Research Update: Conductivity and beyond at the LaAlO3/SrTiO3 interface

In this review, we focus on the celebrated interface between two band insulators, LaAlO3 and SrTiO3, that was found to be conducting, superconducting, and to display a strong spin-orbit coupling. We discuss the formation of the 2-dimensional electron liquid at this interface, the particular electronic structure linked to the carrier confinement, the transport properties, and the signatures of magnetism. We then highlight distinctive characteristics of the superconducting regime, such as the electric field effect control of the carrier density, the unique tunability observed in this system, and the role of the electronic subband structure. Finally we compare the behavior of Tc versus 2D doping with the dome-like behavior of the 3D bulk superconductivity observed in doped SrTiO3. This comparison reveals surprising differences when the Tc behavior is analyzed in terms of the 3D carrier density for the interface and the bulk. GARIGLIO, Stefano, GABAY, M., TRISCONE, Jean-Marc. Research Update: Conductivity and


INTRODUCTION
Without a doubt, transition metal oxides qualify as one of the hot topics of interest as these materials are endowed with a broad range of significant electronic properties ranging from ferroelectricity to metal-insulator transitions as well as from magnetism to superconductivity. Many of these compounds exhibit structural instabilities, strong electronic correlations, and complex phase diagrams with competing ground states. 1 These features are quite desirable from an engineering perspective since they could prove instrumental in the design of novel ultrasensitive sensors with a strong response to small stimuli. Artificial structures of transition metal oxides therefore seem ideal to explore interfacial effects that could possibly lead to new phases. In this respect, the conducting layer at the interface between LaAlO 3 (LAO) and SrTiO 3 (STO) that was observed by Ohtomo and Hwang a decade ago 2 has attracted a considerable amount of attention. It was found that this two-dimensional electron liquid (2DEL) hosts gate tunable insulator to metal, 3 insulator to superconductor 4 transitions and a large interfacial spin-orbit effect. 5,6 Signatures of magnetism have also been reported in several independent studies, 7,8 underscoring the interplay between spin and charge for the electronic states. The mechanisms responsible for these features are still in debate. A significant effort has been devoted to unraveling the physics at play responsible for the formation of the 2DEL. Other key questions include the role played by the various d orbitals which could contribute selectively to a specific charge or spin property, the impact of confinement that might cause a spatial dichotomy between electrons harboring magnetic correlations and those involved in superconductivity in stark contrast with the standard behavior when all electrons participate equally in the different ground states irrespective of their position in the metallic sheet. In this brief overview, we focus on the prototypic heterostructure-LAO/STO-which has been extensively investigated worldwide and we highlight its key properties. While the interested reader may refer to a Electronic address: stefano.gariglio@unige.ch Interesting consequences of the polar catastrophe scenario pertain to [110] and [111] oriented interfaces. For ideal, sharp boundaries the former orientation does not produce a charge discontinuity and hence is not expected to give a 2DEL while the latter has a polar discontinuity as in the [001] orientation. This can possibly impact the characteristics of the 2DEL. Experimentally, both of these interfaces are found to be conducting as discussed below.
Let us also mention that the interfacial properties of the 2D electron liquid appear to be very sensitive to the LAO top surface. Polar adsorbates, for instance, cause a change in the carrier density. 23 A metallic capping can also be used to trigger conductivity in nominally insulating 1 unit-cell thick LAO/STO samples. 24 Applying a bias to an insulating 3 unit-cell thick LAO/STO interface, by means of a back gate 3 or by using a conducting atomic force microscope (AFM) tip, 25 also produces conductivity at the interface. We discuss later how the AFM approach can be exploited to create electronic nanostructures.

