Dataset and article "Duality and degeneracy lifting in two-dimensional electron liquids on SrTiO3(001)"

Article https://doi.org/10.1038/s41467-025-59258-4 Duality and degeneracy lifting in twodimensional electron liquids on SrTiO 3 (001) Igor Sokolović 1 , Eduardo B. Guedes 2 , Thomas P. van Waas 3 ,FeiGuo 4 , Samuel Poncé 3,5 ,CraigPolley 6 , Michael Schmid 1 , Ulrike Diebold 1 , Milan Radović 2 ,MartinSetvín 1,7 &J.HugoDil 2,4 Two-dimensional electron liquids (2DELs) have increasing technological relevance for ultrafast electronics and spintronics, yet significant gaps in their fundamental understanding are exemplified on the prototypical SrTiO 3 .We correlate the exact SrTiO 3 (001) surface structure with distinct 2DELs through combined microscopic angle-resolved photoemission spectroscopy and noncontact atomic force microscopy on truly bulk-terminated surfaces that alleviate structural uncertainties inherenttothislong-studiedsystem.TheSrO termination is shown to develop a 2DEL following the creation of oxygen vacancies, unlike the intrinsically metallic TiO 2 termination. Differences in degeneracy of the 2DELs, with nearly the same band filling and identical band bending, are assigned to polar distortions of the Ti atoms in combination with spin order, supported with the extraction of fundamental electron-phonon coupling strength. These results not only resolve the ambiguities regarding 2DELs on SrTiO 3 thus far, but also pave the way to manipulating band filling and spin order in oxide 2DELs in general. The extensive pursuit for the next-generation electronics steers towards low-dimensional systems. Here, SrTiO 3 —a model cubic perovskite oxide —plays a versatile role. Starting as a promising candidate for high-temperature superconductivity1, through its potential as a gate dielectric with ϵ r in the order of 1032,andfinally as an insulator that hosts highly mobile two-dimensional electron liquids (2DELs) at its bare surface3–10 or when interfaced with other insulators11–13. Since the discovery of a 2DEL at the LaAlO 3 /SrTiO 3 interface14 it was the subject of two decades of research15,buttheconceptscrucialforoxide electronics16 such as the origin, creation, filling, and lifting of the spin degeneracy in these 2DELs remain debated. We directly elucidate and disentangle these fundamental phenomena by studying SrTiO 3 surfaces of unprecedented quality in direct and reciprocal space. Most ambiguities related to the 2DELs on SrTiO 3 (001) stem from its elusive surface structure. They are commonly assumed as bulktruncated, yet without real-space confirmation. Moreover, the tripartite bulk composition is sensitive to stoichiometry changes and the assumption of pristine surfaces is hardly warranted. Such ambiguities of the surface structure lead to inconclusive and commonly contradictory reports on the traits of 2DELs on SrTiO 3 (001). In this work, we reveal the sensitivity of the 2DELs towards the exact surface termination, and directly observe the underlying mechanisms that define their properties. Results and Discussion Bulk-truncated SrTiO 3 (001) surface With our recently developed cleaving technique that exploits the strain-induced ferroelectric phase transition in SrTiO 3 17,weroutinely create surfaces that are truly bulk-terminated, atomically flat, and welldefined at the atomic level as confirmed by noncontact atomic force Received: 8 August 2024 Accepted: 11 April 2025 Check for updates 1 Institute of Applied Physics, TU Wien, Vienna, Austria. 2 Center for Photon Science, Paul Scherrer Institut, Villigen, Switzerland. 3 European Theoretical Spectroscopy Facility, Institute of Condensed Matter and Nanosciences, Université catholique de Louvain, Louvain-la-Neuve, Belgium. 4 Institut de Physique, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland. 5 WEL Research Institute, Wavre, Belgium. 6 MAX IV Laboratory, Lund University, Lund, Sweden. 7 Department of Surface and Plasma Science, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic. e-mail: [email protected];hugo.dil@epfl.ch Nature Communications | (2025) 16:4594 1 1234567890():,; 1234567890():,; microscopy (ncAFM). This is in sharp contrast to differently-prepared surfaces that are either contaminated, reconstructed, or disordered, due to the thermal instability of the (1 × 1)-terminated SrTiO 3 (001) surface18. Figure 1shows ncAFM, angle-resolved photoemission spectroscopy (ARPES), and scanning electron microscopy (SEM) data on a truly bulk-terminated SrTiO 3 (001) surface. Our cleaving procedure always produces surfaces with both terminations (TiO 2 and SrO), each covered with the same concentration of complementary point defects: TiO 2 with 14% of Sr adatoms (Sr ad ) and SrO with 14% of strontium vacancies (V Sr ), resolved by ncAFM in Fig. 1a, b, respectively. Their presence is unavoidable as they compensate the polarity induced during successful cleaving17,19,20, but, in turn, guarantee the structure of our well-cleaved surface areas. The O-terminated ncAFM tip21 detects Sr ad as dark spheres (attraction) and V Sr as bright “x”-shaped features (absence of