate the proposed mechanisms. For instance, how does the electronic\ndensity of states evolve in ultrathin RuO2/TiO2 heterostructures? Without such insight, the\ninterpretation of the experimental data remains speculative. Below, I outline several technical\nconcerns that should be addressed:\nResponse: We thank the reviewer for the constructive suggestion, which has strengthened the\nmanuscript. Following the reviewer’s recommendation, we performed first-principles\ncalculations to investigate the polarization behavior in our system comprised of strained\nTiO /RuO . The calculations also reveal a clear coupling between epitaxial strain and the\n2 2\nelectronic structure, as evidenced by the modified density of states (DOS) near the Fermi level\nin the metallic RuO layer. The inclusion of these results provides direct theoretical support for\n2\nour experimental findings and further substantiates the role of strain in modulating polarization\nand band structure in this system. The corresponding results and discussions have been\nincorporated into the revised manuscript (see Main Text, Pages 7 and 21, and Supplementary\nInformation, Figs. S6-S7 on Pages 4 and 5).\nComment#3: Oxygen Vacancy Formation at the Interface:\nThe authors attribute the observed interfacial polarization to cation displacements. However,\nprior studies (e.g., Phys. Rev. B 86, 140102(R)) suggest that oxygen vacancies can induce\nsimilar effects in nominally non-polar oxides. Given the significant lattice mismatch between\nRuO2 and TiO2, can the authors comment on the possibility of oxygen vacancy formation at\nthe interface? While post-annealing may suppress bulk vacancies, interfacial vacancies may\npersist and play a critical role.\nResponse: We thank the referee for a thoughtful comment. We are completely aware of the\npotential influence of oxygen vacancies and have carefully considered this aspect in our data\ninterpretation. In the revised manuscript, we now discuss this point explicitly and provide our\nrationale for excluding oxygen vacancies as the dominant factor.\nOur RuO /TiO films were grown at 300 °C (thermocouple) and ~ 225 °C (actual temperature,\n2 2\ncalibrated by pyrometer) which is significantly lower than typical perovskite growth\ntemperatures. At these low temperatures, the likelihood of oxygen vacancy formation is small.\nTo confirm this, we annealed TiO substrates under identical growth conditions which remained\n2\nnon-conductive, indicating negligible oxygen deficiency. Conductivity here serves as an\nindirect measure of oxygen vacancies. We further examined conduction in strained RuO /TiO\n2 2\n(110) films from the TiO side and consistent with our substrate annealing experiments, we\n2\nfound the substrate remained insulating even when RuO films were grown on top.\n140102(R)). No measurable displacement was observed, again ruling out oxygen-vacancy-\ninduced cation displacement as the origin of the interfacial polarization.\n[FIGURE REDACTED]\nFig. R1. (upper) Displacement analysis between cations adopted from [Phys. Rev. B 86,\n140102(R)] using cross-sectional multislice electron ptychographic reconstruction of 2.5 nm\nTiO /t = 3.8 nm RuO /2.5 nm TiO heterostructures. (lower) Averaged cation displacements\nof each atomic plane exhibit negligible values, consistent with the cation-only analysis.\nTo reproduce the observed behavior through oxygen deficiency alone, the oxygen\nconcentration would need to reach approximately one-quarter of a monolayer at the interface\nwhich is an amount that would be clearly visible in our STEM images. No such contrast was\ndetected. Finally, we compared the electrical conductivity of the films before and after oxygen\nannealing and found no measurable change, further confirming the absence of a significant\nconcentration of oxygen vacancies (see our prior work: PNAS 122, e2500831122 (2025).\nAlthough not very sensitive, we have also conducted both XPS and XAS measurements [Sci.\nAdv. 11, eadw7125 (2025); PNAS 122, e2500831122 (2025); APL Mater. 9, 091112 (2021)]\nconfirming that the oxygen vacancy concentration in both RuO and TiO layers is below the\n2 2\ndetection limit.\nWe have included these discussions in the revised manuscript (see Main Text, Page 7, and\nSupplementary Information, Page 4).\nComment#4: Interpretation of Work Function Modulation (Fig. 2b): • Grounding\nConfiguration: Fig. 2a indicates that the sample is grounded via the TiO₂ substrate, not the\nRuO₂ film. Considering the higher work function of RuO₂ relative to the electron affinity of\nTiO₂, a Schottky barrier is expected at the interface, especially for thicker RuO₂ films. This\ncould impede electron transfer to ground. Yet, the KPFM data show high signal-to-noise ratio.\nThe authors should clarify the experimental setup and confirm that the measured signals\noriginate from RuO₂. Including data for a sample with RuO₂ thickness = 0 nm would be helpful.\nResponse: We thank the referee for pointing out this typo. All samples were grounded using\nthe top RuO layer. We have corrected Fig. 2a and updated the Methods section to clarify our\n2\nconfiguration. For the case of RuO thickness = 0 nm (i.e., bare TiO ), the corresponding UPS\n2 2\nmeasurements are provided in Supplementary Fig. S11. Because bare TiO is highly insulating,\n(CPD) and often suffer from low signal-to-noise ratios due to trapped charges. Therefore, we\ndetermined the work function values of bare TiO using UPS. These UPS results have now\n2\nbeen included in Fig. 2b for direct comparison.\nComment#5: Thickness Dependence: The abrupt increase in work function is attributed to the\nemergence of polarity in thin RuO₂ films. However, the subsequent decrease in work function\nwith increasing thickness—falling below the bulk value—is counterintuitive. If bulk RuO₂ is\nnonpolar, one would expect the work function to asymptotically approach ~5.1 eV from\nabove. The authors should provide a physical explanation for this trend.\nResponse: The work function of RuO thin films on TiO substrates depends on two factors:\n2 2\n(1) the band alignment effect between film/substrate due to film thickness; (2) interfacial\npolarization due to epitaxial strain. The former effect results in an increase in surface work\nfunction followed by a saturation, whereas the latter yields a peak-like behavior. We have\nillustrated these two factors in a revised Fig. 2e which explain it qualitatively how these two\nfactors can lead to the observed behavior and also included relevant discussion in the revised\nmanuscript. (See Main Text, Page 9, and Rev. Fig 2e.)