Engineering topological band conduction into KTaO3’s two-dimensional electron gases

Engineering topological band conduction into KTaO3’s two-dimensional electron gases | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Engineering topological band conduction into KTaO 3 ’s two-dimensional electron gases Zhi Gang Cheng, Yuting Zou, Hyungki Shin, Haoran Wei, Bruce Davidson, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1579411/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 29 Dec, 2022 Read the published version in npj Quantum Materials → Version 1 posted 12 You are reading this latest preprint version Abstract Two-dimensional electron gas (2DEG) systems generated at oxide interfaces that exhibit novel physics phenomena have opened up a new era for oxide-based electronics, photonics, and spintronics. The recent discovery of superconductivity plus the strong spin-orbital coupling naturally existing in the 2DEGs of KTaO 3 (KTO) makes KTO an exciting platform for the interplay of the electronic and spin degree of freedom to create new physical properties. By directly placing KTO’s 2DEGs next to another strongly-correlated oxide with nontrivial topological nodes, we reveal direct evidence of topological states in the electronic transport properties of the KTO’s 2DEGs, due to the electronic reconstruction caused by the proximity effect. This adds potential for new functionality in KTO heterostructures. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Intensive attention has recently been focused on perovskite oxide heterostructures for two-dimensional electron gases (2DEGS) hosted at interfaces. A rich variety of exotic phenomena has been observed, such as metal-insulator transitions (MIT), magnetic correlations, strong tunability by an electric field, and superconductivity. A typical example is LaAlO 3 /SrTiO 3 (LAO/STO), within which 2DEGs are formed in STO close to the interface by charge transfer due to discontinuity of polarity. It simultaneously exhibits extremely high mobility (10,000 cm 2 V − 1 s − 1 ), superconductivity, ferromagnetism, and a rich electronic phase diagram 1–7 . Especially, the coexistence of ferromagnetism and superconductivity makes LAO/STO an intriguing candidate for unconventional superconductivity. In addition, Rashba-type spin-orbit coupling associated with broken spatial inversion symmetry provides a convenient and promising way to manipulate magnetic structure electrically, making LAO/STO an ideal platform for practice in spintronics 8 . With respect to STO, KTaO 3 (KTO) shares similarities but also distinct features in the crystal structure, transport properties, and band structure 9–11 . KTO-based heterostructures accordingly host 2DEGs when oxygen vacancies are generate in KTO. Some in this series exhibit high mobility, strong spin polarization, and the recently discovered nonconventional superconductivity, etc 12–18 . In particular, with STO-based counterparts for which Ti 3 d orbitals make the main contribution, KTO-based heterostructures incorporate itinerant electrons from Ta 5d -orbitals. Stronger spin-orbit coupling (SOC) is thus expected to introduce non-zero Berry curvature to the reciprocal space 19 . Topological band structures and other phenomena such as Rashba splitting may occure consequently. It has been also pointed out by recent theoretical study that topological superconductivity may be induced by in-plane magnetic field to a two-dimensional metallic system with spin-orbit couplings because spin-orbit coupling creates topologically nontrivial spin textures and could also serve as attractive force for electron parings 20 . Non-trivial topology, together with exsting exotic properties including superconductivity and spin polarization, enrich KTO-based heterostructure with great prospects in both fundamental research and practical applications. For instance, topological superconductivity is theoretically proven to be able to host Majorana zero modes – an essential prerequisite to realizing non-Abelian statistics – and potentially plays a key role in developing topological quantum computation 15–18 . Moreover, the strong SOC can also be used in developing novel spintronic devices such as spin-orbit torque-based magneto-resistive randomized access memory (SOT-MRAM), making KTO-based heterostructure a better candidate in spintronics compared with its STO-based counterpart. It has been reported previously that the heterostructure of LaTiO 3 /KTaO 3 (LTO/KTO) can host two-dimensional electron gas (2DEG) with high mobility 14 . In comparison with LTO, EuTiO 3 (ETO) has distinctive magnetic properties due to the partially-filled 4f orbitals of Eu and their exchange interaction between Ti- 3d and Eu- 5d orbitals 21,22 . G-type antiferromagnetism (AFM) is formed at a Néel temperature of \({T}_{N}=5.5\) K with \(7 {\mu }_{B}\) on each Eu 2+ site 23,24 . Moreover, multiferroic properties due to strong spin-lattice coupling has been shown by first-principle calculations 25 and via strain-effect 22 . Recent experiments reveal evidence of the existence of topology-related phenomena including skyrmion-like Hall effect 26 and Weyl nodes 23 in doped ETO. It is reported that a highly mobile and spin-polarized 2DEG could be realized within the heterostructure of EuO/KTO 27 based on which thermal spin injection was realized 13 and superconductivity was observed 15,16,28 . Similarly, EuO/TaO2 interface can be also realized within the ETO/KTO heterostructure, which may as well host 2DEG with strong SOC and exotic magnetic and topological properties. Here we report electric transport measurements on both LTO/KTO and ETO/KTO heterostructures. LTO and ETO were deposited onto substrates of KTO respectively by the molecular beam epitaxy (MBE) method. We observed Kondo effects for the temperature dependence of resistivity and corrections to magnetoresistance due to superposition of weak anti-localization (WAL) and weak localization (WL) for both samples. The extracted magnetic coherence length \({l}_{\varphi }\) and spin-orbit coupling length \({l}_{SO}\) are smaller for ETO/KTO in comparison with LTO/KTO, suggesting the different origin of SOC. Since Rashba effect should be similar for both heterostructures as both 2DEGs reside in KTO near the interface, the distinguished strong WAL for ETO/KTO should originate from the proximity effect of the topological band structure of ETO, which is supported by its anomalous Hall effect. Our results provide an effective way for tuning and engineering topological properties of band structure into KTO-based heterostructure which can be extended to other interfacial electronic systems. Results Temperature-dependence of resistivity . Samples were prepared by molecular beam epitaxy (MBE) method and high crystalline quality was achieved (see Fig. 1 and Methods ). Both samples have shown the typical densities of 2DEG carriers in KTO (Supplementary Information Fig. 2 ) from oxygen vacancies formed during high temperature annealing, and electronic reconstruction due to the polar nature of KTO 19 . Although polar catastrophe has been proposed to be another origin of 2DEGs, experimental evidence remains missing. Figure 1 (d & e) exhibits the temperature dependence of resistivity below 20 K. Both types of samples exhibit metal-insulator transitions. For LTO/KTO, the transition takes place at 10.2 K, below which it firstly exhibits an upturn with approximate \(\text{l}\text{n}\left(T\right)\) dependence, and starts to saturate from 300 mK down to 30 mK. Such a temperature dependence is characteristic of the Kondo effect originating from the interplay of itinerant electrons and magnetic impurities, and the saturation implies screening of magnetic impurities by bound electrons via spin-exchange interactions. The temperature dependence can be fitted by the empirical relation 29,30 $$\begin{array}{c}R\left(T\right)={R}_{0}+{R}_{K}\left(T\right)={R}_{0}+{R}_{K}\left(0\right){\left[{\left(\frac{T}{{T}_{K}}\right)}^{2}\left({2}^{\frac{1}{s}}-1\right)+1\right]}^{-s}\#\left(1\right)\end{array}$$ where \({R}_{0}\) is temperature independent resistance including residual resistance due to sample disorder and extra resistance associated with weak localization (WL) or weak antilocalization (WAL), \({T}_{K}\) the Kondo temperature, and \(s\) a parameter related with spin. Here we fix \(s=0.22\) for spin \(S=1/2\) 30 and get a satisfactory fitting with \({T}_{K}=1.21\) K. In comparison, the ETO/KTO sample exhibits the metal-insulator transition at 12.1 K and a well-fitted Kondo behavior below 1.50 K with \(s=0.22\) and \({T}_{K}=1.49\) K. There are two wiggle points at 3.85 K and 1.50 K, which lead to the resistance below 1.50 K shifting downwards. The shift may be ascribed to the suppression of electron back-scattering associated with the emergence of topology to conducting band, which will be discussed later. Localization effects of magnetoresistance. Magnetoresistance (MR) has been measured for both samples at multiple temperatures (see Fig. 2 ). MR of the LTO/KTO sample demonstrates a sharp feature within the narrow range of \(\pm 0.05\) T at 0.25 K. With an increasing magnetic field, resistivity firstly increases and starts to decrease for \(\left|B\right|>0.015\) T. Such a feature becomes less obvious as the temperature is raised and vanishes at around 3 K. Besides the MR near the zero field, an extra dip of resistance is observed around zero field at 4 K with a half-width of 0.05 T. The dip develops into a plateau with larger width and smoother edge at lower temperatures, and the edge eventually merged with the universal background. One possible explanation of this is that part of the sample becomes superconducting similar to EuO/KTO and LAO/KTO 15 . However, this scenario cannot be confirmed without further investigation by other techniques such as scanning tunneling spectroscopy (SPS). A similar feature in MR is observed for the ETO/KTO sample in a similar temperature range but with much larger magnitude and in a much wider magnetic field range of \(\pm 0.5\) T. However, no feature of an additional plateau similar to that for LTO/KTO is observed. The superposition of positive and negative MR suggests the coexistence of both weak localization (WL) and weak anti-localization (WAL) 31 . In the diffusive transport process, maintenance of phase coherence causes phase interference, therefore leading to an increase in resistivity, while the existence of SOC causes destructive interference and leads to a decrease in resistivity. Correction of WL and WAL to conductivity can be described by the theory of Iordanskii, Lyanda-Geller, and Pikus (ILP) 32 $${\Delta }\sigma \left(B\right)=-\frac{{e}^{2}}{\pi h}\left[\frac{1}{2}\psi \left(\frac{1}{2}+\frac{{B}_{\varphi }}{B}\right)-\frac{1}{2}\text{ln}\left(\frac{{B}_{\varphi }}{B}\right)-\psi \left(\frac{1}{2}+\frac{{B}_{\varphi }+{B}_{SO}}{B}\right)+\text{ln}\left(\frac{{B}_{\varphi }+{B}_{SO}}{B}\right)-\frac{1}{2}\psi \left(\frac{1}{2}+\frac{{B}_{\varphi }+{2B}_{SO}}{B}\right)+\frac{1}{2}\text{ln}\left(\frac{{B}_{\varphi }+{2B}_{SO}}{B}\right)\right] \left(2\right)$$ where \({B}_{\varphi }=\frac{h}{4e{l}_{\varphi }^{2}}\) is the dephasing magnetic field determined by the phase coherence length \({l}_{\varphi }\) , \({B}_{SO}=\frac{h}{4e{l}_{SO}^{2}}\) is the spin-orbit scattering field determined by the spin-orbit scattering length \({l}_{SO}\) , and \(\psi \left(x\right)\) is the digamma function. We find that Eq. (2) can fit the feature of MR very well for both samples as shown in Fig. 3 and Fig. 4 , and the extracted values of \({l}_{\varphi }\) and \({l}_{SO}\) are plotted in Fig. 3 (e,f) and Fig. 4 (e,f), respectively. On one hand, these two characteristic lengths of both samples share some properties in common: \({l}_{\varphi }\) scales with \({T}^{-1/2}\) , and the exponent of -1/2 indicates that the transport is two-dimensional; \({l}_{SO}\) does not observe to be obviously temperature-dependent. On the other hand, characteristic lengths of LTO/KTO are significantly larger than those of ETO/KTO: for LTO/KTO, \({l}_{\varphi }=200\tilde232\) nm and \({l}_{SO}\approx 190\) nm, while for ETO/KTO, \({l}_{\varphi }=130\tilde180\) nm and \({l}_{SO}\approx 50\) nm. In comparison, mean free path ( \({l}_{mfp}\) ) for both samples are around 20 nm (see Supplementary Fig. 2), smaller than \({l}_{\varphi }\) and \({l}_{SO}\) . The ILP theory is derived for the diffusive regime, i.e. \(B<\frac{\hslash }{2e{l}_{mfp}^{2}}\) . The value of \({l}_{mfp}\) constrain the validity of the ILP model within the magnetic field of \(\pm 0.8\) T, in consistence with valid range of the fitting to the ETO/KTO sample. However, the ILP model fits the MR of the LTO/KTO sample in a much smaller range, probably because spin canting and rotation of TiO6 tetrahedral caused by external field are more obvious due to the smaller magnetic moment of Ti 3+14,24 . The extracted characteristic lengths \({l}_{\varphi }\) and \({l}_{so}\) are plotted in (e) as functions of \({T}^{-\frac{1}{2}}\) . The green dashed line in panel (e) is a linear fit, demonstrating that \({l}_{\varphi }\propto {T}^{-\frac{1}{2}}\) . The fact that \({l}_{\varphi }\) being larger than \({l}_{SO}\) guarantees the phase coherence during the spin-orbit scattering process, leading to the obvious positive MR (or negative magnetoconductance) associated with the WAL effect. We note that the magnitude of conductance change \({\Delta }\sigma\) for the LTO/KTO sample is about one order of magnitude smaller than that for the ETO/KTO sample ( \(\tilde0.01{e}^{2}/h\) vs. \(\tilde0.2{e}^{2}/h\) ). This is because the difference between \({l}_{\varphi }\) and \({l}_{SO}\) is much smaller ( \(\frac{{l}_{\varphi }}{{l}_{SO}}\approx 1.1\) for LTO/KTO vs. 3.0 for ETO/KTO), and the effects of WL partially cancel that of WAL on conductance. However, both characteristic lengths for the LTO/KTO sample are significantly larger than those for the ETO/KTO sample, suggesting either much more scattering sites existing in the ETO/KTO sample to destroy phase coherence and to cause spin flips or the transport process is governed by different nature of conducting band. The former possibility is unlikely thanks to the similar quality of crystalline and interfaces for both samples, while the latter is highly possible due to the much larger magnetic moment on Eu 2+ sites and the possible topological band of ETO 23 . Anomalous Hall effect. Since itinerant electrons reside in KTO for both cases, the magnitude of Rashba coupling should be similar and cannot account for the difference of WAL effect between the two samples. To clarify the origin of the stronger scattering in the ETO/KTO sample, we performed Hall measurements for both samples (Supplementary Information Fig. 1 ). In spite of the quasi-linear dependence of \({\rho }_{xy}\) on the magnetic field, a