REALIZATION OF CONDUCTING INTERFACES
LAO/STO interfaces are commonly prepared by pulsed laser deposition (PLD). On a TiO 2terminated [001]-oriented SrTiO 3 substrate, a thin layer of LaAlO 3 is grown at ∼800 • C in an oxygen pressure ranging from 10 −5 to 10 −2 mbar. Using a laser fluence of 0.5-2 J/cm 2 and 1-5 Hz repetition rate, the films grow layer-by-layer, as observed by in situ reflection high energy electron diffraction, reproducing the step-and-terrace surface morphology of the substrate. Figure 2 illustrates the fabrication and structural properties of LAO/STO interfaces. The effect of the oxygen pressure during (and after) the deposition has been investigated by different groups, [17][18][19]26 revealing the important role played by this parameter for the formation of the 2DEL. Indeed, the exposure of the STO crystal to high temperature and low oxygen pressure during the growth can result in a loss of oxygen from the substrate and substantial electron doping of the crystal. A post-deposition annealing in a high oxygen pressure (0.1-1 bar) at 500 • C before cooling down to room temperature in the same atmosphere however allows an efficient suppression of these vacancies. Molecular beam epitaxy 27 and sputtering 28 have also been successfully employed for growing conducting LAO/STO interfaces. A particularly interesting outcome of the MBE approach has been the discovery of an unexpected dependence of the 2DEL formation on the stoichiometry of the LaAlO 3 layer. Varying FIG. 2. Fabrication and structural properties of LAO/STO interfaces. The fabrication starts with a SrTiO 3 crystal cut perpendicular to the [001] direction. A chemical and thermal treatment allows a single TiO 2 termination to be obtained. 86,87 The substrate surface presents then a step-and-terrace structure due to the slight miscut off the crystallographic plane. Using pulsed laser deposition (schematized above), sputtering, or molecular beam epitaxy, an epitaxial LaAlO 3 layer is grown, usually a few unit cells thick. The schematic view of the PLD deposition process shows the target's carousel and sample holder. The blue line is the laser pulse producing the plume. A high energy electron beam in grazing incidence is reflected on the substrate surface and produces a diffraction pattern on a screen, also shown in the figure. In standard deposition conditions for PLD, the growth proceeds layer-by-layer, resulting in atomically smooth surfaces that reproduce the topography of the substrate (top right). Looking at the chemical contrast in a transmission electron microscope (bottom right), 88 interfaces appear atomically abrupt. For films thinner than ∼20 unit cells, the epitaxial strain is preserved and a high crystalline coherence is observed. the cationic composition of the layer, interfacial conductivity was observed only for La deficient (La/Al ratio < 0.97) films; according to this study, samples prepared by PLD are naturally La deficient (the La/Al ratio is about 0.9). This sensitivity of the 2DEL to the cation stoichiometry of the LaAlO 3 layer has been related to the different role of the defects (La vacancies or Al 2 O 3 vacancies) in the charge transfer mechanism.
Recent work has demonstrated that 2DELs can also be formed using other crystallographic cuts of the STO substrate, opening novel possibilities for the realization of distinct electronic structures. 29,30 The origin of the 2DELs confined along these different orientations is currently investigated. In the case of [110]-oriented STO, the substrate surface is polar while the LAO/STO heterostructure does not present any polar discontinuity; for the [111]-oriented substrate, the surface is also polar but this time there is a polar discontinuity: in both cases, interfacial conductivity is observed above a critical LAO thickness, as in the (001) case. Since a crystal cannot have a polar surface that is highly unstable, these observations raise the question of the atomic configuration of the STO (110) and (111) surfaces and of the driving force behind the formation of the 2DEL for such termination planes. From a structural perspective, scanning transmission electron microscopy rules out faceting of the [110]-oriented substrate and interfaces on such planes are as sharp as in the [001] direction. 31 Efforts to replace the two components of this interface system have been attempted with various degrees of success. The polar LAO layer has been substituted with other polar layers (LaVO 3 , 32 LaTiO 3 , 33 NdGaO 3 34 ), resulting in conducting interfaces with properties similar to the LAO/STO system. Seeking for alternatives to the STO substrate has proven to be more difficult. Recent reports of interfacial conductivity in n-type LAO/ anatase TiO 2 interfaces 35 -anatase TiO 2 being structurally and electronically close to STO-and in LaTiO 3 /KTaO 3 36 are promising and deserve further investigation.