\nComment#6: Clarification of Figure 2e:The schematic for tRuO2>tc suggests the presence of an electric field throughout the film and polarization from the interface\nto mid-film, implying surface charge accumulation. The authors should clarify the physical meaning of these illustrations and\ndistinguish between the cases more explicitly.\nResponse: We refer to our response to the previous comment. Figure 2e is now revised to bring\nclarity. We thank the referee for these suggestions. See Main Text, Page 9, and Rev. Fig 2e.\nComment#7: Carrier Density Trends (Figure 4c):The observed minimum in 2D carrier density\n(n2D) as a function of RuO₂ thickness is not explained. Furthermore, the increase in n2D from\n4 nm to 17 nm suggests that the 3D carrier density (n3D=n2D/tRuO) also increases, without\nsigns of saturation. This implies partial carrier localization even at 17 nm thickness. The\nauthors should discuss the possible origins of this behavior and its correlation with the work\nfunction trend.\nResponse: We thank the referee for raising this point. In a conventional semiconductor, the\nthree-dimensional carrier concentration (n ) can be obtained from the slope of the linear\n3D\ndependence of the two-dimensional carrier density (n ) on film thickness. In our experiments,\n2D\nwe observe a clear deviation from this behavior around a thickness of ~ 4 nm which is an\nanomaly that we attribute qualitatively to an additional interfacial contribution arising from\npolarization-induced carrier localization. For thicker films (t > 4 nm), however, n increases\n2D\nalmost linearly with thickness (on linear scale), indicating a nearly constant slope and,\nconsequently, a fixed n . We have clarified this point in the revised manuscript. See Main\n3D\nText, Pages 11-12.\nReviewer 2\nComment#1: In this paper, the authors report on the realization of RuO2/TiO2 and\nTiO2/RuO2/TiO2 structures grown by oxide molecular beam epitaxy, their characterization,\nand the study of some electronic properties. More precisely, advanced STEM analyses allow\nthe polar displacements in TiO2 and at the TiO2/RuO2 interfaces to be determined. The work\nfunction of RuO2 in RuO2/TiO2 structures is studied as a function of the RuO2 thickness using\nKelvin probe microscopy. Finally, transport properties are realized for both RuO2/TiO2 and\nTiO2/RuO2/TiO2 structures (conductivity, mobility and Hall effect). The important finding is\nthat the work function is found to depend on the thickness of the RuO2 layer in a non-monotonic\nway. It increases a lot (>1eV) between 2 and 5nm before to decrease abruptly. The maximum\nwork function is found to correlate with the thickness at which the RuO2 layer relaxes. The\nSTEM analyses show that a polarity is found in TiO2 layers and in the metallic RuO2 layer at\nthe interfaces. This polar region does not extend over more than a few unit cells – the electric\nfield in this region is thought to modify the work function.\nThis is a nice paper, interesting and well-written. The results are clearly presented and broadly\ninteresting. I think the paper can be published in Nature communications if the authors\nconvincingly answer the comments and questions listed below.\nResponse: We thank the reviewer for the positive remarks and for recommendation.\nComment#2: Comments and questions:\n-A TiO2 buffer layer is used on a TiO2 substrate. Is this necessary because of the unknown\nstate of the substrate “polar” surface?\nResponse: This is exactly why we have used MBE-grown TiO buffer layer to have an identical\n2\nsubstrate template for RuO films. As the referee correctly hinted at the surface states of TiO\n2 2\n(or any commercially-available substrate) can be substantially different from one substrate to\nanother substrate even when they are purchased from the same vendor and in the same batch.\nComment#3: STEM analyses. Can the authors provide the method used to measure the atom\ndisplacements in Figure 2c? Also, it seems that the polarization at the bottom buffer TiO2 layer\nextends to the bottom edge of the reconstructed image. Does the polarization also extends to\nthe surface of the capping TiO2 layer? Furthermore, do the authors have information on what\nis happening at the TiO2 buffer layer and TiO2 substrate interface?\nResponse: The atomic displacements in Fig. 2c were defined as the deviations of the transition-\nmetal ions relative to the centers of their surrounding oxygen octahedra. The detailed procedure\nused to quantify these displacements is described in the revised Main Text and the Methods\nsection of the manuscript. As for the question of polarization extending to the surface of the\ncapping TiO , we have performed additional ptychography reconstruction in a representative\n2\nsample (2.5 nm TiO / 2.1 nm RuO / 2.5 nm TiO heterostructure) where we imaged most of\n2 2 2\nthe TiO capping layer. These results show that polarization approaches nearly zero at the top\n2\nsurface. As for the second question, we have looked at TiO substrate region near the\n2\nsubstrate/buffer layer, and no discernible changes were detected. See Main Text, Page 7. and\nSupplementary Information, Figs. S4-S5 Page 3.\nComment#4: The TiO2 layers are polar. I am not sure to understand the origin of this polarity.\nIs a single TiO2 layer on TiO2 found to be polar or is this linked to the TiO2/RuO2 interface\n(although there is no polar discontinuity at the interface).\nResponse: We kindly refer the reviewer to our response to comment#2 of Refree#1. Also (see\nMain Text, Pages 7 and 21, and Supplementary Information, Figs S6-S7, Page 5.) for\nadditional DFT calculations revealing the strain-induced polarization in TiO .\ntext and conclusions). At the same time, the transport analyses reveal the presence of dead\nlayers (precisely the layer region that is polar). Should the phrasing be modified?\nResponse: We appreciate the reviewer’s insightful comment. We have revised the manuscript\naccordingly. Based on our simple model, the interfacial conductivity is estimated to be ~4,117\nS/cm, which is comparable to values observed in highly doped semiconductors [Phys. Rev.\nMater. 7, 010301 (2023)]. This value is still well above the insulating regime. More importantly,\nit is of the same order magnitude as the representative polar metals, such as La-doped BaTiO\n3\n[Phys. Rev. Mater. 7, 010301 (2023)], where the coexistence of polarization and itinerant\ncarriers often leads to an enhanced resistivity compared to the nonpolar metallic state. We have\nincorporated this discussion into the revised manuscript. Furthermore, instead of describing\nthis as a ‘dead layer,’ we now refer to it as a ‘compensated interfacial layer’, highlighting\nthat while the resistivity is enhanced relative to bulk-like RuO , it remains finite and metallic\n2\n(See Main Text, Pages 4, 11, and 12).