weak anomalous Hall effect can still be observed. Figure 5 shows the anomalous hall resistance \({\rho }_{AHE}\) extracted by subtracting \({\rho }_{xy}\) by an ordinary Hall term \({\rho }_{H}\propto \alpha B\) , where \(\alpha\) is a coefficient determined by a linear fit of \({\rho }_{xy}\) between 3 T and 4 T. \({\rho }_{AHE}\) for LTO/KTO is negative (namely \({\rho }_{AHE}0\) ) and temperature-independent below 5 K. In stark contrast, \({\rho }_{AHE}\) for ETO/KTO is positive and exhibits a strong temperature dependence until it vanishes above 5 K. Furthermore, its magnitude – at 0.5 K for example – is about 10 times larger than that of LTO/KTO. Discussions In Fig. 5 (b), we find that \({\rho }_{AHE}\) at 2 K saturates at about 2 T. This is consistent with the magnetization of ETO 23,33 . Furthermore, the onset temperature of \({\rho }_{AHE}\) is also close to the Neel temperature of ETO ( \({T}_{N}=5.5\) K). Both evidences support that the AHE is highly related with the proximity of ETO. It has been pointed out that non-trivial Berry curvature can be induced and controlled in ETO by applying external magnetic field 23 . Induced Zeeman splitting in the process of canting magnetic moments causes type II Weyl nodes and topologically changes the band structure of ETO. The high similarity between the measured \({\rho }_{AHE}\) and magnetization in ETO suggests that electrons at the ETO/KTO interface are strongly influenced by the topological band structure of ETO. The emergence of \({\rho }_{AHE}\) – becoming obvious below about 5 K – also coincides with the wiggle points appearing in the \(\rho -T\) curve in Fig. 1 (e). The emergence of wiggle point could be due to the suppression of electron back-scattering associated with spin-orbit locking. In contrast, \({\rho }_{AHE}\) for the LTO/KTO sample, being temperature independent and much weaker, should solely stem from the topology induced by Rashba-type SOC in KTO. The Rashba effect is weakly temperature dependent below 5 K because of its higher spin-orbit split band 34,35 , leading to the temperature independence of \({\rho }_{AHE}\) . In summary, we have studied the transport properties of 2DEG residing near the interfaces of both LaTiO3/KTaO3 and EuTiO3/KTaO3 heterostructures, and observed superposition of weak localization and weak anti-localization effects. The extracted phase coherence length \({l}_{\varphi }\propto {T}^{-1/2}\) and \({l}_{SO}\) is temperature independent, confirming the existence of spin-orbit coupling in both heterostructures, while characteristic lengths of ETO/KTO are much smaller, implying the coupling mechanism is different. By analyzing the anomalous Hall effect, we found that AHE for ETO/KTO features with a positive sign, strong temperature dependence, and large magnitude, different from the LTO/KTO sample. We deduce that such a difference, together with the localization effects, stems from the strong topological band induced by the ETO film. Methods Sample preparation and structural characterization. All films were grown on insulating KTO (001) substrates (MTI). The lattice constant of KTO is 3.99 Å, larger than ETO (3.905 Å) and LTO (3.97 Å), which results in the tensile strain in all epitaxial films. The samples were grown in an oxide molecular beam epitaxial (MBE) system (Veeco GenXplor) with a base pressure < 5×10 − 10 torr. The flux ratio between Eu, La, and Ti was calibrated by quartz crystal microbalance, and the film growth process and the number of layers were monitored and determined by in-situ reflection high-energy electron diffraction. At the temperature of 700°C, KTO substrate was annealed for 30 min without oxygen to degas. After that, ETO film was grown on the substrate by co-deposition in a partial pressure of molecular oxygen pressure of 4–5×10 − 8 Torr. LTO film was also grown by co-deposition in a partial pressure of molecular oxygen pressure of 3–4×10 − 8 Torr. After the film growth, all samples were capped with 5 nm of amorphous Ge at room temperature to prevent sample deterioration during the ex-situ measurements. Bare KTO substrate, after the same annealing process and 5 nm of amorphous Ge capping, shows clear insulating behavior. Same growth methods generate insulating/stoichiometric ETO and LTO films on another insulating substrate 24 . After the growth and capping, the films were characterized by X-ray diffraction (XRD, Bruker) in the 2θ-ω mode for the structural information using Cu Kα1 radiation. Electrical transport measurement and data analyses. Electric transport measurements were performed on a dilution refrigerator (Oxford Triton500). Van der Pauw (VdP) method was used for the transport measurements, with both LTO/KTO and ETO/KTO samples in a square shape with dimensions of \(5\times 5\) mm 2 and electric contacts made to four corners by indium-soldering. The Standard lock-in technique was used with a frequency of 17 Hz and a current of 1 \({\mu }\) A. Longitudinal resistance \({R}_{xx}\) was measured by running current through two contacts on the same edge, and Hall resistance \({R}_{xy}\) by running current through two contacts on diagonal. Due to the finite contact size and non-ideal symmetry, anti-symmetrization was performed to extract \({R}_{xy}\) . Pictures were taken for the samples after the contacts were made. Transport processes were then simulated by finite element modeling (FEM) using COMSOL. The simulations were run with \({\rho }_{xx}\) and \({\rho }_{xy}\) as input parameters to match the experimental results. Declarations Acknowledgements The work at IOP-CAS was supported by National Key R&D Program of China (2021YFA1401900 & Grant No. 2018YFA0305604), National Natural Science Foundation of China (NSFC) (No. 11874403), Key Research Program of Frontier Sciences, CAS, (Grant No. ZDBS-LY-SLH0010), and Beijing Natural Science Foundation (Grant No. JQ21002). The work at UBC was supported by Natural Sciences and Engineering Research Council (NSERC) of Canada and Canada Foundation for Innovation (CFI). Author contributions Z.G.C. and K.Z. conceived and designed the experiments, Y.Z., H.S., H.W. and B.A.D. fabricated and measured the devices. Z.G.C. wrote the manuscript with comments from all other authors. Additional Information Competing financial interests: the Authors declare no Competing Financial or Non-Financial Interests. References 1. Ohtomo, A. & Hwang, H. Y. 