attractive signal). At the standard doping level of 0.5 weight percent (wt%) of Nb, the domains of these two surface terminations are sufficiently large to be individually studied by synchrotron-based ARPES with a beam spot diameter of ≈10 μm. On a mesoscopic scale, the two terminations can be distinguished by SEM even after transfer through air: TiO 2 -andSrOterminated surface regions are imaged as dark and bright, respectively (details in the Supplementary Information (SI); Supplementary Note 1). Figure 1c shows a SEM micrograph of the counterpiece (i.e. the other side after cleavage) of the surface studied under synchrotron light; an optical photograph is shown in Fig. 1d. The counterpiece of the cleavage has the same geometry but the opposite distribution of surface terminations22 (more details in Supplementary Note 1), that are recognized as the opposite SEM contrast. The lateral positions of the ARPES measurements are superimposed on this SEM image, indicating that on the surface where ARPES was performed, a split and a degenerate 2DEL appears on the TiO 2 and SrO termination, respectively. Symmetry between the main and the counter-piece of cleaved SrTiO 3 (001) surfaces has been verified for around 100 cleaves over the years22. With SEM acting as a bridge between synchrotron and ncAFM measurements, we proceed to correlate the 2DEL properties with the surface structure. Termination-specific 2DELs The two terminations formally differ in one atomic layer and host almost identical 2DELs,making it hard to discriminate between the two using X-ray photoelectron spectroscopy (Supplementary Note 7), in contrast to some other systems23 where the chemical and electronic environment is significantly different for the two terminations. However, each displays a distinct Fermi surface (FS) as witnessed by ARPES (photon energy hν=47 eV) in Fig. 1e, f. Both are derived from Ti 3d xy orbitals3,buttheTiO 2 termination is characterized by two sharp rings, while the SrO termination is characterized by a single ring. The purity of the cleaved surfaces and the resulting high quality of the ARPES data allow us to detect additional faint bands visible at smaller binding energies (black triangles in Fig. 1g and i) on both the TiO 2 and the SrO termination: two faint bands with smaller splitting on the former, and a single faint band at the latter. These states are assigned to the next N=2 quantum-well replicas24. Spectra acquired at different spots on the sample demonstrate that the presented data is representative of the TiO 2 and SrO terminations throughout the sample, as demonstrated in Supplementary Note 2 where several raw spectra are displayed. It is noteworthy that the spectra presented in Figs. 1and 2is of exceptional quality; in most spectra obtained by us the N=2 quantum-well replicas are not discernable on either surface termination (Supplementary Fig. 1 | Two distinct 2DELs on a truly bulk-terminated SrTiO 3 (001)-(1 × 1) surface. Atomically resolved ncAFM images obtained on the (a)TiO 2 termination with 14% of Sr adatoms and (b) SrO termination with 14% of Sr vacancies. The point defects are intrinsic to a SrTiO 3 (001) surface cleaved via the strain-induced ferroelectric phase transition. An orange grid indicates the surface unit cells. The counterpiece of the cleaved SrTiO 3 (001) surface investigated with ARPES displayed in a (c) secondary-electron SEM image and in an (d) optical photograph: Dark SEM contrast corresponds to TiO 2 - and light gray to SrO-terminated surface regions. Blue markers in (c,d) indicate where the measured Fermi surface shows a double ring (e), while red markers show regions with a single ring (f), obtained with hν=47 eV (FS #1). SEM was performed on a counter-piece of the ARPES-investigated surface, so the contrast is inverted. Black diamonds and broken colored circles are positioned where ARPES detected an ill-defined Fermi surface or a Fermi surface that only weakly resembles one ofthe two well-defined ones, respectively (shown in Supplementary Note 4). Marker sizes are to scale with the 10 μmradiusofthebeam spot. The corresponding band dispersion maps along the k [110] direction (dashed lines, cut #1) are shown in (g, i).MDCs along the dashed lines in (e,f)atE F are shown in (h).The triangular markers in (g,i) indicate the quantum-well replicas of the main bands, visible as faint inner bands. Article https://doi.org/10.1038/s41467-025-59258-4 Nature Communications | (2025) 16:4594 2 Notes 2 and 3). In contrast, conchoidal surface regions, which lack a well-defined atomic structure17, exhibit a variety of less-defined FSs that often resemble a combination of the well-defined FSs obtained on the two terminations (Supplementary Note 4). The assignment of the two distinct 2DELs to two distinct surface terminations is further supported by real-space ncAFM experiments below (Fig. 3). Band maps measured along the k [110] direction (Fig. 1g, i) show that these states at the two terminations have a similar dispersion, while the main difference lies in the splitting of the bands. A comparison of the momentum distribution