\nComment#6: The KPFM measurements reveal a linear increase of the work function and an\nanomalous enhancement between 2 and 5nm. What is the physical reason for the linear\nenhancement with RuO2 thickness?\nResponse: We kindly refer the reviewer to our response to comment#5 of refree#1. The work\nfunction of RuO thin films on TiO substrates depends on two factors: (1) the band alignment\n2 2\neffect between film/substrate due to film thickness; (2) interfacial polarization due to epitaxial\nstrain. The former effect yields an increase in surface work function followed by a saturation,\nwhereas the latter yields a peak-like behavior. We have illustrated these two factors in a revised\nFig. 2e which explains qualitatively how these two factors can lead to the observed behavior.\n(See Main Text, Page 9, and Rev. Fig 2e.)\nComment#7: In line with this question, the data demonstrate that the RuO2 films relax above\n5-6nm. However, there is no marked change in the work function linear increase with thickness\n(not taking into account the anomalous enhancement) – and no clear change on the sheet\nconductance versus thickness – both seem unaffected by the strain relaxation. Is this\nunderstood?\nResponse: As for the question of work function dependence on RuO film thickness, we kindly\n2\nrefer the reviewer to our response to comment#5 of refree#1. As for the effect on electrical\nproperties, we refer to the mobility data (Fig 4e-f) which shows a drop in mobility above the\ncritical thickness and is consistent with the increased scattering owing to increased structural\ndefects related to strain-relaxation. We have noted it in the revised manuscript. Main Text,\nPages 11-12.\nComment#8: One is also tempted to conclude from the data that the work function value can\nsimply be tuned by thickness control of the RuO2 layer.\nResponse: Indeed, tuning the work function (or electron affinity) via the thickness control of\nthin films is a well-established approach based on band alignment engineering [Appl. Phys.\nLett. 105, (2014); J. Phys. Chem. C 126, 13929 (2022)]. The novelty of our work, however,\nlies not only in exploiting this conventional band alignment effect but also in utilizing strain-\ninduced interfacial polarization. This interfacial polarization enables modulation of the RuO\n2\nwork function by more than 1 eV, controlled by small thickness variations of only 2-3 nm,\nwhich is beyond what conventional thickness-dependent band alignment alone can achieve.\nComment#9: A very important point that should be clarified. At 4-5nm thickness, there is an\nabrupt decrease of the work function. As I understand, the authors propose that this abrupt\ndecrease is linked to strain relaxation. But what is the reason for the decrease? What is\nphysically happening? Looking at Fig. 2e, for thick layers, the dipoles are still there – so what\nis affecting the work function when strain is released? What is the explanation for the drop in\nthe work function?\nResponse: We kindly refer the reviewer to our response to comment# 5 of refree#1. The work\nfunction of RuO thin films on TiO substrates depends on two factors: (1) the band alignment\n2 2\neffect between film/substrate due to film thickness; (2) interfacial polarization due to epitaxial\nstrain. The former effect yields an increase in surface work function followed by a saturation,\nwhereas the latter yields a peak-like behavior. We have illustrated these two factors in a revised\nFig. 2e which explains qualitatively how these two factors can lead to the observed behavior.\n(See Main Text, Page 9, and Rev. Fig 2e.)\nComment#10: Following on this, do the authors have STEM and polar displacements profiles\nfor “thick films” – something must be different and this information ideally should allow the\nwork function abrupt change to be understood.\nResponse: We agree with the referee’s suggestion but unfortunately, we are unable to conduct\nadditional ptychography imaging on a thicker film due to practical limitation with the current\ndowntime of both the MBE system and the STEM. However, to address this concern, we kindly\nrefer the reviewer to another sensitive measurement using optical second harmonic generation\n(SHG). Consistent with our observed behavior in this work, the SHG measurements on these\nfilms [https://arxiv.org/abs/2405.05838] show a polar point group for film thickness below 4\nnm and a non-polar phase emerge above strain relaxation. We have cited this work in the\nmanuscript to address this potential concern. (See Main Text, Page 6)\nComment#11: The authors mention SHG measurements and conclude from a change in SHG\nintensity as a function of RuO2 thickness that RuO2 becomes non-polar. I am not sure to\nunderstand this since TiO2 and the TiO2/RuO2 interface remain polar (Fig. 2e) – why would\nthe SHG signal disappear?\nReply: We have clarified this point in the revised manuscript: the SHG is a bulk measurement\nwhere the SHG intensity depends on both interface effect and the bulk of the film. A continuous\nincrease in non-polar SHG intensity with thickness above 4 nm suggests a combined effect\nfrom polar and non-polar contribution which is consistent with our finding in this paper. A\ndetailed symmetry experiment and analysis supporting this interpretation has been presented\nin our previous work [https://arxiv.org/abs/2405.05838]. In the present manuscript, our KPFM\nmeasurements consistently show a large strain-dependent variation in the work function, which\nis fully consistent with this observation. We have cited this work in the manuscript to address\nthis potential concern. (See Main Text, Page 9)\nComment#12: In the conclusion the authors claimed that the intrinsic conductivity of the RuO2\nlayers in the heterostructure has comparable value to bulk RuO2. Can the authors provide an\nexplanation on why can the values of 15875 and 11700 be comparable with 28400 (lines 218\nand 225)? It seems like the values extracted are around half of the bulk value.\nResponse: We have addressed this oversight by rephrasing it throughout the manuscript\nincluding in the conclusion. (See Main Text, Pages 10).\nComment#13: Finally, on Fig. 2c and 2d, the RuO2 film peaks are very difficult to spot – the\nFigure should be improved.\nResponse: We thank the reviewer for the helpful suggestion. We have improved the clarity of\nFig. 2c and 2d by adjusting the contrast and labeling the RuO film peaks in Fig. 2d more\n2\nprominently.\nReviewer 3\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This\nis part of the Nature Communications initiative to facilitate training in peer review and to\nprovide appropriate recognition for Early Career Researchers who co-review manuscripts.