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Additional Declarations (Not answered) Supplementary Files KTOSI20220421final.docx Supplementary Information: Engineering topological band conduction into KTaO3’s two-dimensional electron gases Cite Share Download PDF Status: Published Journal Publication published 29 Dec, 2022 Read the published version in npj Quantum Materials → Version 1 posted Editorial decision: revise 13 Jun, 2022 Review # 3 received at journal 12 Jun, 2022 Review # 1 received at journal 28 May, 2022 Review # 2 received at journal 23 May, 2022 Reviewer # 3 agreed at journal 17 May, 2022 Reviewer # 2 agreed at journal 16 May, 2022 Reviewer # 1 agreed at journal 15 May, 2022 Reviewers invited by journal 15 May, 2022 Submission checks completed at journal 10 May, 2022 Editor assigned by journal 09 May, 2022 Unknown event 09 May, 2022 First submitted to journal 09 May, 2022 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-1579411","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":106117513,"identity":"41f695a5-8710-4394-954e-d9b13d51dc07","order_by":0,"name":"Zhi Gang Cheng","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA00lEQVRIiWNgGAWjYHACNhAhx8bAQ6IWY9K1JDYQrUW+f/GzBx931Kb3Sfcek2CosWPgn92AXwvjjGfmhjPPHM9tkzmXJsFwLJlB4s4B/FqYJc6wSfO2Hcttk8gxk2BgO8BgIJFAwCMgLX/bjqWzgbX8I0ILD38PmzRjW00CWAtjGxFaJCTYzCR72w4YtsmcMbZI7EvmkbhBQIt8/+FnEj/b6uTlZ/cY3vjwzU6OfwYBLQwQZxwGMhhYQGwiYof/AIisA2lh/kBY+SgYBaNgFIxEAACKUTtBtyoTuAAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-9449-6734","institution":"Institute of Physics, Chinese Academy of Sciences","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Zhi","middleName":"Gang","lastName":"Cheng","suffix":""},{"id":106117514,"identity":"7409d7fd-5f73-45d5-99a2-9529eee0e1b3","order_by":1,"name":"Yuting Zou","email":"","orcid":"","institution":"Institute of Physics, Chinese Academy of Sciences","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yuting","middleName":"","lastName":"Zou","suffix":""},{"id":106117515,"identity":"89246f10-6877-461b-b95f-9a76f4896aba","order_by":2,"name":"Hyungki Shin","email":"","orcid":"https://orcid.org/0000-0001-8435-4479","institution":"Quantum Matter Institute, University of British Columbia","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Hyungki","middleName":"","lastName":"Shin","suffix":""},{"id":106117516,"identity":"68abc74a-2b77-4aa1-aadc-7b2d14fe75fe","order_by":3,"name":"Haoran Wei","email":"","orcid":"","institution":"Institute of Physics, Chinese Academy of Sciences","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Haoran","middleName":"","lastName":"Wei","suffix":""},{"id":106117517,"identity":"ce7c1956-6acd-4f2b-b2e1-44f5ac7a7bb4","order_by":4,"name":"Bruce Davidson","email":"","orcid":"","institution":"Quantum Matter Institute, University of British Columbia","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Bruce","middleName":"","lastName":"Davidson","suffix":""},{"id":106117518,"identity":"4e8b08df-32bc-46d3-8dad-0859468b416d","order_by":5,"name":"Ke Zou","email":"","orcid":"https://orcid.org/0000-0002-1181-1779","institution":"University of British Columbia","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Ke","middleName":"","lastName":"Zou","suffix":""}],"badges":[],"createdAt":"2022-04-21 07:01:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1579411/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1579411/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41535-022-00536-5","type":"published","date":"2022-12-29T05:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":21583597,"identity":"a460e76c-5708-4828-9bad-d74b80bdd7ab","added_by":"auto","created_at":"2022-05-17 19:24:50","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":157383,"visible":true,"origin":"","legend":"\u003cp\u003e(a) schematic picture of EuTiO\u003csub\u003e3\u003c/sub\u003e/KTaO\u003csub\u003e3\u003c/sub\u003e (left) and LaTiO\u003csub\u003e3\u003c/sub\u003e/KTaO\u003csub\u003e3\u003c/sub\u003e (right) heterostructures and their atomic and antiferromagnetic spin structures (below). The size of spins on the Eu\u003csup\u003e2+\u003c/sup\u003e and Ti\u003csup\u003e3+\u003c/sup\u003e indicates the relative magnitude of magnetic moments (7\u003csub\u003eμB\u003c/sub\u003e /Eu and 7μB /Ti). (b) in-situ reflection high-energy electron diffraction (RHEED) intensity picture of EuTiO\u003csub\u003e3\u003c/sub\u003e and LaTiO\u003csub\u003e3\u003c/sub\u003e after 10 u.c. growth. (c) XRD scan of 20 u.c. EuTiO\u003csub\u003e3\u003c/sub\u003e/KTaO\u003csub\u003e3\u003c/sub\u003e (red) and 10 u.c. LaTiO\u003csub\u003e3\u003c/sub\u003e/KTaO\u003csub\u003e3\u003c/sub\u003e (purple). The symbol ★ and ▼ indicate the (001) peak of EuTiO\u003csub\u003e3\u003c/sub\u003e and carbon paste defect, respectively. Temperature dependence of resistivity is plotted in (d) for the sample of LTO/KTO and in (e) for the sample of ETO/KTO.\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-1579411/v1/0e7b0c1dad3daa9d0533f748.jpeg"},{"id":21583598,"identity":"10a03aad-148b-4556-b258-f1e46f38d0f4","added_by":"auto","created_at":"2022-05-17 19:24:50","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":188678,"visible":true,"origin":"","legend":"\u003cp\u003eMagnetoresistance of both samples. Δρ=ρ(B)-ρ(0). Curves are vertically shifted, and temperatures for each MR curve are labeled.\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-1579411/v1/3357ffa4b41228988ca73d09.jpeg"},{"id":21583595,"identity":"d2a33850-1c70-44c6-b120-4debb082ed90","added_by":"auto","created_at":"2022-05-17 19:24:50","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":154925,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"Fig3.png","url":"https://assets-eu.researchsquare.com/files/rs-1579411/v1/085b696b73fa64fb6d7951f6.png"},{"id":21584153,"identity":"9dbd8866-bff9-4824-8398-c29fd1c8c48c","added_by":"auto","created_at":"2022-05-17 19:29:50","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":108324,"visible":true,"origin":"","legend":"\u003cp\u003e(a-d) Conductance of the ETO/KTO sample at various temperatures. Grey dots are experimental data and red solid lines are fitting curve based on HLN theory.\u0026nbsp;\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-1579411/v1/ea784176b9309212958e99e5.jpeg"},{"id":21583600,"identity":"5fe95222-724a-4fa2-b671-a5ba440f3b4b","added_by":"auto","created_at":"2022-05-17 19:24:51","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":170686,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"Fig5.png","url":"https://assets-eu.researchsquare.com/files/rs-1579411/v1/951960caab7165d0706d7b3e.png"},{"id":30918852,"identity":"184808f5-fc01-4724-877b-e06401d98b45","added_by":"auto","created_at":"2022-12-30 08:07:57","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":816286,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1579411/v1/7a82be6b-4a9a-40c1-8960-84a938c9df6f.pdf"},{"id":21584152,"identity":"dc6c044d-9d8c-44d3-9f16-da5394008783","added_by":"auto","created_at":"2022-05-17 19:29:50","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":251832,"visible":true,"origin":"","legend":"Supplementary Information: Engineering topological band conduction into KTaO3\u0026#x2019;s two-dimensional electron gases","description":"","filename":"KTOSI20220421final.docx","url":"https://assets-eu.researchsquare.com/files/rs-1579411/v1/0d4f28b6ddfe168a6d021c0e.docx"}],"financialInterests":"(Not answered)","formattedTitle":"Engineering topological band conduction into KTaO\u003csub\u003e3\u003c/sub\u003e’s two-dimensional electron gases","fulltext":[{"header":"Introduction","content":"\u003cp\u003eIntensive attention has recently been focused on perovskite oxide heterostructures for two-dimensional electron gases (2DEGS) hosted at interfaces. A rich variety of exotic phenomena has been observed, such as metal-insulator transitions (MIT), magnetic correlations, strong tunability by an electric field, and superconductivity. A typical example is LaAlO\u003csub\u003e3\u003c/sub\u003e/SrTiO\u003csub\u003e3\u003c/sub\u003e (LAO/STO), within which 2DEGs are formed in STO close to the interface by charge transfer due to discontinuity of polarity. It simultaneously exhibits extremely high mobility (10,000 cm\u003csup\u003e2\u003c/sup\u003eV\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003es\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e), superconductivity, ferromagnetism, and a rich electronic phase