curves (MDCs) at the Fermi level E F in Fig. 1h highlights some important differences between the TiO 2 -and SrO-terminated surfaces. The lines on the former are significantly sharper and the peak maximum of the latter lies between the split bands of the former. This difference cannot be explained by a spectral broadening of the two sharp bands on the TiO 2 termination, making them appear as one band on the SrO side (Supplementary Note 5). The difference in band splitting between the pure TiO 2 -andSrOterminated areas can be clearly observed experimentally when the ARPES spectra is collected from a surface area that contains a smooth transition between the two (Supplementary Note 6). Furthermore, the intensity obtained for the SrO termination (Fig. 1h) needs to be multiplied by a factor 1.4 to be comparable to the TiO 2 termination. Considering the limited mean free path of the photoelectrons, this lower intensity on the SrO termination agrees with the localisation of the 2DEL in the subsurface TiO 2 plane. Figure 2presents more details of the electronic structure of the 2DELs at both terminations, with the extracted experimental values of k F , carrier densities n 2D , and band bottoms E bot laid out in Supplementary Table 1. The observed band filling, as extracted from k F ,is larger than those where the formation of polaronic replicas in the ARPES data can be expected25,26. The absence of dispersion in the photon energy scans (Fig. 2a, b) confirm that the d xy -derived states on both terminations are two-dimensional. Additionally, the resonant enhancements on both terminations occur in the same energy ranges, again indicating their similar orbital composition. At hν=85 eV, in addition to Ti 3d xy states of Fig. 1e–i, the Ti 3d xz - and d yz -derived states3are visible in the FS maps (Fig. 2c, d). The Fermi wavevectors k F andbandbottomsofthese“heavy”bands (Fig. 2e–g) are –within the experimental resolution –the same for both terminations (Supplementary Table 1). The quality of the in-situ cleaved SrTiO 3 (001) surface allows us to clearly record the O 2pband on both terminations (Fig. 2h, i). These measurements were performed with hν=170 eV, allowing the observation of the full first Brillouin zone in the 〈110〉direction. The similar data quality on both terminations reiterates that the differences between the two terminations recorded with ARPES are intrinsic and unrelated to surface quality. In contrast, ARPES collected on ill-defined surface regions (conchoidal) and regions with macroscopic defects (Supplementary Note 4) exhibit a significant reduction in data quality. Origin of the 2DELs A 2DEL is known to appear at SrTiO 3 (001) surfaces after prolonged synchrotron irradiation3,4,7,27–29, hinting towards defect-induced population. Both distinct 2DELs on our cleaved SrTiO 3 (001) surfaces develop much faster: The FS on TiO 2 termination becomes clear and intense in a ≲2stimeframe(ataround5×10 10hν/μm2), whereas the FS at the SrO termination develops more slowly, and becomes welldefined only after ≈30 s (Supplementary Movies 1 and 2). This indicates fundamental differences between the two terminations, but also highlights how very little defects are necessary for their creationon the TiO 2 and SrO terminations. In comparison, conchoidal surface regions that lack proper atomic order and intrinsic polarization exhibited slowly developing, badly defined FSs (Supplementary Note 4). In our scanning tunneling spectroscopy (STS) experiments (Fig. 3d) the TiO 2 termination is observed to be metallic immediately after cleaving17. Positive Sr ad ions compensate the strain-induced polarity during cleaving, yet their presence induces downward band bending on the extrinsically n-doped crystals. The presence of distinct in-gap filled states in STS on the TiO 2 termination is consistent with the ARPES measurements, but the tip-induced shifting of all energy states Fig. 2 | Details of the 2DELs on TiO 2 - and SrO-terminated surfaces. Photonenergy dependence of the 2DEL formed on the (a)TiO 2 -and(b) SrO-terminated surfaces. The Fermi surface maps measured with hν=85 eV (FS #2) are shown in (c,d), and the corresponding band dispersion maps along the k x direction (cut #2) in (e,g), with a comparison of the MDCs at the Fermi level displayed in (f). h,iO2p band of the TiO 2 and SrO-terminated surface, respectively, measured with hν=170 eV. Article https://doi.org/10.1038/s41467-025-59258-4 Nature Communications | (2025) 16:4594 3 in STS and the different tunneling probabilities to distinctd xz/yz and d xy derived states thwart the direct comparison between the two techniques. Ab-initio slab calculations show that for the TiO 2 termination the d xy states are above the heavy bands in energy3,8, not at higher binding energy as seen in the ARPES data. This suggests the possibility that the ≲2 s delay in detection of a 2DEL on TiO 2 is due to the fact that the d xy bands become populated by photo-excited, and incoherently scattered, secondary electrons following a small amount of synchrotron irradiation. Alternatively, a small amount of adsorbates