\nResponse: We thank the reviewer for the positive remarks and for constructive suggestions."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I would like to thank the authors for their thoughtful and thorough revisions in response to the reviewers' comments. The\nmanuscript has significantly improved in clarity, rigor, and overall impact, and I believe it now meets the high standards\nexpected for publication in Nature Communications. I am pleased to recommend acceptance in its current form.", "reviewer_2": "Second referee report on Nature Communications manuscript NCOMMS-25-58504-T\nThe authors have carefully replied to our questions and comments.\nIn particular, STEM analysis details have been provided; DFT calculations have been added and reveal a clear coupling\nbetween the strain state and the electronic structure allowing the modulation of the polarization to be understood.\nThe authors now also do explain how the partial relaxation of the films leads to the reduction (after the peak) of the work\nfunction. Indeed, the correlation with the SHG measurements indicates that, above 6.5nm, the film is non-polar – explaining\nthe observed reduction of the work function.\nWe think that the paper can now be accepted for publication.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_4": "Dear Editor,\nIn the manuscript entitled “Strain-Stabilized Interfacial Polarization Tunes Work Function\nOver 1 eV in RuO2/TiO2 Heterostructures”, the authors reported the interfacial polarization in metallic rutile RuO2 layers in epitaxial RuO2/TiO2 heterostructures. The interfacial polarization enables over 1 eV modulation of the RuO2 work function, as evident by the\nKPFM. The polar metal state in RuO2 is an interesting topic. However, in my viewpoint, the main conclusions are not\nsupported by the provided experimental results. Moreover, some of my comments are close to the concerns raised by the\nprevious referees, yet the authors have not fully addressed them. Shortly, I can not recommend the current version of the\nmanuscript for publication in Nature communications.\nMy main comments are:\n1. I question whether the RuO2 is polar. The authors claim that strain stabilizes a polar phase throughout the film (a\nprerequisite for a \"bulk polar phase\"). However, quantitative STEM analysis in Figure 1d contradicts this. Significant polar\ndisplacements (up to ~10 pm) are almost exclusively confined to the TiO2 layers. Inside the region marked as RuO2, the\ndisplacements drop rapidly to near zero (0-2 pm). This observation invalidates the claim that the metallic RuO2 bulk sustains\na polar structural distortion. The phenomenon is strictly a localized interface dipole, not a bulk phase property. Also,\nalthough there is measured SHG signal (which is weak), it is still not possible to determine whether the signal comes from\nTiO2 or RuO2.\n2. The results of KPFM will be influenced strongly by surface absorption.\n3. the RSM results are poor. The lattice constants used for DFT calculation is 3.119 Å / 6.394 Å for RuO2 and 2.970 Å /\n6.588 Å for TiO2. These data deviate from the values reported in several references (: J. Phys. Chem. C 119, 5, 2692–2702\n(2015), AIP Adv. 9, 015302 (2019), Cryst. Growth Des. 24, 11, 4604–4612 (2024), APL Mater. 12, 101110 (2024), Nature\nCommunications 14:8240 ( 2023),J. Phys.: Condens. Matter 35 405603 (2023) ). Given that the authors regard strain as the\nprimary origin of the interfacial polarization, the lattice constants employed in the calculations should be determined with\nhigher accuracy. Additionally, due to the stress relaxation in the RuO₂ layer, the upper and lower TiO₂ layers should adopt\ndifferent lattice parameters.\nSpecific comments are as follows:\n1. To my knowledge, RuO2 films and TiO2 substrates exhibit the best lattice matching as compared to other substrates such\nas MgO, Al2O3,STO etc.. If the interfacial polarization of RuO2 can be induced by the strain from TiO2 substrates, is it\npossible that such interfacial polarization states are present in the vast majority of RuO2 thin films studied?\n2. The STEM images in Fig.1 show the upward polarization in the top TiO2 layer and the downward polarization in the\nbottom TiO2 layer. Is this a universal phenomenon, or could the results vary across different STEM regions? The authors\nshould provide microscopic characterization results from additional regions.\n3. Moreover, STEM characterization clearly reveals that the polarization is primarily confined within the TiO2 layers and\nsubsequently extends into the RuO2 layer. Because the TiO2 bottom layer is not subjected to any substrate strain, its\npolarized state should originate from interfacial coupling with the RuO2 layer above it. This is puzzling: why an only 2 u.c.\nRuO2 layer with a small polarization can induce a significantly larger polarization in a 8 u.c. TiO2 layer that is not strained by\nthe substrate? If further increasing the thickness of TiO2 bottom layer, does the polarization state still exist\n4. I agree with the previous reviewer: the polar state is not induced within the metallic RuO2 layer, and the term “polar metal”\nshould therefore be avoided in the manuscript. Although the authors argue that their RuO₂ behaves like a highly doped\nsemiconductor, this description does not justify retaining the “polar metal” label.\n5. Figure 3 compares the work function modulations across various materials and methods. I'm not sure about the\nimportance of work function modulation, which needs to be emphasized in the introduction section. Moreover, this figure\ncompares the result of RuO2 only with those of typical metallic systems; however, as they themselves state, the polarized\nRuO2 layer is semiconducting. I therefore recommend that the figure also include data for commonly studied semiconductors\nwhose work functions have been tuned by different strategies.\n6. In the reply to the second Reviewer, the author said that the TiO2 buffer layer on TIO2 substrate is important since \" it can\nmaintain the surface states of TiO2 from one substrate to another substrate even when they are purchased from the same\nvendor and in the same batch”. Why the RuO2 layer used for KPFM measurement is deposited on TiO2 substrate\ndirectly？Is the polarization state of this layer similar with the trilayer sample shown in Figure 1. Therefore，I suggest the\nauthor to also give a STEM result for the bilayer sample adopted for KPFM.\n7. Misleading quantification of \"1 eV\" modulation (Substrate Effect vs. Tuning)\nThe title and abstract claim to tune the work function of RuO2 by \"Over 1 eV\". However, Figure 2b shows that the work\nfunction naturally increases from 4.25 eV (ultrathin limit, explicitly identified as close to the bulk TiO2 value) to 5.05 eV (bulk\nRuO2 value).