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Superconducting Interfaces Between Insulating Oxides

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Science  31 Aug 2007:
Vol. 317, Issue 5842, pp. 1196-1199
DOI: 10.1126/science.1146006

Abstract

At interfaces between complex oxides, electronic systems with unusual electronic properties can be generated. We report on superconductivity in the electron gas formed at the interface between two insulating dielectric perovskite oxides, LaAlO3 and SrTiO3. The behavior of the electron gas is that of a two-dimensional superconductor, confined to a thin sheet at the interface. The superconducting transition temperature of ≅ 200 millikelvin provides a strict upper limit to the thickness of the superconducting layer of ≅ 10 nanometers.

In pioneering work, it was demonstrated that a highly mobile electron system can be induced at the interface between LaAlO3 and SrTiO3 (1). The discovery of this electron gas at the interface between two insulators has generated an impressive amount of experimental and theoretical work (28), in part because the complex ionic structure and particular interactions found at such an interface are expected to promote novel electronic phases that are not always stable as bulk phases (911). This result also generated an intense debate on the origin of the conducting layer, which could either be “extrinsic” and due to oxygen vacancies in the SrTiO3 crystal or “intrinsic” and related to the polar nature of the LaAlO3 structure. In the polar scenario, a potential develops as the LaAlO3 layer thickness increases that may lead to an “electronic reconstruction” above some critical thickness (5). Another key issue concerns the ground state of such a system; at low temperatures, a charge-ordered interface with ferromagnetic spin alignment was predicted (4). Experimental evidence in favor of a ferromagnetic ground state was recently found (6). Yet, rather than ordering magnetically, the electron system may also condense into a superconducting state. It was proposed that in field effect transistor configurations, a superconducting, two-dimensional (2D) electron gas might be generated at the SrTiO3 surface (12). It was also pointed out that the polarization of the SrTiO3 layers may cause the electrons on SrTiO3 surfaces to pair and form at high temperatures a superconducting condensate (13, 14). In this report, we explore the ground state of the LaAlO3/SrTiO3 interface and clarify whether it orders when the temperature approaches absolute zero. Our experiments provide evidence that the investigated electron gases condense into a superconducting phase. The characteristics of the transition are consistent with those of a 2D electron system undergoing a Berezinskii-Kosterlitz-Thouless (BKT) transition (1517). In the oxygen vacancy scenario the observation of superconductivity provides a strict upper limit to the thickness of the superconducting sheet at the LaAlO3/SrTiO3 interface.

The samples were prepared by depositing LaAlO3 layers with thicknesses of 2, 8, and 15 unit cells (uc) on TiO2-terminated (001) surfaces of SrTiO3 single crystals (5, 18). The films were grown by pulsed laser deposition at 770°C and 6× 10–5 mbar O2, then cooled to room temperature in 400 mbar of O2, with a 1-hour oxidation step at 600°C. The fact that only heterostructures with a LaAlO3 thickness greater than three uc conduct (5) was used to pattern the samples (19). Without exposing the LaAlO3/SrTiO3 interface to the environment, bridges with widths of 100 μm and lengths of 300 μm and 700 μm were structured for four-point measurements, as well as two-uc-thick LaAlO3 layers for reference (18).

Transmission electron studies (18) were performed on reference samples grown under conditions identical to those described above. Cross-sectional cuts were prepared by mechanical polishing followed by low-energy, low-angle ion milling and investigated by scanning transmission electron microscopy (STEM) (18). Figure 1A shows a high-angle annular dark field (HAADF) STEM image of the sharp interface between a 15-uc-thick LaAlO3 film and the SrTiO3 substrate. The film is found to be coherent with the substrate with no obvious defects or dislocations at the interface, resulting in biaxial tensile strain of ≅ 3%, as measured from STEM images (18). The out-of-plane lattice constant of the LaAlO3 film is ≅ 3.78 Å, which is close to the bulk value and suggests either a rather small Poisson ratio as previously reported (20) or out-of-plane relaxation in the thin film (21). To obtain an upper limit on the extent of electronic structure and compositional changes below the interface, electron energy-loss spectroscopy (EELS) in the STEM was used to probe the chemistry of the heterostructure at the atomic scale. Simultaneously recorded O-K and Ti-L2,3 edges close to and far away from the interface are shown in Fig. 1, B and C. By 1.5 nm away from the interface, the changes in the O-K edge are very slight, suggesting an upper limit to the oxygen vacancy concentration of 3%. At 6 nm away from the interface, the changes in the O-K and Ti-L2,3 edges compared with bulk SrTiO3 fall below the noise level (<1% oxygen vacancy concentration). The small changes of the Ti-L2,3 edges are consistent with a slight increase in Ti3+, either from oxygen deficiency (22) or a compensating interface charge (18).