that trap the charges are quickly removed by the synchrotron light via dissociation/ association and desorption21. In either scenario, the creation of defects under synchrotron irradiation is clearly not necessary for a TiO 2 termination to host a fully developed 2DEL. The SrO termination is wide-gap semiconducting immediately upon cleaving17, promoted by the negative V Sr s that cause an upward band bending (Fig. 3d). The formation mechanism of a 2DEL, i.e., the semiconductor-to-metal transition on SrO, was investigated separately by progressive irradiation with in-house X-ray and electron sources at T=100 K, summarized in Fig. 3.PhotoemissionbyAlKαX-rays (measured as photo-current “e−↑”)significantly reduces the upward band bending and brings the conduction band onset down by 1.5 eV towards the Fermi level due to the surface photovoltaic effect30.Thisdownshift saturates with increasing X-ray dose (Fig. 3d) and, according to STS, is not enough to turn SrO metallic. Ionic defects were not observed with ncAFM following X-ray irradiation, except for the appearance of adsorbates (green hollow arrows in Fig. 3a), which can most likely be attributed to the contamination from the residual gas during X-ray irradiation of a sample held at 100 K. The formation of a 2DEL requires additional downward band bending. Without a synchrotron source, this was achieved by irradiation of the SrO termination with electrons of sufficient energy to create positively charged oxygen vacancies (V O s) via the Knotek-Feibelman mechanism31,32.TheV O s were observed in ncAFM as dark defects in the O sublattice33 only after 47 eV electron irradiation, marked by red filled arrows in Fig. 3b. A total of 0.05 monolayers coverage of V O s was sufficient to bring the onset of the conduction band within 50 meV of the Fermi level according to STS (Fig. 3d). Taking into account tip-induced band bending, this will either be enough or a slightly higher concentration is expected to populate the conduction band. Therefore, in the 30 s of 47 eV synchrotron irradiation, a joint effect of reducing the band bending by photoemission and causing additional downward band bending by the creation of V O s gradually develops a stable 2DEL on the SrOterminated surface. The electronic structure of a metallic TiO 2 termination remained unaffected under the same irradiation conditions, and no ionic defects were observed in ncAFM even after the highest dose of 47 eV electrons (Fig. 3c). In fact, the TiO 2 termination with Sr ad sismoreproneto adsorption of oxygen to neutralize the Sr ions18 than the formation of V O s. Therefore, we can safely exclude the relevance of oxygen vacancies for the formation of a 2DEL on the TiO 2 -terminated surface, while their presence is necessary for a 2DEL on the SrO termination. In contrast to the pristine TiO 2 termination with scattered Sr ad s, the presence of two types of oppositely charged defects (V Sr and V O )on the irradiated SrO termination can be expected to lead to larger fluctuations of the electrostatic potential and directly influence the wave function of the 2DEL below through electrostatic Gaussian disorder34, thus explaining the larger linewidth and the observed multiple contributions, in contrast to the pristine TiO 2 termination. In layer-by-layer MBE growth of SrTiO 3 films on a SrTiO 3 substrate, it is possible to control the preferential surface termination and it was found that the 2DEL develops more rapidly on the SrO-terminated Fig. 3 | 2DEL formation mechanism on the SrO-terminated surface emulated with the irradiation of laboratory Al KαX-rays and 47 eV electrons. Atomically resolved ncAFM images obtained on (a) the SrO termination irradiated with several doses of X-rays (measured as photocurrent “e−↑''; 1× hνdose equals 1013e−↑/cm2), (b) SrO termination and (c)TiO 2 termination after two different doses of electron irradiation (1× e−dose equals 1015e−/cm2). Green hollow arrows indicate features attributed to adsorbates and red filled arrows indicate oxygen vacancies that appear exclusively on the SrO termination after irradiation with 47 eV electrons. 2 nm scale bar in all ncAFM panels. dSTS shows the effect of the irradiation on the density of states: metallic TiO 2 with a distinct DOS feature just below the Fermi level (−40 meV) is unaffected, while photoemission and the formation of oxygen vacancies bring the onset of the SrO conduction band closer to the Fermi level following progressive X-ray and electron irradiation. eIllustration of the conduction band (CB), valence band (VB), Fermi level (full line E F ), and in-gap states (broken lines on TiO 2 ) of the two terminations upon irradiation: TiO 2 remains metallic with an intrinsic 2DEL, while the upward band bending on SrO is reduced through photoemission followed by the additional downward band bending induced by the formation of oxygen vacancies. Article https://doi.org/10.1038/s41467-025-59258-4 Nature Communications | (2025) 16:4594 4 surface9. Unfortunately, that study gave no insight in the exact atomic structure at the surface and direct comparison with our