ELECTRONIC PROPERTIES
The confinement of the electron liquid at the (001) interface has important consequences on the electronic structure of the 2DEL: on the one hand it produces a subband structure and determines the orbital order of the different subbands and, on the other hand, it is thought to be at the origin of the strong spin-orbit interaction observed in the system. X-ray spectroscopy has revealed that the Ti 3d − t 2g bands, which are three-fold degenerate at the Γ point for a cubic crystal, exhibit an energy splitting at the center of the Brillouin zone due to the constrained motion in the direction perpendicular to the interface: as shown in Figure 3(b), the zero point energy of states with d x y -symmetry is lower than that of states with d x z /d y z -symmetry; the former predominantly reside in TiO 2 planes close to the interface while the latter extend further in the direction perpendicular to the interface as illustrated in Figure 3(a). 37 This particular electronic structure has been captured by ab-initio calculations 38,39 which also reveal that the band structure for the 2DEL is different from that of the bulk. This "interfacial" electronic structure has important consequences for the electric transport: in field effect devices, where the carrier density can be tuned with a gate voltage, the conductance was shown to change from single band to multi-band behavior upon charge filling. 40,41 Transport at low temperature is quantitatively described by weak localisation physics, as expected for a 2D electron system. The surprise is that the Rashba spin-orbit interaction that is a common occurrence in asymmetric confining potentials, for instance in semiconductor quantum wells, 42 can be dramatically tuned by the gate voltage in LAO/STO interfaces. 5 The spin-orbit strength is found to sharply rise as the carrier density is increased and reaches very large values on the order of 10 meV. The doping range over which the spin-orbit interaction exhibits the steep increase appears to correlate with the appearance of superconductivity. Several physical interpretations of the sharp interfacial spin-orbit strength increase 5,41,43,44 have been proposed: it has been suggested that it is the change in the confinement profile induced by the electric field and related variation of the carrier density that is responsible for the modulation of the strength of the spin-orbit interaction; it could also be that the spin-orbit interaction is amplified when the Fermi level is close to an avoided crossing point-marked by a dashed line on Figure 3 Once charges are transferred at the interface, they sit on the SrTiO 3 side in t 2g electronic states: the ones close to the interface are spatially localized states with d x y -symmetry and extend parallel to the conduction plane; d x z /d y z -symmetry states extend deeper into the substrate. 89 The band alignment shown comes from ab-initio calculations. 9 (b) and (c): d electronic bands of the 2DEL with their different symmetries: their ordering in energy is a consequence of the hopping term perpendicular to the interface. Band structure calculations show that atomic spin-orbit interaction (SOI) and polar distortions in the TiO 2 planes due to broken inversion symmetry lift the degeneracy of d x z /d y z -symmetry bands causing avoided band crossings. 41,43,44 When the Fermi level (dashed line) reaches such avoided crossings, the spin-orbit interaction can be amplified.
magnetic field in plane could be satisfactorily fitted using semi-classical Boltzmann transport theory in combination with spin-orbit coupling. 45 The spin-momentum entanglement of the charge carriers is expected to have profound consequences, beyond the ones on transport, also on magnetic and superconducting properties of the system. But, if the contribution of spin-orbit coupling to the magnetoconductance behavior is clear from the data, its impact on magnetism and superconductivity still needs to be experimentally determined as discussed below.