\nThis baseline increase of 0.8 eV represents the natural transition from the substrate's electronic structure to the film's bulk\nproperties (band alignment), which would occur regardless of polarization. The actual modulation attributable to the specific\n\"strain-stabilized polarization\" mechanism is effectively limited to the \"overshoot\" peak above the bulk value (approx. 5.40\neV peak - 5.05 eV bulk 0.35 eV). Attributing the entire transition range to polarization is scientifically misleading. The authors\nmust explicitly decouple the intrinsic thickness-dependent recovery from the polarization-induced shift.\n8. Invalid mechanism for work function dropping with strain relaxation). The authors attribute the sharp drop in work function\nabove 4 nm to strain relaxation (Fig. 2e). In heteroepitaxy, interfacial layers clamped to the substrate typically retain their\nstrained state even when the upper bulk relaxes. If the work function shift is driven by the buried interface dipole, the\nrelaxation of the top layers should not retroactively destroy the dipole already established at the bottom interface. The\nauthors' model implies a non-physical \"action-at-a-distance\" where surface relaxation erases the electronic signature of the\nburied interface.\n9. Chemical intermixing and interface definition. Given the high growth temperatures, cationic intermixing is probable. If the\nfirst unit cell layer labeled as \"RuO2\" contains a significant fraction of Ti cations (forming a RuxTi1-xO2 solid solution), the\nminor residual polarization in this layer could be attributed to Ti cations rather than metallic Ru. I suggest the author to\nprovide element-specific spectroscopic mapping (e.g., EELS or EDX line scans) to prove the polarized layer is chemically\npure RuO2."}, "author_response": "Responses to the reviewers’ comments\nBlack font: Referee’s comments\nBlue font: Our response\nWe sincerely thank the reviewers for their thorough and insightful evaluation of our manuscript.\nA detailed, point-by-point response is provided below.\nReviewer 1\nI would like to thank the authors for their thoughtful and thorough revisions in response to the\nreviewers' comments. The manuscript has significantly improved in clarity, rigor, and overall\nimpact, and I believe it now meets the high standards expected for publication in Nature\nCommunications. I am pleased to recommend acceptance in its current form.\nResponse: We thank the reviewer for the positive remarks and recommendation. We truly\nappreciate the thoughtful feedback and constructive comments, which helped us significantly\nimprove the quality and clarity of the paper.\nReviewer 2\nSecond referee report on Nature Communications manuscript NCOMMS-25-58504-T The\nauthors have carefully replied to our questions and comments. In particular, STEM analysis\ndetails have been provided; DFT calculations have been added and reveal a clear coupling\nbetween the strain state and the electronic structure allowing the modulation of the\npolarization to be understood. The authors now also do explain how the partial relaxation of\nthe films leads to the reduction (after the peak) of the work function. Indeed, the correlation\nwith the SHG measurements indicates that, above 6.5nm, the film is non-polar – explaining the\nobserved reduction of the work function. We think that the paper can now be accepted for\npublication.\nResponse: We sincerely thank the reviewer for their positive evaluation of the revised\nmanuscript, and for their recommendation.\nReviewer 3\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This\nis part of the Nature Communications initiative to facilitate training in peer review and to\nprovide appropriate recognition for Early Career Researchers who co-review manuscripts.\nResponse: We thank the reviewer for the positive remarks and for constructive suggestions.\nReviewer 4\nDear Editor,\nIn the manuscript entitled “Strain-Stabilized Interfacial Polarization Tunes Work Function\nOver 1 eV in RuO2/TiO2 Heterostructures”, the authors reported the interfacial polarization\nin metallic rutile RuO2 layers in epitaxial RuO2/TiO2 heterostructures. The interfacial\npolarization enables over 1 eV modulation of the RuO2 work function, as evident by the KPFM.\nThe polar metal state in RuO2 is an interesting topic. However, in my viewpoint, the main\nconclusions are not supported by the provided experimental results. Moreover, some of my\ncomments are close to the concerns raised by the previous referees, yet the authors have not\nfully addressed them. Shortly, I can not recommend the current version of the manuscript for\npublication in Nature communications.\nResponse: We thank the reviewer for their careful evaluation of our revised manuscript and are\npleased that they find the topic interesting. We have carefully addressed all specific questions\n1\nand comments by incorporating additional experiments, analyses, and calculations in the\nrevised manuscript.\nComment#1: My main comments are: 1. I question whether the RuO2 is polar. The authors\nclaim that strain stabilizes a polar phase throughout the film (a prerequisite for a \"bulk polar\nphase\"). However, quantitative STEM analysis in Figure 1d contradicts this. Significant polar\ndisplacements (up to ~10 pm) are almost exclusively confined to the TiO2 layers. Inside the\nregion marked as RuO2, the displacements drop rapidly to near zero (0-2 pm). This\nobservation invalidates the claim that the metallic RuO2 bulk sustains a polar structural\ndistortion. The phenomenon is strictly a localized interface dipole, not a bulk phase property.\nAlso, although there is measured SHG signal (which is weak), it is still not possible to\ndetermine whether the signal comes from TiO2 or RuO2.\nResponse: The reviewer raises two points: (1) bulk RuO film can’t be claimed as polar, and\n2\n(2) the sensitivity of SHG to determine whether the signal arises from the RuO film or the\nthe interface and that it is a strain-stabilized interfacial polarization as discussed throughout the\nmanuscript. In fact, both the title (“Strain-Stabilized Interfacial Polarization”) and the text\nexplicitly focus on interfacial polarization. Our discussion is strictly limited to the polar\nstructural distortion that emerges near the RuO /TiO interface. We have revised the text in the\n2 2\nconclusion to further clarify this point to avoid any misunderstanding (see Main Text, Page\n13).\nAs for the point#2, we have added additional experimental data to clarify this point (new\nSI Fig. S4). This is also shown below (Fig. R1) for samples with bare TiO (110) substrate and\n2\n2.2 nm RuO /TiO (110) films exhibit strongly modified SHG intensity, and the SHG signal is\n2 2\nabruptly changed with RuO layers near 4 nm and increases monotonically with RuO thickness.