results is thus impossible. It should be noted that the general development of the 2DEL was much slower than reported here, with a significantly lower band filling. In that context the 2DEL found on MBE-9and PLD-grown7 films resemble each other with the added advantage of controlling the surface termination in the former. This highlights the importance to start from well-definedsurfacesandtheroleplayedbytheexact atomic structure on the 2DEL formation and properties. Population The nearly identical charge density of the 2DEL on both surface terminations as observed in ARPES (Supplementary Table 1), indicates a limit of the 2DEL carrier density at SrTiO 3 (001) determined by the dielectric response of the material to the presence of a metallic surface, through a mechanism similar to Fermi level pinning at a metalsemiconductor interface. The observed similarities in the carrier densities on the two terminations (Supplementary Table 1) cannot be rationalized by electron donation from the the intrinsic or irradiationinduced defects on the TiO 2 and SrO termination, respectively: Real space measurements (Fig. 3) show that the concentration of these defects differs by an order of magnitude. Instead, the highly mobile 2DEL electrons stem from the bulk of the sample once the downward band-bending makes the Ti 3d xy states energetically available. The V O s on the SrO termination (and Sr ad sontheTiO 2 termination) hence serve primarily as a band-bending-reversal mechanism, demonstrating a pathway to populating 2DELs with a small amount ( ≈1%) of external defects and thus maintaining relatively low defect scattering. The presented study of the 2DELs at the bare surface of cleaved SrTiO 3 (001) enables us to correlate the concentration of surface defects with the population of the 2DELs. Such a correlation is hard to achieveforthe2DELsconfined at the interface of two materials, like the well-known interface between LaAlO 3 and SrTiO 3 14,becausetheir atomic structure is accessible only via areaand volume-averaging techniques such are transition electron microscopy (TEM)35 and surface X-ray diffraction (SXRD)36, that are not particularly sensitive to the presence of (incoherently distributed) defects. It is possible that the role of Sr adatoms in inducing the downward band bending on our cleaved TiO 2 terminations is similar to the minimum number of LaAlO 3 layersgrownonSrTiO 3 11 necessary to populate the interface 2DEL without the need of further excitation. Degeneracy lifting Correlating distinct 2DELs with their well-defined surface terminations allows us to exclude interpretations of split bands on SrTiO 3 surfaces as discrete 2DEL eigenstates in the surface potential wedge4,5,37.Our TiO 2 and SrO terminations share the same band bending according to the bottom of the heavy bands (Figs. 2e–gand3d, e) and the Luttinger volume of the 2DEL (Supplementary Table 1), stabilized and saturated by the pinned Fermi level. The duality of 2DELs’electronic structure in all aspects but the band splitting, calls for an explanation based on lifting of the Kramers degeneracy7,38–40 by symmetry breaking in the lattice. The displacement of the 2DEL-hosting Ti atoms from an inversion center on the TiO 2 termination is promoted by their under-coordination at the interface with vacuum, and the out-of-plane polar distortions inherited from the strain-induced phase transition during cleaving. Such distortions are not expected to degrade the spectra quality as long as they are coherent, as observed on other metallic surfaces with sharp band splitting41–43. In analogy with ferroelectric systems44–47, opposite displacements are expected on the SrO-terminated regions, but the distortions are in part suppressed by the full coordination of Ti atoms in the O-octahedra, and further rendered incoherent through the introduction of O vacancies required for band bending reversal. Furthermore, transition metal oxides are prone to self-trapping charges in the form of polarons48–52 leading to local lattice polarization around Ti3+ atoms. Localized polarons can be recognized as distinct in-gap states53–55 visible in the STS of the as-cleaved TiO 2 termination (states below the Fermi level in Fig. 3d) and in the ARPES valence band spectra of both terminations (Supplementary Note 7). A Rashba-like lifting of the band degeneracy56 can emerge from such coherent structural distortions on the TiO 2 termination, and has been predicted to significantly alter the spin texture due to a hybridisation between the d xy and d xz,yz derived bands6.However,the Rashba effect is expected to affect the d xz,yz orbitals more strongly than the d xy orbitals57, because of the absence of a node along the zdirection in the latter. Furthermore, our self-energy-based analysis of the bands (Supplementary Note 11) indicates not Rashba, but Zeemantype splitting. In the absence of an external magnetic field, which would affect both distinct 2DELs, or an intrinsic ferromagnetic order, the Zeemantype lifting of the 2DEL degeneracy suggests that the band splitting on the TiO 2 termination stems from magnetic