A possible superconductor-like state at elevated temperatures near metal electrodes in an LaAlO3/SrTiO3 interface

We experimentally investigated the transport properties near metal electrodes installed on a conducting channel in a LaAlO3/SrTiO3 interface. The local region around the Ti and Al electrodes has a higher electrical conductance than that of other regions, where the upper limits of the temperature and magnetic field can be well defined. Beyond these limits, the conductance abruptly decreases, as in the case of a superconductor. The samples with the Ti- or Al-electrode have an upper-limit temperature of approximately 4 K, which is 10 times higher than the conventional superconducting critical temperature of LaAlO3/SrTiO3 interfaces and delta-doped SrTiO3. This phenomenon is explained by the mechanism of electron transfer between the metal electrodes and electronic d-orbitals in the LaAlO3/SrTiO3 interface. The transferred electrons trigger a phase transition to a superconductor-like state. Our results contribute to the deep understanding of the superconductivity in the LaAlO3/SrTiO3 interface and will be helpful for the development of high-temperature interface superconductors.

difficult to find evidence for the enhancement of carrier mobility due to doping in these reports. Recently, a more effective method has been suggested to control the population of these d-orbitals: adjusting the charge transfer between the conducting channel and the metal overlayer deposited on the LAO surface 30,31 . In particular, Ti and Al were tested as a metal overlayer and an increase in carrier density was experimentally observed, implying a tunable occupation of the d-orbitals 32,33 . Even for an insulating LAO/STO interface, an Al overlayer enables the formation of a conducting channel by this charge transfer process 34 .
In this study, we also attempted to perform electron transfer from Ti (or Al) to an LAO/STO interface. Instead of a metal overlayer on a LAO surface as used in previous studies, we deposited Ti (or Al) electrodes after removing (or breaking) the LAO layer, which allowed for direct access of the electrons in these metals to the LAO/ STO interface. Although the method of d-orbital occupation is similar to that of previous studies, the results are quite different; we observed a high conducting state in this local region, and its conductance varied dramatically with the temperature and magnetic field, indicating a type of phase transition. This new phase has a well-defined threshold temperature and magnetic field reminiscent of a superconductor. Furthermore, this threshold temperature is approximately 4 K, which is 10 times higher than the conventional critical temperature of superconductors in the conducting channels of LAO/STO and delta-doped STO. Thus, the observed states are clearly distinguishable from the superconducting phases that have been reported thus far. We believe that these results are due to the Lifshitz transition 35-37 : i.e., the electrodes give electrons to Ti +3 ions in the LAO/STO interface, and these excess electrons occupy the high energy d-orbitals and trigger a phase transition to a superconductor-like state.

Results
Four samples were prepared in this work: two Ti-electrode samples, called sample 1 and sample 2, and two individual samples with Al and Au electrodes. Sample 1 and the Al and Au electrode samples were fabricated using the same LAO/STO wafer. After depositing metal electrodes near the LAO/STO interface and allowing electron transfer in the metal into the conducting channel, the electrodes were also used as electric terminals for current flow and voltage measurements. In this study, channel resistance near an electrode is distinguished from a resistance which was not affected by the electrode. 'Internal resistance' is the term used in this paper to describe resistance free from the influence of the electrodes, and it represents certain intrinsic properties of the conducting channel in a LaAlO 3 /SrTiO 3 interface. Accordingly, the 'internal region' refers to the part of the channel that is far enough from the electrodes to not be affected by them. The resistance was measured using a DC current source and a voltmeter. To perform measurements near the electrodes, we collected signals using various measurement configurations: two-, three-, and four-terminal configurations, as depicted in Fig. 1(c). For the two-terminal configuration, the measured resistance included the local resistance near the two electrodes as well as the internal resistance. For the three-terminal configuration, the local resistance near a single electrode was measured, excluding the internal resistance, while only the internal resistance was measured for the four-terminal configuration. In the three-terminal configuration, the middle electrode, as shown in the second panel in Fig. 1(c), acted as both the current and voltage terminals and the right voltage probe has non-zero distance from the middle electrode. This finite distance allowed the signal from this configuration to contain a voltage drop on the local LAO/ STO channel near the middle electrode. Naturally, the resistance obtained from this three-terminal configuration involved the contact resistance that came from the junction of two different materials, i.e., LAO/STO and the metallic electrode. Additionally, this three-terminal signal contained the channel resistance of the LAO/STO interface near the electrode. In particular, the Ti and Au electrodes were designed to be wide and close to each other; the length and width of these electrodes shown in Fig. 1(a) are 5 μm and 400 μm, respectively. This design makes the local resistance around the electrodes account for a great part of the measured signal. Measurements were performed in a temperature-controllable system. In order to search for some enhanced superconductor-like properties at elevated temperatures, we focused on a temperature range that was higher than the critical superconducting temperature of the internal region. Figure 1(d) shows the magnetoresistance of the Ti electrode sample for the three measurement configurations at 1.8 K with a magnetic field B parallel to the electric current. The resistance was constant for the four-terminal configuration, which implied that the internal region was not affected by the magnetic field. For the other two cases, the resistance increased abruptly when the field magnitude exceeded 20 mT. The resistance change was approximately 7.5 mΩ for the three-terminal configuration, and this value doubled for the two-terminal configuration. The number of electrodes related to local effect in the two-and three-terminal configuration were two and one, respectively. Thus, these data indicate that the magnetic field only affects the local region near the electrodes (not the internal region) and that this phenomenon occurs equally for each electrode.