MAGNETISM
We just discussed the large gate tunable Rashba spin-orbit effect. We now return to this point as we review the debated experimental claims of magnetism in LAO-STO heterostructures. A search for signatures of spin-polarized states has been conducted using a variety of techniques which include magnetotransport, 46 torque 8 and SQUID magnetometry, 7 XMCD, 47,48 polarized neutron reflectometry, 49 and magnetic force microscopy. 50 Several studies concluded that a ferromagnetic alignment of magnetic moments occurs, with ordering temperatures in the range of 300 K for very low carrier concentrations (insulating limit) and of 100 K for samples that superconduct. By contrast others did not detect any fingerprint of magnetism. These clearly contradictory results raise the question of the intrinsic versus extrinsic character of the effect. In the former category, it is proposed that almost all the carriers transferred to the 2DEL during the electronic reconstruction process are localized at the interface due to disorder and/or correlations and that the residual fraction is mobile, delocalized within the conducting sheet and mediates a ferromagnetic exchange between the spins of the localized electrons. In the latter category, it is suggested that oxygen vacancies pinned near the interface are the source of the localized and extended electronic carriers in the 2DEL. 51 Both explanations contain a puzzling feature. The characteristic energy scales pertaining to the ferromagnetic state, to the Rashba spin textures, and to superconductivity are in the ballpark of a few tens of meV, a few meV a few tens of µeV, respectively. Consequently one would expect spin polarization to overpower the other states, at variance with what is reported experimentally. In an attempt to resolve this puzzle one might imagine an inhomogeneous system with magnetic patches interspersed with conducting regions. Alternative scenarios advocating an orbital selectiveness of the d-type carrier involved in the various orderings have been proposed. These can be tested experimentally as they predict that the interplay between spin-orbit and ferromagnetism produces a spiral state albeit with a large spatial periodicity, that the superconducting state might be FFLO-like 52 and that it exhibits a Jaccarino-Peter effect. 53 At this stage it is safe to say that magnetism remains an outstanding open issue.

SUPERCONDUCTIVITY
In 2007, superconductivity was discovered at the LAO/STO interface with a critical temperature of ∼250 mK. 54 Shortly after, a back gate was used to tune the carrier density. 4 Figure 4(a) displays the sheet resistance versus temperature for several gate voltages below 700 mK. As can be seen, applying an electric field allows one to switch back and forth between a zero resistance state and a resistive state at low temperature. Recording the temperature at which the resistance is reduced to 50% of its normal state value gives a widely adopted experimental mean field estimate of T c . A typical plot of T c versus the sheet conductance σ 2D is shown in Figure 4(d). Salient features of this phase diagram include a quantum critical point (QCP) separating a localized from a superconducting region at low dopings, a dome shaped curve culminating at T max c ∼ 300 mK, a superconductor to metal boundary at higher dopings. Without gating, virgin standard samples exhibit a T c of about 250 mK. A caveat regarding the so-called forming process is in order at this stage: before probing the interface properties for different values of V g , one applies a positive bias V max g to the sample first; then the measured observables will not depend on the voltage sweeps, so long as V g < V max g . Even so, there are sample to sample deviations in the values of T c for a given value of V g . If however one plots the measured transport quantity against the sheet conductance σ 2D , all FIG. 4. Tuning of the superconducting state by field effect. In field effect devices, the carrier density can be tuned, resulting in a strong change of the transport properties. (a) Resistive superconducting transitions, sheet resistance R S versus T , upon different gate voltages (V g ). By changing V g the critical temperature can be reduced ("depletion" state-blue curves), reaches its maximum value close to the original doping state (red curves), and decreases again (accumulation state-brown curves). When superconductivity is suppressed for negative gate voltages, weak-localization is observed. Superconducting transitions for an underdoped (b) and an overdoped state (c). (d) Superconducting dome plotted vs the sheet conductance σ 2D . A criterion of 50% of the normal state resistance was used to define T c .