interactions similar to altermagnets40,58. In such systems, lifting of the Kramers degeneracy arises from the in-equivalence of Ti atoms with an unpaired spin in the near surface region and does not require significant spin-orbit coupling, while certain spin configurations still generate spin textures in reciprocal space that observe time-reversal symmetry59. More specifically, a non-coplanar spin texture observing combined time reversal and translational symmetry (T⋅t) is expected to be facilitated by slight displacements between neighbouring Ti3+ atoms. Along these lines, the SrO surface with a degenerate 2DEL represents an antiferromagnet with the spin sublattices connected by translation symmetry, or lacks the spin order entirely. Further experiments with spin resolution in real and reciprocal space and advanced theoretical approaches will be needed to refine this scenario. Electron-phonon coupling The strong coupling between electronic and structural degrees of freedom on the TiO 2 -terminated surface is observed in a photoemission kink in the d xy -derived bands seen in Fig. 1g and quantified previously6at binding energies comparable to the SrTiO 3 phonon bandwidth60, hinting at sizable electron-phonon coupling (EPC)61.In Fig. 4a, we show the data from Fig. 1g together with the bare dispersions (parameters in Supplementary Table 1) and MDC maxima. Using our recently developed self-consistent extraction method based on Bryan’s implementation of the maximum entropy method62, we determine the Eliashberg spectral function α2F(ω)63 of the outer right-hand branch, while accounting for the photoemission matrix element64 and quantifying the magnitudes of the electronelectron65 and electron-impurity self-energies66. The real Σ0ðEÞand minus imaginary Σ00ðEÞparts of the complex electron self-energy ΣðEÞ=Σ0ðEÞ+iΣ00ðEÞ67 interpreted as being on the renormalized band68 are shown in the inset of Fig. 4b, whereas the extracted α2F(ω)is presented in the main panel. The latter shows large spectral weight at ω=56 meV, ω=69 meV, and ω=84 meV, likely related to the respective LO 3 ,TO 4 ,andLO 4 phonon modes60, which display moderate to strong EPC in undoped bulk SrTiO 3 at similar energies69. However, contributions from surface phonons, found in first-principles calculations at similar energies70, cannot be excluded. Notably, due to charges accumulated at the surface in the form of the 2DEL and ingap states, our LO 4 mode is red-shifted by approximately 8 meV with respect to first-principles calculations for undoped bulk SrTiO 3 69,71. The intensity and width of the large spectral weight near ω=40 meV suggests a mixed coupling. We repeat the analysis for the outer lefthand branch (Supplementary Note 7), where the high-energy phonon modes are well-reproduced. By contrast, the mixed feature near ω=40 meV is blue-shifted for the left-hand side, suggesting that the extraction procedure is more reliable for higher phonon energies. The calculated charge density of n 2D =3.51×10 13 cm−2for the outer Article https://doi.org/10.1038/s41467-025-59258-4 Nature Communications | (2025) 16:4594 5 branch (Supplementary Table 1) places our results in the highdensity26 or Fermi liquid regime. Whereas the LO 4 mode was previously quantified from polaronic sidebands shifted from the band bottom by integer multiples of the mode energy25,26, the extraction of α2F(ω) complements this approach for systems in the Fermi liquid regime. Furthermore, we quantify the electron-phonon coupling parameter λ∂Σ0ðEÞ=∂EjE=EF=0:63, in reasonable agreement with λ=0.71 quantified previously6. The exceptional data quality for the TiO 2 -terminated surface has allowed us to identify the dominant modes in the Eliashberg function and to quantify the magnitude of the EPC. The combination of spin order and the strong coupling between electronic and lattice degrees of freedom opens up the thrilling prospect of coherently controlling the spin texture, and thus also the spin-to-charge conversion47,via ultrashort laser pulses. In conclusion, our results highlight that a precise knowledge and control of the surface structure is crucial to understand the fundamental mechanisms and engineer the properties of 2DELs on oxide surfaces. We shine new light on 2DELs on SrTiO 3 (001) by studying and manipulating truly bulk-terminated surfaces with unambiguous surface structure. Two well-defined terminations, differing in a single atomic layer only, host two distinct 2DELs, while the atomically illdefined surface areas (conchoidal) can host a myriad of various 2DELs of lesser quality. The distinct 2DELs on both terminations are populated by charges from the bulk of the material, which is found to be self limiting with nearly identical band filling. Irrespective of these similarities, the Kramers degeneracy is lifted on the TiO 2 ,andpreservedon the SrO termination, indicating a structural cause and the connection between polar distortions and non-relativistic spin order. The presence of strong electron-phonon coupling makes these surfaces a promising venue to explore such coupling mechanisms on ultrashort