diagram\u003csup\u003e1\u0026ndash;7\u003c/sup\u003e. Especially, the coexistence of ferromagnetism and superconductivity makes LAO/STO an intriguing candidate for unconventional superconductivity. In addition, Rashba-type spin-orbit coupling associated with broken spatial inversion symmetry provides a convenient and promising way to manipulate magnetic structure electrically, making LAO/STO an ideal platform for practice in spintronics\u003csup\u003e8\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eWith respect to STO, KTaO\u003csub\u003e3\u003c/sub\u003e (KTO) shares similarities but also distinct features in the crystal structure, transport properties, and band structure\u003csup\u003e9\u0026ndash;11\u003c/sup\u003e. KTO-based heterostructures accordingly host 2DEGs when oxygen vacancies are generate in KTO. Some in this series exhibit high mobility, strong spin polarization, and the recently discovered nonconventional superconductivity, etc\u003csup\u003e12\u0026ndash;18\u003c/sup\u003e. In particular, with STO-based counterparts for which Ti 3\u003cem\u003ed\u003c/em\u003e orbitals make the main contribution, KTO-based heterostructures incorporate itinerant electrons from Ta \u003cem\u003e5d\u003c/em\u003e-orbitals. Stronger spin-orbit coupling (SOC) is thus expected to introduce non-zero Berry curvature to the reciprocal space\u003csup\u003e19\u003c/sup\u003e. Topological band structures and other phenomena such as Rashba splitting may occure consequently. It has been also pointed out by recent theoretical study that topological superconductivity may be induced by in-plane magnetic field to a two-dimensional metallic system with spin-orbit couplings because spin-orbit coupling creates topologically nontrivial spin textures and could also serve as attractive force for electron parings\u003csup\u003e20\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eNon-trivial topology, together with exsting exotic properties including superconductivity and spin polarization, enrich KTO-based heterostructure with great prospects in both fundamental research and practical applications. For instance, topological superconductivity is theoretically proven to be able to host Majorana zero modes \u0026ndash; an essential prerequisite to realizing non-Abelian statistics \u0026ndash; and potentially plays a key role in developing topological quantum computation\u003csup\u003e15\u0026ndash;18\u003c/sup\u003e. Moreover, the strong SOC can also be used in developing novel spintronic devices such as spin-orbit torque-based magneto-resistive randomized access memory (SOT-MRAM), making KTO-based heterostructure a better candidate in spintronics compared with its STO-based counterpart.\u003c/p\u003e \u003cp\u003eIt has been reported previously that the heterostructure of LaTiO\u003csub\u003e3\u003c/sub\u003e/KTaO\u003csub\u003e3\u003c/sub\u003e (LTO/KTO) can host two-dimensional electron gas (2DEG) with high mobility\u003csup\u003e14\u003c/sup\u003e. In comparison with LTO, EuTiO\u003csub\u003e3\u003c/sub\u003e (ETO) has distinctive magnetic properties due to the partially-filled \u003cem\u003e4f\u003c/em\u003e orbitals of Eu and their exchange interaction between Ti-\u003cem\u003e3d\u003c/em\u003e and Eu-\u003cem\u003e5d\u003c/em\u003e orbitals\u003csup\u003e21,22\u003c/sup\u003e. G-type antiferromagnetism (AFM) is formed at a N\u0026eacute;el temperature of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({T}_{N}=5.5\\)\u003c/span\u003e\u003c/span\u003e K with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(7 {\\mu }_{B}\\)\u003c/span\u003e\u003c/span\u003e on each Eu\u003csup\u003e2+\u003c/sup\u003e site\u003csup\u003e23,24\u003c/sup\u003e. Moreover, multiferroic properties due to strong spin-lattice coupling has been shown by first-principle calculations\u003csup\u003e25\u003c/sup\u003e and via strain-effect\u003csup\u003e22\u003c/sup\u003e. Recent experiments reveal evidence of the existence of topology-related phenomena including skyrmion-like Hall effect\u003csup\u003e26\u003c/sup\u003e and Weyl nodes\u003csup\u003e23\u003c/sup\u003e in doped ETO. It is reported that a highly mobile and spin-polarized 2DEG could be realized within the heterostructure of EuO/KTO\u003csup\u003e27\u003c/sup\u003e based on which thermal spin injection was realized\u003csup\u003e13\u003c/sup\u003e and superconductivity was observed\u003csup\u003e15,16,28\u003c/sup\u003e. Similarly, EuO/TaO2 interface can be also realized within the ETO/KTO heterostructure, which may as well host 2DEG with strong SOC and exotic magnetic and topological properties.\u003c/p\u003e \u003cp\u003eHere we report electric transport measurements on both LTO/KTO and ETO/KTO heterostructures. LTO and ETO were deposited onto substrates of KTO respectively by the molecular beam epitaxy (MBE) method. We observed Kondo effects for the temperature dependence of resistivity and corrections to magnetoresistance due to superposition of weak anti-localization (WAL) and weak localization (WL) for both samples. The extracted magnetic coherence length \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{\\varphi }\\)\u003c/span\u003e\u003c/span\u003e and spin-orbit coupling length \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{SO}\\)\u003c/span\u003e\u003c/span\u003e are smaller for ETO/KTO in comparison with LTO/KTO, suggesting the different origin of SOC. Since Rashba effect should be similar for both heterostructures as both 2DEGs reside in KTO near the interface, the distinguished strong WAL for ETO/KTO should originate from the proximity effect of the topological band structure of ETO, which is supported by its anomalous Hall effect. Our results provide an effective way for tuning and engineering topological properties of band structure into KTO-based heterostructure which can be extended to other interfacial electronic systems.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003e \u003cb\u003eTemperature-dependence of resistivity\u003c/b\u003e. Samples were prepared by molecular beam epitaxy (MBE) method and high crystalline quality was achieved (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cem\u003eMethods\u003c/em\u003e). Both samples have shown the typical densities of 2DEG carriers in KTO (Supplementary Information Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) from oxygen vacancies formed during high temperature annealing, and electronic reconstruction due to the polar nature of KTO\u003csup\u003e19\u003c/sup\u003e. Although polar catastrophe has been proposed to be another origin of 2DEGs, experimental evidence remains missing.