Introduction

A combination of broken inversion symmetry and strong spin–orbit coupling in two-dimensional (2D) superconductors gives rise to mixed-parity superconductivity,1 topological Weyl superconductivity,2 a superconducting diode effect,3 and an upper critical field exceeding the Pauli–Chandrasekhar–Clogston limit.4,5 2D weak anti-localization has been used to probe surface states in topologically nontrivial systems.6,7 The recent discovery of 2D superconductivity8 and predictions of topologically nontrivial states9 at the KTaO3 (111) surface makes this material system a candidate platform for the coexistence of topologically nontrivial electronic states and unconventional superconductivity.

KTaO3 is an incipient ferroelectric,10 in which superconductivity emerges at low temperatures in heavily doped samples.11 A robust 2D electron system is reported at the interfaces of KTaO3 with LaTiO3,12 LaVO3,13 EuO,14 LaAlO3,15 TiOx16 and LaCrO3.16 The KTaO3 conduction states are derived from Ta 5d and have a smaller effective mass and higher mobility and spin–orbit coupling compared to Ti 3d states in SrTiO3.17,18 Spin–orbit coupling lifts the degeneracy of the Ta 5d states and splits them into J = 3/2 and J = ½ with a 0.4-eV energy gap, where J is the total angular momentum.19 Recently, an exotic 2D superconductivity was discovered at the (111)8 and (110)20 KTaO3 interfaces with EuO and LaAlO3, which shows nearly two orders of magnitude enhancement in the critical temperature of superconductivity (TC) compared to its 3D counterpart.11 Interestingly, KTaO3 (100) interfaces do not show a superconducting transition. The superconducting state in the KTaO3 (111) surface is highly susceptible to the interfacial structure, and a remnant resistance is observed below the superconducting transition temperature.21 This failed superconductor state22 is an ideal platform for the experimental realization of simultaneous superconductivity and nontrivial topology.

Here, we report on the observation of a superconducting transition at the TiOx/KTaO3(111) interfaces. A true superconducting ground state (Rs = 0), however, does not emerge as the superconducting puddles fail to reach phase coherence. Signatures of weak anti-localization are observed below the superconducting transition temperature, suggesting the coexistence of superconductivity and topologically nontrivial states at the KTaO3 (111) surfaces.

Materials and Methods

Mobile carriers were introduced to the (111) surface of the KTaO3 single crystals using a 3-nm TiOx layer which induces oxygen vacancies. Here, the TiOx layer acts as an oxygen getter and is grown using an oxide molecular beam epitaxy system with 2 × 10−10 Torr base pressure. An ultra-high purity Ti source from a high-temperature effusion cell (Veeco) was used to grow a TiOx layer. The substrate temperature was kept at 400°C during growth to create an abrupt interface. Recently, atomically abrupt interfaces were demonstrated on KTaO3 interfaces grown at 600°C using an EELS map.23 The Ti adatoms leach oxygen from KTaO3, forming a TiOx layer, and donating itinerant charge carriers to a Ta 5d-derived conduction band in KTaO3. The reflection high-energy electron diffraction, measured during deposition, confirms the growth of an amorphous TiOx on the (111) KTaO3 surface (Supplementary materials, S1). Magneto-transport measurements were performed using the Van der Pauw configuration, and gold contacts were deposited using a sputter system at the corners of the samples through a shadow mask. The temperature-dependent magneto-transport measurements were carried out in a Quantum Design physical property measurement system with a lock-in amplifier (SR830; Stanford Research Systems) in AC mode with an excitation current of 10 µA and a frequency of 13.33 Hz. Sub-Kelvin magneto-transport measurements were carried out in a Triton dilution refrigerator (Oxford Instruments).

Oxygen vacancies introduce itinerant electrons to the Ta 5d-derived surface states. The conduction electrons at the low-temperature limit are derived from J = 3/2, Ta 5d states due to the large spin–orbit coupling gap in KTaO3 (0.4 eV)17,19. Figure 1(a) shows a metallic behavior, dR/dT > 0, in sheet resistance with the temperature extending from room temperature to ~ 15 K. Here, oxygen stoichiometry plays an important role in transport phenomena. The oxygen vacancies donate itinerant charge carriers to the KTaO3 conduction band and, similar to other point defects,24 scatter itinerant carriers.25 The transport in TiOx, however, is negligible, since this layer is only 3 nm and expected to have low mobility. The sheet resistance changes somewhat linearly with temperature in this range. A resistance upturn emerges below 15 K, followed by a sharp drop below 3 K (Fig. 1(b)). The abrupt drop in sheet resistance is consistent with recently discovered 2D superconductivity at the (111) KTaO3 interface.8 Hall measurements were performed to determine the sheet carrier density. The Hall carrier density, \(n=-1/(e{R}_{H})\), where \({R}_{H}\) is the Hall coefficient and e is the elementary charge. The Hall coefficient, \({R}_{H}=d{R}_{xy}/dB\), is extracted from a linear fit to the transverse resistance shown in Fig. 1c. The sheet carrier density is ~ 1 × 1014 cm−2 at 3 K. This carrier density is consistent with optimal doping for the critical temperature of superconductivity in (111) KTaO3 interfaces.8