This resistance change was independent of the direction of the magnetic field. We varied the field direction with respect to the interface and current direction. In Fig. 1(e), all of the measured curves from different field directions were merged into a single curve. Thus, the conducting state of the system was only influenced by the field magnitude, regardless of its direction. It was unusual that the magnetoresistance was constant with respect to the magnetic field direction because the electronic orbitals around the LAO/STO interface had strong directional properties because they were sandwiched between two different insulators, LAO and STO. Thus, they had no degrees of freedom to move perpendicular to the interface. If the magnetoresistance is governed by the Lorentz force, it should be dependent on the field direction, which is inconsistent with the observed curves in Fig. 1e. Additionally, the resistance in our device increased at the critical magnetic field, but in typical ferromagnetic materials, the magnetoresistance decreases with increasing field strength when the magnetic field is applied perpendicular to the bias current. Thus, anisotropic magnetoresistance, which is related to ferromagnetism, can be ruled out in our results. The anomalous Hall effect also depends on the magnetization direction and is not applicable to our system. Ruling out the Lorentz force and magnetism, a suitable candidate for the causative mechanism is superconductivity. In a superconductor, the magnetic field exceeding a critical value breaks the superconductivity, which makes the resistance abruptly increase. This critical field is usually independent of the field direction, as in the present cases 38 . In this connection, it is speculated that our samples have a high conducting local phase near the electrode and that this phase has a definite upper limit of the magnetic field, as does the superconductivity.
One feature of magnetoresistance is its high dependence on the metallic element of the electrode. As shown in Fig. 1(f), the samples fabricated with Ti or Al electrodes had a superconductor-like magnetoresistance. However, the Au electrode sample did not show an abrupt jump in resistance; the resistance versus field curve was quadratic, displaying a typical ordinary magnetoresistance caused by the Lorentz force 39 . These different behaviors for various metallic electrode were related to the work function of the metal, which governs the occupation of electronic orbitals in the LAO/STO interface. We discuss this issue later. The difference in signal strength between the Ti and Al electrode sample was attributed to the different fabrication processes of these two metals on the LAO/STO interface (see the Methods section for details). The relatively high disorder around the electrode was accompanied by the fabrication of Al, which resulted in a small signal in the Al electrode sample in comparison with the Ti electrode sample.
The apparent jump in resistance at a specific magnetic field for the Ti and Al electrode samples allows for a clear definition of a threshold magnetic field, indicating a boundary between the low and high conducting states. The high conducting state below the threshold magnetic field shows a dramatic variation with temperature T. As shown in Fig. 2(a), the high-conducting region in the magnetic field becomes narrower with an increase in temperature. A threshold magnetic field of 22 mT at 1.8 K decreases to 5 mT at 3.5 K, and finally, the high-conducting state disappears at approximately 4 K. Thus, the system has a threshold temperature above which the high-conducting state does not exist regardless of the magnetic field strength. The threshold temperature is  Fig. 2(b), where the resistance as a function of temperature is shown. In the absence of a magnetic field, the resistance jumped at 3.7 K, indicating a threshold temperature, and this threshold temperature decreased with an increasing magnetic field.
The well-known superconductivity in the conducting channel of the LAO/STO interface arises in the internal region (far from the electrodes) and is distinguishable from the underlying high-conducting state near the electrodes in this work. The data shown in Fig. 2(b) bear a similarity to those of internal superconductivity 40 except for the resistance offset. A significant difference between them is the characteristic temperature. The critical temperature of the internal superconductivity has been reported to be several hundred millikelvins, while the threshold temperature of the present sample reached 3.7 K. The inset in Fig. 2(b) shows the temperature dependence of the resistance above the threshold temperature, which has the well-known characteristics of the LAO/STO interface: a metallic behavior above 10 K and Kondo effect 41 from 3.75 K to 10 K. The Kondo effect, a clear upturn of the resistance with decreasing temperature, is caused by the interplay between the carrier localization and mobile charge. Brinkman et al. 2 . observed this effect in LAO films grown under high oxygen pressure, and Han et al. 42 analyzed this effect in connection with localized Ti 3+ ions and oxygen pressure. The Kondo temperature of our sample was 10.43 K, which can be described well by a model proposed in ref. 43 . Above the threshold temperature, our sample showed the temperature dependence of a conventional non-superconducting channel in the LAO/ STO interface. Below the threshold temperature, however, the internal region was still in a non-superconducting state, while the region near the electrode was in a superconductor-like state. Therefore, compared to a conventional superconductor, the measured resistance in Fig. 2(b) does not decrease to zero.