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(d \u0026amp; e) exhibits the temperature dependence of resistivity below 20 K. Both types of samples exhibit metal-insulator transitions. For LTO/KTO, the transition takes place at 10.2 K, below which it firstly exhibits an upturn with approximate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{l}\\text{n}\\left(T\\right)\\)\u003c/span\u003e\u003c/span\u003e dependence, and starts to saturate from 300 mK down to 30 mK. Such a temperature dependence is characteristic of the Kondo effect originating from the interplay of itinerant electrons and magnetic impurities, and the saturation implies screening of magnetic impurities by bound electrons via spin-exchange interactions. The temperature dependence can be fitted by the empirical relation\u003csup\u003e29,30\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e \u003cdiv id=\"Equa\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\begin{array}{c}R\\left(T\\right)={R}_{0}+{R}_{K}\\left(T\\right)={R}_{0}+{R}_{K}\\left(0\\right){\\left[{\\left(\\frac{T}{{T}_{K}}\\right)}^{2}\\left({2}^{\\frac{1}{s}}-1\\right)+1\\right]}^{-s}\\#\\left(1\\right)\\end{array}$$\u003c/div\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{0}\\)\u003c/span\u003e\u003c/span\u003e is temperature independent resistance including residual resistance due to sample disorder and extra resistance associated with weak localization (WL) or weak antilocalization (WAL), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({T}_{K}\\)\u003c/span\u003e\u003c/span\u003e the Kondo temperature, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(s\\)\u003c/span\u003e\u003c/span\u003e a parameter related with spin. Here we fix \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(s=0.22\\)\u003c/span\u003e\u003c/span\u003e for spin \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(S=1/2\\)\u003c/span\u003e\u003c/span\u003e\u003csup\u003e30\u003c/sup\u003e and get a satisfactory fitting with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({T}_{K}=1.21\\)\u003c/span\u003e\u003c/span\u003e K.\u003c/p\u003e \u003cp\u003eIn comparison, the ETO/KTO sample exhibits the metal-insulator transition at 12.1 K and a well-fitted Kondo behavior below 1.50 K with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(s=0.22\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({T}_{K}=1.49\\)\u003c/span\u003e\u003c/span\u003e K. There are two wiggle points at 3.85 K and 1.50 K, which lead to the resistance below 1.50 K shifting downwards. The shift may be ascribed to the suppression of electron back-scattering associated with the emergence of topology to conducting band, which will be discussed later.\u003c/p\u003e \u003cp\u003e \u003cb\u003eLocalization effects of magnetoresistance.\u003c/b\u003e Magnetoresistance (MR) has been measured for both samples at multiple temperatures (see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). MR of the LTO/KTO sample demonstrates a sharp feature within the narrow range of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm 0.05\\)\u003c/span\u003e\u003c/span\u003e T at 0.25 K. With an increasing magnetic field, resistivity firstly increases and starts to decrease for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|B\\right|\u0026gt;0.015\\)\u003c/span\u003e\u003c/span\u003e T. Such a feature becomes less obvious as the temperature is raised and vanishes at around 3 K. Besides the MR near the zero field, an extra dip of resistance is observed around zero field at 4 K with a half-width of 0.05 T. The dip develops into a plateau with larger width and smoother edge at lower temperatures, and the edge eventually merged with the universal background. One possible explanation of this is that part of the sample becomes superconducting similar to EuO/KTO and LAO/KTO\u003csup\u003e15\u003c/sup\u003e. However, this scenario cannot be confirmed without further investigation by other techniques such as scanning tunneling spectroscopy (SPS). A similar feature in MR is observed for the ETO/KTO sample in a similar temperature range but with much larger magnitude and in a much wider magnetic field range of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm 0.5\\)\u003c/span\u003e\u003c/span\u003e T. However, no feature of an additional plateau similar to that for LTO/KTO is observed.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe superposition of positive and negative MR suggests the coexistence of both weak localization (WL) and weak anti-localization (WAL)\u003csup\u003e31\u003c/sup\u003e. In the diffusive transport process, maintenance of phase coherence causes phase interference, therefore leading to an increase in resistivity, while the existence of SOC causes destructive interference and leads to a decrease in resistivity. Correction of WL and WAL to conductivity can be described by the theory of Iordanskii, Lyanda-Geller, and Pikus (ILP)\u003csup\u003e32\u003c/sup\u003e\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$${\\Delta }\\sigma \\left(B\\right)=-\\frac{{e}^{2}}{\\pi h}\\left[\\frac{1}{2}\\psi \\left(\\frac{1}{2}+\\frac{{B}_{\\varphi }}{B}\\right)-\\frac{1}{2}\\text{ln}\\left(\\frac{{B}_{\\varphi }}{B}\\right)-\\psi \\left(\\frac{1}{2}+\\frac{{B}_{\\varphi }+{B}_{SO}}{B}\\right)+\\text{ln}\\left(\\frac{{B}_{\\varphi }+{B}_{SO}}{B}\\right)-\\frac{1}{2}\\psi \\left(\\frac{1}{2}+\\frac{{B}_{\\varphi }+{2B}_{SO}}{B}\\right)+\\frac{1}{2}\\text{ln}\\left(\\frac{{B}_{\\varphi }+{2B}_{SO}}{B}\\right)\\right] \\left(2\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({B}_{\\varphi }=\\frac{h}{4e{l}_{\\varphi }^{2}}\\)\u003c/span\u003e\u003c/span\u003e is the dephasing magnetic field determined by the phase coherence length \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{\\varphi }\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({B}_{SO}=\\frac{h}{4e{l}_{SO}^{2}}\\)\u003c/span\u003e\u003c/span\u003e is the spin-orbit scattering field determined by the spin-orbit scattering length \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{SO}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\psi \\left(x\\right)\\)\u003c/span\u003e\u003c/span\u003e is the digamma function.\u003c/p\u003e \u003cp\u003eWe find that Eq.\u0026nbsp;(2) can fit the feature of MR very well for both samples as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, and the extracted values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{\\varphi }\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{SO}\\)\u003c/span\u003e\u003c/span\u003e are plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e (e,f) and Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (e,f), respectively. On one hand, these two characteristic lengths of both samples share some properties in common: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{\\varphi }\\)\u003c/span\u003e\u003c/span\u003e scales with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({T}^{-1/2}\\)\u003c/span\u003e\u003c/span\u003e, and the exponent of -1/2 indicates that the transport is two-dimensional; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{SO}\\)\u003c/span\u003e\u003c/span\u003e does not observe to be obviously temperature-dependent. On the other hand, characteristic lengths of LTO/KTO are significantly larger than those of ETO/KTO: for LTO/KTO, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{\\varphi }=200\\tilde232\\)\u003c/span\u003e\u003c/span\u003e nm and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{SO}\\approx 190\\)\u003c/span\u003e\u003c/span\u003e nm, while for ETO/KTO, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{\\varphi }=130\\tilde180\\)\u003c/span\u003e\u003c/span\u003e nm and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{SO}\\approx 50\\)\u003c/span\u003e\u003c/span\u003e nm. In comparison, mean free path (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{mfp}\\)\u003c/span\u003e\u003c/span\u003e) for both samples are around 20 nm (see Supplementary Fig.\u0026nbsp;2), smaller than \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{\\varphi }\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{SO}\\)\u003c/span\u003e\u003c/span\u003e. The ILP theory is derived for the diffusive regime, i.e. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(B\u0026lt;\\frac{\\hslash }{2e{l}_{mfp}^{2}}\\)\u003c/span\u003e\u003c/span\u003e. The value of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{mfp}\\)\u003c/span\u003e\u003c/span\u003e constrain the validity of the ILP model within the magnetic field of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm 0.8\\)\u003c/span\u003e\u003c/span\u003e T, in consistence with valid range of the fitting to the ETO/KTO sample. However, the ILP model fits the MR of the LTO/KTO sample in a much smaller range, probably because spin canting and rotation of TiO6 tetrahedral caused by external field are more obvious due to the smaller magnetic moment of Ti\u003csup\u003e3+14,24\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe extracted characteristic lengths \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{\\varphi }\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{so}\\)\u003c/span\u003e\u003c/span\u003e are plotted in (e) as functions of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({T}^{-\\frac{1}{2}}\\)\u003c/span\u003e\u003c/span\u003e. The green dashed line in panel (e) is a linear fit, demonstrating that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{\\varphi }\\propto {T}^{-\\frac{1}{2}}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe fact that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{\\varphi }\\)\u003c/span\u003e\u003c/span\u003e being larger than \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{SO}\\)\u003c/span\u003e\u003c/span\u003e guarantees the phase coherence during the spin-orbit scattering process, leading to the obvious positive MR (or negative magnetoconductance) associated with the WAL effect. We note that the magnitude of conductance change \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\Delta }\\sigma\\)\u003c/span\u003e\u003c/span\u003e for the LTO/KTO sample is about one order of magnitude smaller than that for the ETO/KTO sample (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\tilde0.01{e}^{2}/h\\)\u003c/span\u003e\u003c/span\u003e vs. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\tilde0.2{e}^{2}/h\\)\u003c/span\u003e\u003c/span\u003e). This is because the difference between \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{\\varphi }\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{SO}\\)\u003c/span\u003e\u003c/span\u003e is much smaller (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{{l}_{\\varphi }}{{l}_{SO}}\\approx 1.1\\)\u003c/span\u003e\u003c/span\u003e for LTO/KTO vs. 3.0 for ETO/KTO), and the effects of WL partially cancel that of WAL on conductance. However, both characteristic lengths for the LTO/KTO sample are significantly larger than those for the ETO/KTO sample, suggesting either much more scattering sites existing in the ETO/KTO sample to destroy phase coherence and to cause spin flips or the transport process is governed by different nature of conducting band. The former possibility is unlikely thanks to the similar quality of crystalline and interfaces for both samples, while the latter is highly possible due to the much larger magnetic moment on Eu\u003csup\u003e2+\u003c/sup\u003e sites and the possible topological band of ETO\u003csup\u003e23\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003cb\u003eAnomalous Hall effect.\u003c/b\u003e Since itinerant electrons reside in KTO for both cases, the magnitude of Rashba coupling should be similar and cannot account for the difference of WAL effect between the two samples. To clarify the origin of the stronger scattering in the ETO/KTO sample, we performed Hall measurements for both samples (Supplementary Information Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). In spite of the quasi-linear dependence of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }_{xy}\\)\u003c/span\u003e\u003c/span\u003e on the magnetic field, a weak anomalous Hall effect can still be observed. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows the anomalous hall resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }_{AHE}\\)\u003c/span\u003e\u003c/span\u003e extracted by subtracting \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }_{xy}\\)\u003c/span\u003e\u003c/span\u003e by an ordinary Hall term \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }_{H}\\propto \\alpha B\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\alpha\\)\u003c/span\u003e\u003c/span\u003e is a coefficient determined by a linear fit of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }_{xy}\\)\u003c/span\u003e\u003c/span\u003e between 3 T and 4 T. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }_{AHE}\\)\u003c/span\u003e\u003c/span\u003e for LTO/KTO is negative (namely \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }_{AHE}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(B\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e) and temperature-independent below 5 K. In stark contrast, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }_{AHE}\\)\u003c/span\u003e\u003c/span\u003e for ETO/KTO is positive and exhibits a strong temperature dependence until it vanishes above 5 K. Furthermore, its magnitude \u0026ndash; at 0.5 K for example \u0026ndash; is about 10 times larger than that of LTO/KTO.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Discussions","content":"\u003cp\u003eIn Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(b), we find that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }_{AHE}\\)\u003c/span\u003e\u003c/span\u003e at 2 K saturates at about 2 T. This is consistent with the magnetization of ETO\u003csup\u003e23,33\u003c/sup\u003e. Furthermore, the onset temperature of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }_{AHE}\\)\u003c/span\u003e\u003c/span\u003e is also close to the Neel temperature of ETO (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({T}_{N}=5.5\\)\u003c/span\u003e\u003c/span\u003e K). Both evidences support that the AHE is highly related with the proximity of ETO. It has been pointed out that non-trivial Berry curvature can be induced and controlled in ETO by applying external magnetic field\u003csup\u003e23\u003c/sup\u003e. Induced Zeeman splitting in the process of canting magnetic moments causes type II Weyl nodes and topologically changes the band structure of ETO. The high similarity between the measured \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }_{AHE}\\)\u003c/span\u003e\u003c/span\u003e and magnetization in ETO suggests that electrons at the ETO/KTO interface are strongly influenced by the topological band structure of ETO. The emergence of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }_{AHE}\\)\u003c/span\u003e\u003c/span\u003e \u0026ndash; becoming obvious below about 5 K \u0026ndash; also coincides with the wiggle points appearing in the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\rho -T\\)\u003c/span\u003e\u003c/span\u003e curve in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(e). The emergence of wiggle point could be due to the suppression of electron back-scattering associated with spin-orbit locking. In contrast, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }_{AHE}\\)\u003c/span\u003e\u003c/span\u003e for the LTO/KTO sample, being temperature independent and much weaker, should solely stem from the topology induced by Rashba-type SOC in KTO. The Rashba effect is weakly temperature dependent below 5 K because of its higher spin-orbit