Fig. 1.

STEM and EELS analysis of a LaAlO3/SrTiO3 heterostructure. (A) High-angle annular dark field image of a 15-uc-thick LaAlO3 film grown on SrTiO3 showing a coherent interface. (B) O-K EELS spectra of the SrTiO3 close to (1.5 nm) and far away from the interface. Even at 1.5 nm from the interface, the O-K fine structure is only very slightly damped compared with the bulk. The damping could be caused by the presence of a low concentration of oxygen vacancies. (C) Small changes of the Ti-L2,3 fine structure close to the interface are consistent with a small concentration of Ti3+, which falls below the detection limit by 6 nm from the interface and beyond.

Two samples were analyzed by transport measurements and found to be conducting (Fig. 2A), their 2-uc-thick control structures being insulating (resistance R >30 MΩ) at all temperatures T (32 mK < T < 300 K). At T ≅ 4.2 K, the Hall carrier densities of the 8-uc and 15-uc samples equal ≅ 4 × 1013/cm2 and ≅ 1.5 × 1013/cm2, and the mobilities ≅ 350 cm2/Vs and ≅ 1000 cm2/Vs, respectively. Whether the differences in the sample properties present an intrinsic effect that is caused by the variation of the LaAlO3 thickness remains to be explored. The Hall response is only weakly temperature dependent [Hall resistance RH(300 K)/RH(4.2 K) ≅ 0.8 and 0.95 for the 8-uc and 15-uc samples, respectively]. Magnetic fields up to μ0 H = 8 T were applied to the 8-uc-thick sample, revealing a positive magnetoresistance. The samples investigated here do not show a hysteretic magnetoresistance. No minimum is found in the R(T) characteristics of the 8-uc sample, such as was reported recently for LaAlO3/SrTiO3 samples fabricated under different conditions (6). For the 15-uc sample, a shallow minimum in the R(T) curve was observed at 4 K.

Fig. 2.

Transport measurements on LaAlO3/SrTiO3 heterostructures. (A) Dependence of the sheet resistance on T of the 8-uc and 15-uc samples (measured with a 100-nA bias current). (Inset) Sheet resistance versus temperature measured between 4 K and 300 K. (B) Sheet resistance of the 8-uc sample plotted as a function of T for magnetic fields applied perpendicular to the interface. (C) Temperature dependence of the upper critical field Hc2 of the two samples.

At ≅ 200 mK and ≅ 100 mK, respectively, the 8-uc and 15-uc samples undergo a transition into a state for which no resistance could be measured (Fig. 2A). The widths of the transitions (20% to 80%) of the 8-uc and 15-uc samples are ≅ 16 mK and ≅ 51 mK, respectively. The resistance drops by more than three orders of magnitude to below the noise limit of the measurement (18). Application of a magnetic field μ0 H = 180 mT perpendicular to the interface completely suppresses this zero-resistance state (Fig. 2B). Figure 3A displays the voltage versus current (V-I) characteristics of a bridge in the 8-uc sample, measured using a dc technique. At low temperatures, the V-I characteristics show a well-defined critical current Ic. The occurrence of the zero-resistance state and the characteristic R(T,H) and V(I,H) dependencies provide clear evidence for superconductivity.

Fig. 3.

V(I) measurements of the 8-uc LaAlO3/SrTiO3 heterostructure. (A) Temperature-dependent voltage-current characteristics of a 100 × 300 μm2 bridge. (B) Measured temperature dependence of the linear critical current density, as obtained from (A).

The Tc(H) dependence, where Tc is defined as R(Tc) = 0.5 × R(1 K), provides a measure for the upper critical field Hc2(T). The Hc2(T) curve is shown in Fig. 2C; Hc2(0 K) ≅ 65 mT and ≅ 30 mT for the 8-uc and 15-uc samples, corresponding to coherence lengths ξ(0 K) ≅ 70 nm and ≅ 105 nm, respectively. Figure 3B shows the temperature dependence of the critical currents per unit width. The maximal values of Ic are 98 μA/cm and 5.6 μA/cm for the 8-uc and 15-uc samples, respectively. A steplike structure in the V(I) curves displayed by the 15-uc sample (not shown) indicates that the low Ic of this sample is caused by inhomogeneities. Just below Ic, the samples develop a small voltage drop which is proportional to the current and increases with temperature. As Fig. 4A shows for the 8-uc-thick sample, at 30 mK the associated resistance is at least four orders of magnitude smaller than the normal state resistance. With T increasing from 30 mK to 180 mK, the resistance grows exponentially from ≅ 0.1 Ω to 10 Ω. Between 180 mK and Tc, the step at Ic disappears and power-law type V(I) curves are measured.