Fig. 1
figure 1

Normal state electronic transport at the TiOx/KTaO3(111) interfaces. (a) Sheet resistance with temperature (300–2 K) showing a linear scaling. (b) Magnetic field dependence of the sheet resistance–temperature behavior (10–2 K). (c) Transverse magnetoresistance at 3 K, resolving the 2D carrier density (~ 1 × 1014 cm−2)

Full size image

Results and Discussion

The residual resistivity ratio (\(\left( {{{\rho_{300K} } \mathord{\left/ {\vphantom {{\rho_{300K} } {\rho_{2K} }}} \right. \kern-\nulldelimiterspace} {\rho_{2K} }}} \right)\)) is 2.3 and the carrier mobility increases from ~ 8 cm2/Vs at room temperature to ~ 19 cm2/Vs at 3 K. The moderate enhancement of the carrier mobility, despite the screening of the longitudinal optical phonons at low temperatures, can be explained by the interfacial scattering of itinerant electrons.26,27,28 The spatial distribution of “two-dimensional” charge carriers controls their exposure to the interfacial structure and, as a result, the mean free path of charge carriers. Here, despite the modest low-temperature carrier mobility, the sheet resistance remains below the 2D Mott–Ioffe–Regel limit (~ 20 kΩ/□). Figure 1b shows a growing positive magnetoresistance with decreasing temperature (10–2 K). The positive magnetoresistance, particularly above 4 K, cannot be explained by the emergence of superconductivity alone, and could be partially due to the weak anti-localization correction to the longitudinal resistance. 2D electron systems at the surface of the KTaO3 show large coherence length and signatures of weak anti-localization.16,25,29,30

Figure 2a shows the normalized resistance with temperature from 20 to 0.1 K. The resistance at 2 K and the zero field was used as normal state resistance (RN) in Fig. 2. The sharp drop in resistance is consistent with the observed superconducting transition at the interfaces of (111) KTaO3 with EuO and LAlO3.8 A remnant resistance, however, is observed below the superconducting transition temperature (mid-point TC ~ 1.1 K). The sheet resistance saturates to a nonzero value below the transition temperature, which is insensitive to the presence of cryo-filters, excluding the possibility of radiation thermalization. Furthermore, the KTaO3(111)/LaCrO3 interfaces, in which the normal state resistance is above the 2D Mott–Ioffe–Regel limit (~ 33 kΩ/□ at 3 K), do not show an abrupt drop in sheet resistance (Supplementary information, S2). Recently, a gate tunable remnant resistance was reported at the KTaO3(111)/LaAlO3 interfaces below the superconducting transition temperature,21 highlighting the role of interfacial structure on the emergence of a true superconducting ground state (Rs = 0). A residual resistance has been observed in a wide range of 2D superconductors.31,32,33,34 Here, the remnant resistance below the superconducting transition provides a unique platform for the experimental realization of 2D superconducting fluctuations coexisting with weak anti-localization.

Fig. 2
figure 2

Superconducting transition at the TiOx/KTaO3(111) interfaces. (a) Superconducting transition with temperature (mid-point TC ~ 1.1 K); a remnant, saturating resistance is observed below the superconducting transition temperature. (b) Longitudinal magnetoresistance shows the superconducting transition and low field signatures of weak anti-localization (inset) at 0.3 K; the resistance at 2 K and the zero field was used as normal state resistance ®N)

Full size image

The normalized longitudinal magnetoresistance shows that the relative change of resistance with the magnetic field (\({R}_{5\mathrm{T}}-{R}_{0\mathrm{T}}/{R}_{0\mathrm{T}}=0.24,\mathrm{ at }0.3\mathrm{ K})\) is large compared to the resistance change with temperature (\({R}_{3\mathrm{K}}-{R}_{0.3\mathrm{K}}/{R}_{0.3\mathrm{K}}=0.198,\mathrm{ at }0\mathrm{ T})\), alluding to the presence of both pair formation/breaking and weak anti-localization corrections in sheet resistance below the transition temperature.35 Furthermore, a sharp change in the resistance with the magnetic field is observed at low field (inset in Fig. 2), consistent with the weak anti-localization.36 The low field magneto-conduction, however, could not be explained by the Hikami–Larkin–Nagaoka model37 due to the mixed weak anti-localization and superconducting corrections (Supplementary materials, S3).