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Gariglio, Gabay, and Triscone APL Mater. 4, 060701 (2016) curves essentially collapse on top of each other. Some of the ingredients that are likely key players in producing the characteristic shape of the phase diagram and in explaining the reproducibility issue are fluctuations, dimensionality, disorder, spin-orbit interactions. Their interplay is subtle and far from being fully understood. For instance, the rise of the spin-orbit strength that is seen upon ramping up V g beyond the QCP correlates with the filling of the d x z /d y z states. These orbitals probe a significant number of unit cells of STO, making the 2DEL effectively less two-dimensional. Is the appearance of superconductivity also linked to the filling or the proximity of the d x z /d y z states? Not all data do agree on this point 41 and there may be a low doping superconducting regime dominated by d x y states. Dimensionality impacts the nature of the phase transition and fluctuations in its vicinity. Beyond the quantum critical point, in a doping range where the physics may still be largely dominated by the d x y states, superconductivity possibly sets in through a Kosterlitz-Thouless (KT) transition. Scaling analysis of the I-V characteristics and of resistance versus T is consistent with this picture. 54 Note that spatial disorder and inhomogeneities in the normal state and superfluid densities have also been proposed as an explanation for the observed broadening of the superconducting transitions. 55,56 Measurements of the T dependence of the parallel (to the interface) critical field for the destruction of superconductivity H c// are in excellent agreement with a two-dimensional behavior. 57 From the determination of the perpendicular and parallel critical fields, one may extract the thickness d of the superconducting sheet. H c// significantly exceeds the value expected for the Pauli limit and the difference gives a measure of the strength of the spin-orbit effect when V g is increased. In this same 2D regime, evidence of a pseudogap phase above T c has been reported in two-point tunneling experiments. 58 This may be interpreted as a signal for the formation of uncorrelated Cooper pairs or fluctuating superconducting regions above the KT transition. The temperature where the pseudogap develops then provides an estimate of the mean field T c . According to this picture the mean field T c increases steadily as σ 2D decreases-not in line with the estimate of T c using the 50% reduction of the resistance criterion-reaching a maximum value of about 500 mK near the QCP. Let us mention that recent measurements on quantum dots suggest pairing without phase coherence at temperature as high as 900 mK. 59 Remarkably the pseudogap line appears to merge with the superconducting boundary beyond the top of the dome, suggestive of a more three-dimensional type of transition in this region of doping. In order to test this proposal one can overlay the T c curves of LAO/STO interfaces and of bulk, oxygen reduced, STO crystals by plotting T c /T max c versus σ/σ(T max c ). Using dimensionless variables mitigates the difficulty in comparing changes of T c with V g on the one hand, with oxygen content on the other, that is, changes of T c with 2D or 3D tuning parameters, respectively.
The data (not shown) reveal that all the curves fall quite nicely on top of each other in a broad range of reduced conductivities larger than that giving T max c , indeed suggesting a more 3D behavior for the interface in this region of the phase diagram. For lower reduced conductivities deviations are observed. One still needs to clarify the influence of disorder on the phase diagram. Scaling analysis of the "zero resistance" T c versus V g near the QCP yields a critical exponent zν = 2/3 (z dynamical-, ν coherence length-critical exponents) 4 which would be expected for a clean, fermionic system. However the measured sheet resistance at the QCP is in the ballpark of 6.4 kΩ, which coincides with the value predicted by the dirty boson model. 60 A possible way to reconcile these results has been proposed by Hurand et al. 61 based on data analysis of LTO/STO and of LAO/STO samples.
Finally let us return to the comparison between bulk STO and the LAO/STO interface. Bulk STO can be doped by replacing Sr by La, Ti by Nb, or by reducing the oxygen content. [62][63][64] Superconductivity is found in a broad range of dopings as can be seen in Figure 5(a). Inspection of the data reveals that superconductivity spans several orders of magnitude in carrier density, that it appears at very low doping, a few 10 17 cm −3 , and that it exhibits a dome-shape structure with a maximum T c of about 0.3 K.