Fig. 4.

Low-temperature transport properties of the 8-uc LaAlO3/SrTiO3 heterostructure. (A) V(I) curves on a logarithmic scale. The color code is the same as that in Fig. 3A. The numbers provide the value of T, measured in mK, at which the curves were taken. The short black lines are fits of the data in the transition. The two long black lines correspond to V = RI and VI3 dependencies and show that 187 mK < TBKT < 190 mK. (B) Temperature dependence of the power-law exponent a, as deduced from the fits shown in (A). (C) R(T) dependence of the 8-uc sample (I = 100 nA), plotted on a [dln(R)/dT]–2/3 scale. The solid line is the behavior expected for a BKT transition with TBKT = 190 mK.

Is the bulk of the SrTiO3 superconducting or is it only a thin sheet at the interface layer? How thick is the superconducting layer? If the heterostructures were 2D superconductors, the transition into the superconducting state would be a BKT transition, characterized by a transition temperature TBKT at which vortex-antivortex pairs unbind (23). A simple estimate of TBKT, assuming that the sheet superconducting carrier density equals 4 × 1013/cm2, would suggest that in the samples, the BKT and mean field temperatures almost coincide. However, in case of large vortex fugacity, a high density of vortex-antivortex pairs is thermally generated and an ionic-like vortex-antivortex crystal is formed (24). For such a system, the melting of this lattice represents the BKT transition, which then occurs at lower temperatures. At the BKT transition, the current-induced Lorentz force causes dislocation-antidislocation pairs to unbind, resulting in a VI a behavior, with a (TBKT) = 3.

The samples indeed show clear signatures of the BKT behavior, such as a VIa power-law dependence (Fig. 4A). As revealed by Fig. 4B, at T = 188 mK, the exponent a approaches 3; this temperature is therefore identified as TBKT. The V(I,T) characteristics (Fig. 4A) are very similar to the results of simulations treating finite-size 2D systems (25). The ohmic regime observed below TBKT at small currents is expected for finite size samples and agrees quantitatively with an analysis (18) based on (24).

In addition, the R(T) characteristics are consistent with a BKT transition, for which, close to TBKT, a R = R0exp(–bt–1/2) dependence is expected (26). Here, R0 and b are material parameters and t = T/TBKT – 1. As shown by Fig. 4C, the measured R(T) dependence is consistent with this behavior and yields TBKT ≅ 190 mK, in agreement with the result of the a-exponent analysis. The superconducting transition of the samples is therefore consistent with that of a 2D superconducting film. Hence, the superconducting layer is thinner than ξ ≅ 70 nm.

Analysis of the superconducting transition temperature provides an independent bound on the layer thickness. If the superconductivity were due to oxygen defects in SrTiO3–x, a carrier density of ≳ 3×1019/cm3 would be required for a Tc of 200 mK (27). The measured sheet carrier densities thus give an upper limit for the thickness of the superconducting sheet of ≅ 15 nm. Considering that the carrier concentration of the SrTiO3–x layer cannot be constant but has to conform to a profile following Poisson's equation as treated with consideration to the field-dependent SrTiO3 susceptibility (28), one can set an upper limit for the thickness of the superconducting sheet of ≅ 10 nm, a value much smaller than that suggested in (7, 8) for the thickness of the conducting layer in reduced LaAlO3/SrTiO3 heterostructures. The carrier density profile at interfaces in oxygen-deficient SrTiO3–x has also been calculated in (8). As a result of this model, a sheet carrier density > 5 × 1014/cm2 is needed to provide a carrier concentration of 3 × 1019/cm3. Because the sheet carrier densities of our samples equal only 1.5 to 4 × 1013/cm2, according to this model the superconductivity of the LaAlO3/SrTiO3 interface cannot be caused by doped SrTiO3–x alone.

The experiments presented here do not allow us to determine whether the observed superconductivity is due to a thin doped SrTiO3 sheet or a novel phenomenon occurring at this artificial interface. Although the Tc of the heterostructures falls in the transition range of oxygen-deficient SrTiO3–x, the transport properties of the samples differ to some extent from the ones of doped SrTiO3. Whereas in oxygen-deficient SrTiO3–x and Nb-doped SrTiO3 films the Hall constant increases markedly below 100 K (29), it is less temperature dependent in LaAlO3/SrTiO3 heterostructures. In addition, the upper critical field of the heterostructures is an order of magnitude smaller than that of Nb-SrTiO3 with the same Tc. Finally, our observation of both superconducting and insulating behavior on the same sample, depending on the precise LaAlO3 layer thickness, is very hard to reconcile with a pure oxygen vacancy scenario.

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www.sciencemag.org/cgi/content/full/1146006/DC1

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