Hysteresis of physical quantities is normally accompanied by a phase transition and is one of the most interesting phenomena observed in the LAO/STO system. Many researchers have insisted that hysteresis in magnetoresistance is related to the ferromagnetic phase 2,24,40 . All of the magnetoresistance curves of the Ti and Al electrode samples showed hysteretic behaviors, a shift of the measured resistance along the sweep direction of the magnetic field. The observed hysteresis was reproducible and independent of the field-sweep rate in the range below 0.1 mT/s. Thus, the present hysteresis does not originate from a time-dependent transient nature 36 . Figure 3(a) shows the systematic behavior of the hysteretic magnetoresistance in our sample. Despite different historical paths produced by the sweeping control of magnetic field, all of the curves are merged into one of two curves: one is the response to an increasing field and the other to a decreasing field, which are typical characteristics of a rate-independent hysteresis associated with irreversible thermodynamic changes, such as phase transitions. Generally, when an external parameter such as a magnetic field causes a phase transition of the system, the natural inertia inherent in the system restrains the system from triggering the phase transition, which results in a hysteretic behavior. Therefore, the hysteresis shown in Fig. 3(a) confirms that our system undergoes a phase transition between two different states. Although the curves illustrate a minor loop and memory effect, further study is necessary to clarify whether this hysteresis is related to ferromagnetism. A phase diagram differentiating the high-and low-conducting states near the electrodes is depicted in Fig. 3(b). The overall shape was similar to the phase diagram of the internal region 44 . However, there was a 10-fold difference in the physical quantities between them. The threshold temperature was 10 times greater than the critical temperature of the internal region, and the threshold magnetic field was 10 times less than the critical field of the internal region. This scaling tendency suggests that the observed phase transition in this work may be an extension of the internal one to the limit of a high-temperature and low-magnetic-field regime.
It has been widely accepted that superconductivity in a LAO/STO interface is related to the emergence of high-mobility carriers 45,46 . We believe that the observed high-conducting phase can be attributed to the electric population of the high-mobility states near the Ti (or Al) electrodes, which are rare in the internal region. Electronic transport properties come from the d-orbital electrons in Ti +3 ions at the TiO 2 -terminated interface. Only a small fraction of those electrons contribute to electrical conductance, and most of them reside in localized states fixed to Ti ions because of strong Hubbard and nearest-neighbor Coulomb interactions 47 . Among the d-orbitals, d xy , d xz , and d yz are responsible for the electric current, and their schematic energy diagrams are shown in Fig. 4. The energy of d xy is lower than the energy of d xz and d yz because of the asymmetric confinement potential at the interface [15][16][17] . Thus, carriers in a LAO/STO interface can be classified into two types: high-density electrons residing in the d xy state and low-density high-mobility electrons occupying a hybrid state, d xz /d yx , combined with   35,37 and the work function of a metal electrode (right panel). The dyz and dxz orbitals have higher energy than the Fermi level of the channel, E F,2DEG . For an electrode with small work function such as Ti and Al, the Fermi level difference causes electrons to be transferred to the channel, and the electrons occupy the dyz and dxz orbitals. A Lifshitz transition occurs when E F,2DEG passes through the Lifshitz point and the dyz and dxz orbitals begin to be occupied. For a simple view, the energy band and the Lifshitz point are depicted assuming the absence of spin-orbit coupling. With spin-orbit coupling, the dyz and dxz orbitals are strongly coupled and form a hybrid orbital, dyz/dxz 35 . Two Fermi levels, E F,2DEG and E F,metal in this diagram, show the state before electron transfer occurs between the channel and the metal electrode.