time scales and drive spin phenomena by external stimuli. Methods SrTiO 3 single crystals with 0.5 wt% of Nb 2 O 5 doping (0.7 at% Nb at the BsitesofSrBO 3 ) were used in this study. The custom shaped 3.5 × 2 × 7 mm3SrTiO 3 samples were purchased from MaTeck GmbH. Pristine bulk-terminated strontium titanate SrTiO 3 (001) surfaces were achieved by cleaving SrTiO 3 single crystals at room temperature, through our recently developed procedures17,22. Cleaving devices made out of stainless steel were thoroughly cleaned ex situ before each cleaving, and were not degassed in vacuum sincethe investigated SrTiO 3 (001) surfaces were not exposed to temperatures higher than room temperature. All surfaces shown in the main text were cleaved in situ: samples studied with ncAFM were cleaved inside an UHV chamber with a base pressure lower than 1 × 10−10 mbar, and samples studied with ARPES were cleaved inside a baked UHV loadlock with the pressure lower than 1 × 10−8mbar. After cleaving, the samples were introduced to the measurement chambers with lower pressure as soon as possible, within several minutes. It is noteworthy that we do not expect significant surface chemistry to occur on our samples at room temperature where the samples were cleaved. This surface preparation technique guarantees the same surface treatment of all terminations on a single cleaved SrTiO 3 surface, and we did not observe temporal degradation of our samples during measurements. ARPES measurements were performed at MAX IV synchrotron facility in Lund, Sweden, at the Bloch beamline. Cleaved samples were held at T=21.5 K during measurements in an UHV chamber with a base pressure of 1 × 10−10 mbar. All ARPES measurements were performed with linear vertical, i.e. s-polarized light and the slit of the Scienta DA30 electron analyzer was perpendicular to the scattering plane, and parallel to the [110] orientation of the crystal. All ARPES data is presented in a gray color scale, where black and white represent the maximum and the minimum photoelectron count, respectively. The experiments were reproduced on four samples during two experimental runs, with up to 100 measurement sites per sample. The separate terminations were investigated in random order, and no degradation with time was observed, i.e., spectra pertaining to a single termination did not change depending on the time between SrTiO 3 (001) cleavage and ARPES investigation. During the ARPES measurements, ex-situ optical microscopy of the cleaved SrTiO 3 (001) counter-piece surface was used as a guide towards well-defined areas, and the crystal edges were used as position markers to correlate ARPES, optical microscopy, and SEM. Highest-quality ARPES measurements were performed at those positions on a SrTiO 3 (001) surface where a single domain was sufficiently large, such that we did not observe contributions from the other termination(s) when moving tens of micrometers. Atomically resolved ncAFM measurements were performed with a low-temperature Omicron qPlus STM/AFM head, located in UHV with base pressure below 10−11 mbar. Bias sweeps used for recording STS measurements and Kelvin parabolas were performed in the same measurement head, by applying bias to the sample. The sample bias was modulated with a frequency of 123 Hz and an amplitude of 10 mV during STS measurements, and the current signal was differentiated using a Zürich Instruments lock-in amplifier. All STM/ncAFM measurements were performed close to the LHe temperature, i.e., at T≈5K. Electrochemically etched tungsten tips cleaned in situ by selfsputtering with Ar+ions72 were used, after thorough functionalization on a Cu(110) single crystal surface. All images in the main text were achieved by a tip thatwasadditionally functionalized with an O atom at the tip apex21. Custom-design high-quality-factor (≈50000) qPlus tuning forks with a separate wire for the tunneling current were used73. Fig. 4 | Bare bands, MDC maxima, and the right-hand outer Eliashberg spectral function for the TiO 2 -terminated surface. a Bare bands (lines) and MDC maxima for the outer left (red), inner left (green), inner right (orange), and outer right (blue) branches, together with the faint band Fermi wavevectors (black dots). bThe Eliashberg function α2F(ω) (magenta) with a 95% confidence interval (pink), determined from the right-hand outer real Σ0ðEÞ(blue) and minus imaginary Σ00ðEÞ (purple) self-energy data shown in the inset with 95% confidence intervals and accompanied by continuous lines reconstructed from the obtained α2F(ω). Article https://doi.org/10.1038/s41467-025-59258-4 Nature Communications | (2025) 16:4594 6 The cantilever deflection was measured using a cryogenic differential preamplifier74. A bungee-cord suspension system was employed for removing mechanical noise during measurements75. X-ray and electron irradiation were both performed at a sample held in an electrically grounded manipulator cooled to T=100 K, in an UHV chamber with a base pressure below 1 × 10−10 mbar. The irradiated surfaces were subsequently studied after their reintroduction to the ncAFM