The angle-dependent longitudinal magnetoresistance was measured to confirm the presence of the weak anti-localization effect. Figure 3a shows a transition from linear positive magnetoresistance to a parabolic behavior, with rotating the magnetic field from out-of-plane (90°) to in-plane (0°), respectively, suggesting a 2D weak anti-localization correction. To parse out the superconducting and weak anti-localization components, the longitudinal magnetoresistance was measured and compared between superconducting, KTaO3 (111), and non-superconducting, KTaO3 (100), interfaces (Fig. 3b). Both interfaces show a positive and linear magnetoresistance with the out-of-plane magnetic field. The superconducting interface, however, shows stronger weak anti-localization correction to resistance. The large magnetoresistance at (111) interfaces could also be explained by the pre-formed Cooper pairs.35 The in-plane magnetoresistance of the superconducting interface shows only 1% positive magnetoresistance at 3 K and 5 T, suggesting that the pair-breaking correction could not explain the large positive magnetoresistance at the superconducting interfaces.

Fig. 3
figure 3

Weak anti-localization at the TiOx/KTaO3 interfaces. (a) Angle-dependent magnetoresistance at the TiOx/KTaO3(111) interface; the transition from positive linear (out-of-plane field) to parabolic (in-plane field) suggests a 2D weak anti-localization. (b) Out-of-plane (90°) magnetoresistance shows weak anti-localization in superconducting, (111), and non-superconducting, (100), TiOx/KTaO3 interfaces

Full size image

To briefly summarize the results, our main findings are as follows: (1) TiOx/KTaO3(111) interfaces show an abrupt superconducting transition; (2) The superconducting transition is sensitive to the normal state resistance and a nonzero, saturating resistance persists below the transition temperature; and (3) superconducting transition emerges near weak anti-localization, suggesting that superconducting fluctuations coexist with quantum coherent quasiparticle effects.

The first important conclusion from these results is that the emergence of superconductivity at the KTaO3 interfaces depends strongly on the interfacial structure. Here, interfacial defects, microstructure, and inhomogeneity could suppress superconducting order parameters, and give rise to a remnant resistance below the transition temperature. KTaO3, unlike SrTiO3, does not experience structural instability and remains cubic at low temperature.17,38 This excludes structural domains39,40,41 as the source of the observed superconducting behavior. Here, the transition could be sensitive to the relaxation time of charge carriers, as the interfaces with sheet resistance above the Mott–Ioffe—Regel limit (\(h/\tau \sim {E}_{F}\), where \(h\), \(\tau \), and \({E}_{F}\) are Planck’s constant, relaxation rate, and Fermi energy, respectively) do not show a superconducting transition. This is consistent with a recent report demonstrating electric field control of a superconductor–insulator transition at the LaAlO3/KTaO3 (111) interface.21 Alternatively, the inhomogeneity of TiOx layer could create an inhomogeneous 2D electron system and superconductivity. The observation of a remnant resistance below the transition temperature means that the superconducting puddles form, but fail to coalesce or reach a global phase coherence mediated by Josephson coupling.32,42,43,44 Here, the fluctuations of superconducting order parameter in different puddles could limit the long-range phase coupling.32

Next, we discuss the observation of weak anti-localization near superconducting transition. 2D electron systems at the KTaO3 interfaces show signatures of weak anti-localization.16,29,30 Furthermore, topologically nontrivial states are predicted at the KTaO3 (111) surface.9 The observed weak anti-localization correction, however, is present in both (111) and (100) interfaces. The large weak anti-localization, i.e., the coherence length, at the (111) interface could be due to the topologically nontrivial states.7 Resolving the topological nature of surface electronic states, however, requires further study. The 2D Hikami–Larkin–Nagaoka model37 does not describe the low-field magneto-conduction behavior at 30 mK, due to the mixed superconducting and weak anti-localization corrections (Supplementary materials, S3). The KTaO3 samples are air-sensitive, and exposure to ambient oxygen fills the surface vacancies, and the 2DEG carrier density declines with exposure to ambient or oxygen annealing.16 We observe a similar carrier density drop and suppression of the superconductivity in samples without a capping layer, due to the strong dependence of superconductivity to carrier density (Supplementary materials, S4). Interestingly, these samples show a linear positive magnetoresistance, after the demise of superconductivity, which could be explained by a 2D Hikami–Larkin–Nagaoka fit, with a resolved coherence length of 103 nm (Supplementary materials, S5), consistent with a previous report.30

In summary, our results, especially the coexistence of superconducting fluctuations and quantum coherent quasiparticle effects, should be of interest for the experimental realization of non-abelian excitations in a single material. We stress that our findings warrant further study of the topological nature of surface states in KTaO3 (111) and the coexistence of topologically nontrivial states with superconductivity.