\n2 2\nThis clear thickness dependence cannot originate from the TiO substrate alone. Instead, it\n2\ndemonstrates that a non-centrosymmetric polarization emerges at the RuO /TiO interface and\n2 2\nevolves with the RuO film thickness, consistent with our structural (STEM analyses) and work\n2\nfunction, and transport measurements. We have included these discussions in the revised\nmanuscript (see Main Text, Page 6, and Supplementary Information, Page 3).\nFig. R1. (Left) Azimuthal-angle-dependent optical second-harmonic generation (SHG) intensity (I ) patterns\nSHG\nfor TiO (110) single crystals and RuO /TiO (110) heterostructures with two different RuO thicknesses t. Upper\n2 2 2 2\nand lower panels correspond to PP and SS polarization channels, respectively. (Right) Thickness dependence of\nangular-averaged I for RuO /TiO (110). The polarization of the fundamental and SHG beams was set either\nSHG 2 2\nparallel (P) or perpendicular (S) to the incidence plane, corresponding to PP, PS, SP, and SS channels. All\nmeasurements were performed at 300 K.\nResponse: We agree with the reviewer that KPFM measurements performed under ambient\nconditions can be influenced by surface adsorption. However, our conclusions are not about\nthe absolute value of the work function on one sample; Rather, they are based on a reproducible\ntrend observed across multiple independently prepared samples, all measured under identical\nKPFM conditions. The sample work function is obtained from Φ = Φ – qV , where q and\ntip CPD\nV are charge and contact potential difference between the tip and sample surface,\nCPD\nrespectively. The tip work function Φ is calibrated using a reference sample which is itself\ntip\nsubject to similar surface adsorption effects. As a result, any extrinsic contributions due to\nadsorption are common-mode and do not affect the relative work-function differences extracted\nfrom our measurements. Therefore, our key claim – an over 1 eV modulation of the work\nfunction in RuO2/TiO2 heterostructures as a function of film thickness – remains robust\nand unaffected by such extrinsic effects. Moreover, both our electrical transport measurements\n(Fig. 4) and SHG results (Fig. R1 above) reveal the same interfacial-polarization-driven\nbehavior identified by KPFM, providing additional independent confirmation.\nComment#3: the RSM results are poor. The lattice constants used for DFT calculation is 3.119\nÅ / 6.394 Å for RuO2 and 2.970 Å / 6.588 Å for TiO2. These data deviate from the values\nreported in several references (: J. Phys. Chem. C 119, 5, 2692–2702 (2015), AIP Adv. 9,\n015302 (2019), Cryst. Growth Des. 24, 11, 4604–4612 (2024), APL Mater. 12, 101110 (2024),\nNature Communications 14:8240 ( 2023),J. Phys.: Condens. Matter 35 405603 (2023) ). Given\nthat the authors regard strain as the primary origin of the interfacial polarization, the lattice\nconstants employed in the calculations should be determined with higher accuracy.\nAdditionally, due to the stress relaxation in the RuO layer, the upper and lower TiO layers\n2 2\nshould adopt different lattice parameters.\nResponse: The reviewer raises three main points: (1) the weak signal in the measurements due\nto the very thin films, (2) the strain state of the bottom and top TiO2 layers, and (3) the choice\nof lattice values used in our calculations.\nPoint #1: Measurement signal from thin films. To address the concern about weak signal,\nwe grew a layered structure rather than a single thin film, while still keeping each RuO2 layer\nthin enough to avoid strain relaxation. Specifically, we fabricated a structure with five repeating\nlayers of 2 nm RuO2 and 6.5 nm TiO2. This increases the total material volume contributing\nto the measurement and therefore strengthens the signal. The resulting data are now included\nin the revised manuscript (new Supplementary Fig. S14). These results show clear and well-\ndefined features, demonstrating that both RuO2 and TiO2 layers are fully strained to the TiO2\n(110) substrate along both in-plane directions.\nPoint #2: Strain state of the top and bottom TiO2 layers. The same measurements also\ndirectly address this point. They show that all TiO2 layers – both at the bottom and the top of\nthe structure – are coherently strained to the substrate. As a result, all TiO2 layers experience\nthe same strain state. This clarification has been added to the revised manuscript (Main Text,\npage 9, and Supplementary Information, page 8).\nPoint #3: Lattice values used in calculations. Regarding the lattice values used in our\ncalculations, it is well known that calculated values can differ slightly from experimental ones,\ndepending on the specific computational approach. Our goal is not to exactly match a particular\nexperiment, but to use a consistent and controlled model to understand how strain affects the\nelectronic behavior of the materials. In particular, we focus on how strain changes the electronic\nstates of RuO2 and induces polarization in TiO2. To directly address the reviewer’s concern,\nwe have now expanded our calculations to cover a range of in-plane lattice values for RuO2,\nrather than using a single value. These new results, included in the revised manuscript (new\nstrain. This confirms that our conclusions are robust and do not depend on the choice of one\nspecific lattice value.\nComment#4: Specific comments are as follows:1. To my knowledge, RuO2 films and TiO2\nsubstrates exhibit the best lattice matching as compared to other substrates such as MgO,\nAl2O3,STO etc.. If the interfacial polarization of RuO2 can be induced by the strain from TiO2\nsubstrates, is it possible that such interfacial polarization states are present in the vast majority\nof RuO2 thin films studied?\nResponse: We agree with the reviewer that large epitaxial strain can, in principle, induce\nsimilar interfacial polarization effects in RuO2 films grown on other substrates. Our combined\nstudy using experiments and calculations explicitly demonstrate this strain-driven effect for the\nRuO2/TiO2(110) system. However, for substrates such as MgO, Al2O2, and SrTiO3,\ndifferences in crystal symmetry, growth orientation, and interfacial chemistry make the strain\nstate and resulting interfacial behavior fundamentally different. As a result, we cannot reliably\nassess whether comparable interfacial polarization states would be present in those systems.\nWe hope the reviewer agrees that addressing this question is beyond the scope of the present\nmanuscript.