split band\u003csup\u003e34,35\u003c/sup\u003e, leading to the temperature independence of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }_{AHE}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eIn summary, we have studied the transport properties of 2DEG residing near the interfaces of both LaTiO3/KTaO3 and EuTiO3/KTaO3 heterostructures, and observed superposition of weak localization and weak anti-localization effects. The extracted phase coherence length \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{\\varphi }\\propto {T}^{-1/2}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{SO}\\)\u003c/span\u003e\u003c/span\u003e is temperature independent, confirming the existence of spin-orbit coupling in both heterostructures, while characteristic lengths of ETO/KTO are much smaller, implying the coupling mechanism is different. By analyzing the anomalous Hall effect, we found that AHE for ETO/KTO features with a positive sign, strong temperature dependence, and large magnitude, different from the LTO/KTO sample. We deduce that such a difference, together with the localization effects, stems from the strong topological band induced by the ETO film.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e \u003cb\u003eSample preparation and structural characterization.\u003c/b\u003e All films were grown on insulating KTO (001) substrates (MTI). The lattice constant of KTO is 3.99 \u0026Aring;, larger than ETO (3.905 \u0026Aring;) and LTO (3.97 \u0026Aring;), which results in the tensile strain in all epitaxial films.\u003c/p\u003e \u003cp\u003eThe samples were grown in an oxide molecular beam epitaxial (MBE) system (Veeco GenXplor) with a base pressure\u0026thinsp;\u0026lt;\u0026thinsp;5\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;10\u003c/sup\u003e torr. The flux ratio between Eu, La, and Ti was calibrated by quartz crystal microbalance, and the film growth process and the number of layers were monitored and determined by in-situ reflection high-energy electron diffraction.\u003c/p\u003e \u003cp\u003eAt the temperature of 700\u0026deg;C, KTO substrate was annealed for 30 min without oxygen to degas. After that, ETO film was grown on the substrate by co-deposition in a partial pressure of molecular oxygen pressure of 4\u0026ndash;5\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e Torr. LTO film was also grown by co-deposition in a partial pressure of molecular oxygen pressure of 3\u0026ndash;4\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e Torr. After the film growth, all samples were capped with 5 nm of amorphous Ge at room temperature to prevent sample deterioration during the ex-situ measurements. Bare KTO substrate, after the same annealing process and 5 nm of amorphous Ge capping, shows clear insulating behavior. Same growth methods generate insulating/stoichiometric ETO and LTO films on another insulating substrate\u003csup\u003e24\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eAfter the growth and capping, the films were characterized by X-ray diffraction (XRD, Bruker) in the 2θ-ω mode for the structural information using Cu Kα1 radiation.\u003c/p\u003e \u003cp\u003e \u003cb\u003eElectrical transport measurement and data analyses.\u003c/b\u003e Electric transport measurements were performed on a dilution refrigerator (Oxford Triton500). Van der Pauw (VdP) method was used for the transport measurements, with both LTO/KTO and ETO/KTO samples in a square shape with dimensions of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(5\\times 5\\)\u003c/span\u003e\u003c/span\u003e mm\u003csup\u003e2\u003c/sup\u003e and electric contacts made to four corners by indium-soldering. The Standard lock-in technique was used with a frequency of 17 Hz and a current of 1 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }\\)\u003c/span\u003e\u003c/span\u003eA. Longitudinal resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{xx}\\)\u003c/span\u003e\u003c/span\u003e was measured by running current through two contacts on the same edge, and Hall resistance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{xy}\\)\u003c/span\u003e\u003c/span\u003e by running current through two contacts on diagonal. Due to the finite contact size and non-ideal symmetry, anti-symmetrization was performed to extract \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{xy}\\)\u003c/span\u003e\u003c/span\u003e. Pictures were taken for the samples after the contacts were made. Transport processes were then simulated by finite element modeling (FEM) using COMSOL. The simulations were run with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }_{xx}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }_{xy}\\)\u003c/span\u003e\u003c/span\u003e as input parameters to match the experimental results.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe work at IOP-CAS was supported by National Key R\u0026amp;D Program of China (2021YFA1401900 \u0026amp; Grant No. 2018YFA0305604), National Natural Science Foundation of China (NSFC) (No. 11874403), Key Research Program of Frontier Sciences, CAS, (Grant No. ZDBS-LY-SLH0010), and Beijing Natural Science Foundation (Grant No. JQ21002). The work at UBC was supported by Natural Sciences and Engineering Research Council (NSERC) of Canada and Canada Foundation for Innovation (CFI).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eZ.G.C. and K.Z. conceived and designed the experiments, Y.Z., H.S., H.W. and B.A.D. fabricated and measured the devices. Z.G.C. wrote the manuscript with comments from all other authors.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAdditional Information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting financial interests:\u0026nbsp;\u003c/strong\u003ethe Authors declare no Competing Financial or Non-Financial Interests.\u003c/p\u003e"},{"header":"References","content":"\u003cp\u003e1.\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Ohtomo, A. \u0026amp; Hwang, H. Y. 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B\u003c/em\u003e \u003cstrong\u003e80\u003c/strong\u003e, 121308 (2009).\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"npj-quantum-materials","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjquantmats","sideBox":"Learn more about [npj Quantum Materials](http://www.nature.com/npjquantmats/)","snPcode":"41535","submissionUrl":"https://mts-npjquantmats.nature.com/cgi-bin/main.plex","title":"npj Quantum Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-1579411/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1579411/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTwo-dimensional electron gas (2DEG) systems generated at oxide interfaces that exhibit novel physics phenomena have opened up a new era for oxide-based electronics, photonics, and spintronics. The recent discovery of superconductivity plus the strong spin-orbital coupling naturally existing in the 2DEGs of KTaO\u003csub\u003e3\u003c/sub\u003e (KTO) makes KTO an exciting platform for the interplay of the electronic and spin degree of freedom to create new physical properties. By directly placing KTO\u0026rsquo;s 2DEGs next to another strongly-correlated oxide with nontrivial topological nodes, we reveal direct evidence of topological states in the electronic transport properties of the KTO\u0026rsquo;s 2DEGs, due to the electronic reconstruction caused by the proximity effect. 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