measurement head. The samples were not warmed up following the irradiation at T=100 K as they were transferred to the measurement head using a pre-cooled wobblestick at a temperature lower than T=100 K. Al KαX-rays were generated from a dual-anode X-ray source (SPECS XR50, Mg/Al Kα, operated with 400 W power at a distance of ≈10 mm to the sample). Low-energy electrons were emitted from the filament of the low-energy electron diffraction (LEED) setup and were focused on the sample through integrated electron optics. Electrons with 47 eV were chosen in order to excite the KnoteckFeibelman mechanism31. The spot size for X-ray irradiation was ≈1cm 2, while the electron irradiation was focused to ≈1mm 2. Uniform irradiation of the entire sample was achieved by rastering the sample position below a fixed X-ray or electron source. The X-ray and electron doses were varied by changing the irradiation time while all the other parameters were kept fixed. The X-ray and electron count indicated in Fig. 3were converted from the measured sample current during irradiation, adjusted for the spot size and the duration of irradiation. SEM images were acquired with a FEI Quanta 200F measurement setup, with a nominal vacuum of 1 × 10−5mbar. The working distance was ≈8 mm. Secondary electrons were detected with an Everhart-Thornley detector. All SEM images are presented in a gray color scale, where white and black represent the maximum and the minimum secondary electron count, respectively. All surfaces imaged with SEM were acquired under same conditions. An electron energy of 5 kV was used. SEM imaging was performed at the USTEM facility of the TU Wien. Optical photographs were taken using an Olympus SZX12 microscope equipped with a DF PLAPO 1X PF lens, and an attached Olympus E-330 camera with a 14–45 mm lens. Data acquired with ncAFM was processed for drift correction, background subtraction, and noise reduction using ImageJ software (imagej.net) augmented with procedures developed by Michael Schmid. ARPES data was analyzed and processed using the pesto Python library (pesto.readthedocs.io) developed by Craig Polley, in combination with IGOR Pro software (wavemetrics.com). Self-energy and Eliashberg function extraction were performed with a private version of xARPES, whose description is laid out in Supplementary Notes 8–11. Data availability The data that support the analysis for this study are available from the corresponding authors upon request. 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Schmid, M., Setvín, M. & Diebold, U. Device for suspending a load in a vibration-insulated manner. US patent WO/2018/037102 (2018). Acknowledgements I.S., M.Sc., U.D. and M.Se. acknowledge support by the Austrian Science Fund (FWF) projects Solids4Fun (F-1243) and SuPer (P32148-N36). U.D. also acknowledges support by the FWF SFB project TACO (GrantDOI:10.55776/F81); for open access purposes the author has applied a CC BY public copyright license to any author accepted manuscript version arising from this submission. T.P. v.W. is a Research Fellow of the F.R.S.-FNRS. S.P. acknowledges financial support from the F.R.S.-FNRS (Belgium) and the Walloon Region in the strategic axe FRFS-WEL-T. M.R. and E.B.G were supported by SNSF Research Grant 200021_182695. M.Se. also acknowledges support from the Czech Science Foundation GACR 20-21727X and GAUK Primus/20/SCI/009. F.G. and J.H.D. acknowledge support from the Swiss National Science Foundation (SNSF) Project No. 200021-200362. We acknowledge MAX IV Laboratory for time on the Bloch Beamline under Proposal 20210244. Research conducted at MAX IV, a Swedish national user facility, is supported by the Swedish Research council under contract 2018-07152, the Swedish Governmental Agency for Innovation Systems under contract 2018-04969, and Formas under contract 2019-02496. Article https://doi.org/10.1038/s41467-025-59258-4 Nature Communications | (2025) 16:4594 8 Author contributions I.S., E.B.G., F.G., C.P. and J.H.D. acquired, analyzed, and presented experimental ARPES data; I.S. acquired, analyzed, and presented experimental ncAFM/STM data; T.P.v.W., S.P. and J.H.D. analyzed experimental ARPES data to extract 2DEL parameters and extracted selfenergies and the Eliashberg function; S.P., M.Sc., U.D., M.R., M.Se. and J.H.D. verified the presented findings; U.D., M.Se. and J.H.D. conceived the project and acquired funding. I.S., E.B.G., T.P.v.W. and J.H.D. compiled the first paper draft, all Authors wrote and proofed the final version of the manuscript. Competing interests The authors declare no competing interests. Additional information Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s41467-025-59258-4. Correspondence and requests for materials should be addressed to Igor Sokolovićor J. Hugo Dil. Peer review information Nature Communications thanks Rui-Hua He and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available. Reprints and permissions information is available at http://www.nature.com/reprints Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. 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