\nComment#5: 2. The STEM images in Fig.1 show the upward polarization in the top TiO2 layer\nand the downward polarization in the bottom TiO2 layer. Is this a universal phenomenon, or\ncould the results vary across different STEM regions? The authors should provide microscopic\ncharacterization results from additional regions.\nResponse: We believe the reviewer is referring to the downward polarization in the top TiO\n2\nlayer and the upward polarization in the bottom TiO layer. This result is robust and has been\n2\nreproduced at multiple locations and in multiple samples. We have added additional data from\nanother sample (new SI Fig. S5) in the manuscript and have clarified this point.\nComment#6: Moreover, STEM characterization clearly reveals that the polarization is\nprimarily confined within the TiO2 layers and subsequently extends into the RuO2 layer.\nBecause the TiO2 bottom layer is not subjected to any substrate strain, its polarized state\nshould originate from interfacial coupling with the RuO2 layer above it. This is puzzling: why\nan only 2 u.c. RuO2 layer with a small polarization can induce a significantly larger\npolarization in a 8 u.c. TiO2 layer that is not strained by the substrate? If further increasing\nthe thickness of TiO2 bottom layer, does the polarization state still exist\nResponse: We attribute this behavior to the difference in mechanical stiffness between RuO\n2\nand TiO . RuO has a larger Young’s modulus (275-330 GPa, [Mater. Sci. Semicond. Proc. 15,\n2 2\n331-339 (2012)]) than TiO (~225 GPa, [Phys. B: Condens. Matter. 407, 958-965 (2012)]), so\n2\neven an ultrathin RuO layer, as long as it remains coherently strained, can impose a significant\n2\ninterfacial distortion on the adjacent TiO layers, as seen in our present work combining both\n2\nexperiments and calculations. This interpretation is consistent with our prior studies [arXiv\npreprint arXiv:2405.05838 (2024)] showing that, as RuO films thicken, strain relaxation can\n2\noccur through crack formation in the underlying TiO substrate. Similar crack-mediated strain\n2\naccommodation has also been reported for ultrathin IrO /TiO heterostructures [Nat.\n2 2\nNanotechnol. 18, 1005 (2023)].\nThe bottom TiO layer is grown homoepitaxially on a thick TiO substrate and therefore is\n2 2\nnot expected to exhibit a strong thickness dependence on polarization. In contrast, we included\nadditional data from different RuO thickness samples (new SI Fig. S5) and found that the\n2\npenetration depth of the polarization into the TiO buffer layer increases with RuO thickness\n2 2\n4\nwithin the strained regime. This supports the strain-induced polarization effects at RuO /TiO\n2 2\ninterfaces. We note that it is conceivable that the elastic modulus of RuO2 films varies with\nincreasing film thickness, which could justify this observation even when the films remain\ncoherently strained.\nComment#7: I agree with the previous reviewer: the polar state is not induced within the\nmetallic RuO2 layer, and the term “polar metal” should therefore be avoided in the manuscript.\nAlthough the authors argue that their RuO behaves like a highly doped semiconductor, this\n2\ndescription does not justify retaining the “polar metal” label.\nResponse: We would like to clarify that it was never our intention to claim that the interfacial\nRuO layer behaves as a doped semiconductor. Our discussion “The estimated interfacial\n2\nconductivity values is of the same order of magnitude as that of highly doped semiconductors\nand known polar metals (e.g., La-doped BaTiO )” was intended solely in a phenomenological\n3\nsense, based on an interfacial conductivity only. The extracted conductivity of bulk region is\napproximately 15,875 S/cm, indicating a highly conductive RuO film. To avoid any potential\n2\nmisunderstanding, we have removed discussion to “highly doped semiconductors” in the\nrevised manuscript. Our emphasis is on the strain-stabilized interfacial polarization as\nemphasized upon in our response to reviewer’s comments#1.\nComment#8: Figure 3 compares the work function modulations across various materials and\nmethods. I'm not sure about the importance of work function modulation, which needs to be\nemphasized in the introduction section. Moreover, this figure compares the result of RuO2 only\nwith those of typical metallic systems; however, as they themselves state, the polarized RuO2\nlayer is semiconducting. I therefore recommend that the figure also include data for commonly\nstudied semiconductors whose work functions have been tuned by different strategies.\nResponse: As pointed out above, it was never our intention to state that the interfacial RuO2\nlayer is semiconducting. In fact, the RuO in our heterostructure remains intrinsically metallic,\n2\nas confirmed by transport and optical conductivity measurements. The interfacial conductivity\nextracted from transport analysis is comparable to that reported for known polar metals.\nTherefore, our system is not semiconducting in the conventional sense, and its electronic\nbehavior differs fundamentally from that of band-gap semiconductors.\nIn semiconductors, the work function is not a fixed material parameter but depends strongly\non Fermi-level pinning, doping concentration, defect states, and surface termination. As a result,\nreported “work function modulation” values in semiconductors do not represent intrinsic\nchanges to the electronic structure, but rather reflect extrinsic surface or defect effects. Whereas,\nin contrast, in metallic systems, the work function is a well-defined and physically meaningful\nquantity that directly reflects interfacial dipoles and polarization-induced electrostatic shifts.\nFor this reason, Fig. 3 focuses exclusively on metallic systems, where work-function\ncomparison is physically appropriate and quantitatively meaningful.\nWe have revised the Introduction with additional reference to better emphasize the\ntechnological and scientific relevance of work function modulation in metallic systems,\nparticularly in applications involving catalysis, electronics, and energy harvesting applications\n[Phys. Rev. Applied 19, 037001 (2023)] (see Main Text, Page 4).\nComment#9: In the reply to the second Reviewer, the author said that the TiO2 buffer layer on\nTIO2 substrate is important since \" it can maintain the surface states of TiO2 from one\nsubstrate to another substrate even when they are purchased from the same vendor and in the\nsame batch”. Why the RuO2 layer used for KPFM measurement is deposited on TiO2 substrate\ndirectly？Is the polarization state of this layer similar with the trilayer sample shown in Figure\n5\n1. Therefore，I suggest the author to also give a STEM result for the bilayer sample adopted\nfor KPFM.