A number of studies have investigated ways to populate d-orbitals. It has been theoretically and experimentally confirmed that metals with low-work functions deposited atop an LAO/STO structure can supply carrier electrons to the LAO/STO interface across the LAO layer 30,31 . The low-work function relative to that of STO causes a Fermi level difference, and electrons are transferred from the metal toward the STO to align the Fermi level on both sides. The work functions of Ti and Al are 4.3 and 4.2 eV, respectively, and are especially effective for this carrier transfer process 33,34 : they increase the carrier density of the interface channel by more than 6 × 10 13 cm −2 32 . In this study, the Ti and Al electrodes supply electrons to the interface channel, as in the previous studies mentioned above (refer to the schematic in Fig. 4). For more effective electron transfer, however, we removed the barrier, i.e., the LAO layer, and made the electrodes directly contact the interface channel. Our results are quite different from those of previous studies: there is clear evidence of the high-mobility electronic state arising from the charge transfer and a dramatic phase change of this state similar to a superconducting transition. This effective doping process provides excess electrons to the d xz /d yz orbitals and triggers a superconductor-like transition. The abrupt conductance variation observed in this study can be attributed to the Lifshitz transition 35,37 , which occurs when the carrier density exceeds a critical value and new orbitals are populated. In the region far from the Ti deposition layer, the system lies below a critical carrier density and most electrons reside in the d xy states. Near the Ti or Al electrodes, however, the supply of excess electrons makes the Fermi energy enter the d xz /d yz orbitals. This transition is also very sensitive to temperature and magnetic fields, providing a clear definition of the threshold temperature and magnetic field. According to the above scenario, a metal electrode with a high work function cannot induce such a transition. The work function of Au is approximately 5.3 eV, which is high enough relative to the STO's electron affinity, 4.1 eV. Therefore, electron transfer from the Au electrode to STO does not take place and the d xz /d yz orbitals in the STO cannot be populated. We used a gold electrode, and as expected, the results shown in Fig. 1(f) do not indicate any sign of a transition to a high conducting state.

Discussion
Since the concept of interface superconductivity 11 was introduced 50 years ago 54 , ground-breaking works on insulator interfaces have been conducted, leading to the discovery of a superconducting phase at LAO/STO interface in 2007 1 . Our results suggest the reasonable possibility of dramatically enhancing this superconductivity in terms of the critical temperature and magnetic field. The phase diagram obtained in this work covers the temperature and magnetic field regime, which has not been reported in previous research 44 . In addition to the superconducting phase, coexistence with the ferromagnetic phase in LAO/STO interfaces is an emerging issue 12,13 . The systematic hysteresis behavior of magnetoresistance in this study suggests the coexistence of these two phases because hysteresis of magnetoresistance in LAO/STO interfaces is considered to be a sign of a ferromagnetic phase 2,24,40 . Furthermore, inhomogeneity of conductance is another important issue in LAO/STO interfaces [12][13][14] , the origin of which is still an open question. We also observed a strong local nature exhibiting high conductance near metal electrodes and elucidate the origin of this inhomogeneity by the effective doping process induced by electron transfer from low-work-function electrodes. For engineering purposes, this effective doping method can be used to pattern a conducting channel in the LAO/STO interfaces 34 , which may lead to a noble nanoscale fabrication technology. Thus, our results may be major step toward a fundamental understanding and future device applications of interface superconductivity in an LAO/STO structure.

Methods
We grew a LAO layer on a TiO 2 -terminated STO (001) single crystal substrate using pulsed laser deposition. The substrates were connected to a resistive heater and positioned 5 cm from the target. A KrF excimer laser beam (wavelength of 248 nm) was focused on a LAO single-crystal target with an energy density of 1.5 J/cm 2 at 2 Hz. The LAO thin films were grown at a substrate temperature of 700 °C with 1 mTorr of oxygen pressure. The thickness of the deposited LAO film was five-unit cells. The carrier density and mobility of the LAO/STO interface were, respectively, 2 × 10 13 cm −2 and 900 cm 2 /V·s at 1.8 K in the as-grown condition. The epitaxial growth of a LAO layer on a STO substrate was confirmed via a cross-sectional high-resolution transmission electron microscopy image (see Fig. 1(b)). The metal electrodes were fabricated using two methods: Ti or Au electrodes were made by deposition using a DC sputter and Al electrodes were made by wire wedge bonding. Ti or Au was deposited on the LAO/STO interface after the LAO layer was removed by Argon ion-beam etching. This etching was performed in a RF plasma system operated at low pressure (2×10 −3 Torr) with a power of 20 W and a discharge voltage less than 100 V. During this process, etching and deposition were performed without vacuum breaking. We took resistance measurements for the exposed regions of the Argon ion-beam and confirmed that those regions were not electrically conductive. The junction size of each Ti (or Au) electrode was 400 × 400 μm 2 , and the length between individual electrodes was approximately 5 μm (refer Fig. 1(a)). The junction size of the Al electrode was approximately 50 × 100 μm 2 , and the length between them was 500 μm. The resistance was measured using the standard DC technique: a DC current was applied by a Keithley 6221 current source, and the voltage drop was measured by a Keithley 2182 A nano-voltmeter. These instruments had a high enough output and input impedances, 10 14 Ω and 10 10 Ω, respectively, to ensure a stable pair of source and meter. The voltmeter had a resolution of 1 nV with a digit of 6.5, which provided enough precision to discern resistance changes in our samples. To reduce possible noise, we repeated measurements more than 50 times for each data point and performed a numerical average of them.