\nResponse: KPFM is a surface-sensitive technique and therefore requires the RuO surface to\n2\nbe directly exposed in order to reliably probe its work function. In contrast, STEM\nmeasurements – particularly for RuO films – require the presence of a protective capping layer\n2\nto prevent surface damage during focused-ion-beam sample preparation. For this reason, all\nSTEM measurements were performed on capped samples. Indeed, our attempts to carry out\nSTEM on uncapped RuO films resulted in severe film degradation, rendering such\n2\nmeasurements unreliable.\nRegarding the use of the TiO buffer layer, it is employed to mitigate surface-related\n2\nvariability and improve sample-to-sample reproducibility; it should not be interpreted as a\nprerequisite for the epitaxial growth of RuO films. At present, we are unable to perform\n2\nadditional growth with a TiO buffer layer due to a temporary issue with the MBE system and\n2\ntherefore cannot address this specific request through new experiments. Nevertheless, we\nemphasize that our conclusions are robust and do not rely on a single characterization technique.\nInstead, they are supported by a consistent set of observations obtained from SHG, KPFM,\nSTEM ptychography, and electrical transport measurements.\nComment#10: Misleading quantification of \"1 eV\" modulation (Substrate Effect vs. Tuning)\nThe title and abstract claim to tune the work function of RuO2 by \"Over 1 eV\". However, Figure\n2b shows that the work function naturally increases from 4.25 eV (ultrathin limit, explicitly\nidentified as close to the bulk TiO2 value) to 5.05 eV (bulk RuO2 value).\nThis baseline increase of 0.8 eV represents the natural transition from the substrate's electronic\nstructure to the film's bulk properties (band alignment), which would occur regardless of\npolarization. The actual modulation attributable to the specific \"strain-stabilized polarization\"\nmechanism is effectively limited to the \"overshoot\" peak above the bulk value (approx. 5.40\neV peak - 5.05 eV bulk 0.35 eV). Attributing the entire transition range to polarization is\nscientifically misleading. The authors must explicitly decouple the intrinsic thickness-\ndependent recovery from the polarization-induced shift.\nResponse: We have clarified this point further in the revised manuscript by including new\nanalyses (See new SI Fig. S15). We have also revised the manuscript to clarify this distinction,\nexplicitly defining the polarization-induced work-function modulation relative to the intrinsic\nthickness-dependent baseline.\nUsing this physically motivated baseline (see new SI Fig. S15), the experimentally\nobserved peak at ~5.40 eV corresponds to a modulation exceeding 1 eV relative to the intrinsic\nband-alignment expectation. This clearly indicates an additional polarization-driven\ncontribution superimposed on the monotonic background. We have included this analysis and\nthe corresponding discussions to the revised manuscript (see Main Text, Page 10, and\nSupplementary Information, Page 8).\nComment#11: Invalid mechanism for work function dropping with strain relaxation). The\nauthors attribute the sharp drop in work function above 4 nm to strain relaxation (Fig. 2e). In\nheteroepitaxy, interfacial layers clamped to the substrate typically retain their strained state\neven when the upper bulk relaxes. If the work function shift is driven by the buried interface\ndipole, the relaxation of the top layers should not retroactively destroy the dipole already\nestablished at the bottom interface. The authors' model implies a non-physical \"action-at-a-\ndistance\" where surface relaxation erases the electronic signature of the buried interface.\nResponse: Our proposed mechanism for the sharp decrease in work function for film\nthicknesses t > 4 nm is based on quantitative, thickness-dependent SHG measurements that\n6\nreveal a structural transition from a polar mm2 phase to a centrosymmetric 4/mmm phase at\napproximately 4 nm (Fig. R1). This transition coincides with structural data from RSM that\nshows the onset of strain relaxation. Consistent with this interpretation, our prior work on\nRuO /TiO (110) has shown that strain relaxation is accompanied by the formation of misfit\n2 2\ndislocations at the interface [arXiv preprint arXiv:2405.05838 (2024)]. While interfacial layers\nthat remain clamped to the substrate are, in principle, possible, this is not universally the case.\nIn the present system, we argue that once strain relaxation occurs, the underlying TiO layer\n2\nloses its polarization. This loss of interfacial polarization naturally explains the observed abrupt\nreduction in the work function. We have included the SHG experimental results and the\nadditional discussion to the revised manuscript (see Main Text, Page 9, and Supplementary\nInformation, Page 3).\nComment#12: Chemical intermixing and interface definition. Given the high growth\ntemperatures, cationic intermixing is probable. If the first unit cell layer labeled as \"RuO2\"\ncontains a significant fraction of Ti cations (forming a RuxTi1-xO2 solid solution), the\nminor residual polarization in this layer could be attributed to Ti cations rather than metallic Ru.\nI suggest the author to provide element-specific spectroscopic mapping (e.g., EELS or EDX line\nscans) to prove the polarized layer is chemically pure RuO2.\nResponse: This an an excellent question raised by the reviewer for which we are thankful.\nWe have addressed this question through additional film growth and characterizations. First, we\nnote that EELS measurements, unfortunately, can’t be conducted due to the significant spectral\noverlap between Ru M-edge and Ti L-edge. We, therefore, to address the reviewer’s questions,\nhave grown new set of RuO films on TiO substrate with intentional alloying with Ti, and have\n2 2\nused SHG to investigate the film symmetry. Ti alloyed samples show relatively lower SHG\nsignal (i.e. lower polarization) compared to fully-strained RuO /TiO (110) film. With\n2 2\nincreasing Ti alloying we found that the film symmetry changes to monoclinic, m which is\ndistinct from the case of phase-pure RuO /TiO (110) sample both using SHG and STEM\n2 2\nptychography analyses in the current study. These results demonstrate that Ti incorporation\ndoes not enhance – but instead suppresses – the polar response. We therefore argue that the\npronounced polarization observed in ultrathin RuO cannot be attributed to Ti-rich intermixed\n2\nlayers. We have added these experimental results and the corresponding discussion to the\nrevised manuscript (see Main Text, Page 7, and Supplementary Information, Page 6).\n7"}]

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