To compare doped bulk STO and LAO/STO, one has to convert the interfacial 2D sheet carrier density into a 3D one. The carrier density is not uniform and is decaying as one is moving away from the interface but, as a first step, one can simply estimate the conducting thickness d and calculate n 3D , n 3D = n 2D /d. superconducting thickness d is about 10 nm and the carrier density typically 5 × 10 13 cm −2 , leading to n 3D = 5 × 10 19 cm −3 (notice here that the 2D mobile carrier density is typically found to be lower than the value expected from the polar catastrophe scenario). Figure 5(a) shows that this doping, identified by an arrow, is close to that giving the maximum T c . Field effect allows n 2D to be changed by a factor of 3-5 and the areal density for which the LAO/STO samples are not superconducting anymore translates into an n 3D around 10 19 cm −3 . As can be seen in Figure 5(a), bulk STO is strongly superconducting for this value of the density. Hence, superconductivity at the interface appears at much higher doping levels than in the bulk. This behavior may be linked to the particular interfacial band structure that we evoked previously. At the interface, using the simplified electronic structure shown in Figure 3(b), one sees that the lowest sub-bands have a d x y character with a low effective mass. Several of these have to be partially filled before the Fermi level reaches the energy of the heavier (higher density of states) d xz /d y z sub-bands which then become occupied. By contrast, the lowest energy hybridized band in tetragonal bulk STO (taking spin-orbit into account) becomes rapidly heavy at moderate doping and hence gives rise to high density of states. From BCS theory we know that a higher density of states promotes a higher T c . Accordingly, we may expect that for low dopings Cooper pairing is favorable in bulk STO more so than at the LAO/STO interface. Note that this scenario would naturally explain the low superfluid density (as compared to the total mobile carrier density) observed in scanning SQUID experiments. 65 One should bear in mind the fact that we use here the superconducting thickness obtained from critical field measurements. Establishing a direct connection between this thickness, the 3D carrier density profile and the extension of the different sub-bands is far from obvious but the issue is important and definitely deserves further attention. Recent calculations support the picture discussed above. The above scenario is also consistent with measurements of superconductivity in [110] oriented LAO/STO samples for which the orbital ordering is different from that of the [001] orientation. 66 In this case, T c does not disappear at low doping levels.
There is an additional twist to this scenario. Very fresh experiments aimed at probing the extension of the superconducting layer across the phase diagram have revealed an unexpected behaviour of the gas confinement upon gate tuning. When extracting the superconducting thickness from H c⊥ and H c// analyses, one finds that the thickness is essentially constant crossing the phase diagram from the QCP to optimal doping. 67 On the "overdoped" side, the superconducting thickness d increases by a factor of three as the doping is increased. Surprisingly, if we divide n 2D by d we see that n 3D initially increases with increasing V g (increasing σ 2D ) but then decreases upon further increase of V g . n 3D is not a single valued function of n 2D , V g , or σ 2D such that transport experiments only probe a limited portion of the T c versus n 3D phase diagram. The peculiar T c versus n 3D behavior for the interface system is shown by the blue line in Figure 5(b). This observation may be important for understanding the decrease of T c for high conductance and has serious consequences. The magnetoconductance in the underdoped regime is very different from the one observed for the "overdoped" state. 5,40,41 n 3D is not an appropriate control parameter to monitor this evolution since it is not evolving monotonically but one might choose the mobility-that is increasing dramatically as one is crossing the 2D phase diagram 68 -or the sheet conductance instead. The electronic structure is directly linked to the confining potential. If the latter changes, the sub-band structure will change and we just discussed the importance of the sub-band structure for superconductivity.
The superconducting behavior that one observes for the underdoped state is quite different from the one pertaining to the "overdoped" regime except for the fact that both span a rather similar n 3D range. As can be seen in Figure 4(b), for negative V g , the transition is much more rounded, a possible signature of fluctuations. As mentioned above, tunneling data show a markedly different behavior for the two doping regimes. If the correct mean field T c is the one extracted from the gap behavior-the green dashed line in Figure 5(b)-then the connection between superconductivity and the d x z /d y z sub-bands would be less compelling.
To conclude this section, let us briefly return to spin-orbit and its possible influence on the superconducting state. Spin and momentum of charge carriers are entangled at the LAO/STO interface. It was mentioned above that the strength of the spin-orbit interaction increases dramatically as superconductivity develops. Such a large spin-orbit interaction-typically 10 meV-that is much larger than the superconducting gap (40 µeV) will lead to a non s-wave symmetry of the order parameter and a parallel critical field that should be substantially higher than the Pauli limit. Experimentally, a factor of three increase of the parallel critical field was observed at optimum doping with a critical field above 2 T as the Pauli limit is about 0.5-0.6 T. 57 Future experiments sensitive to the symmetry of the order parameter will allow us to better understand the interplay between spin-orbit coupling and superconductivity.

SUMMARY AND PERSPECTIVES
Since Ohtomo and Hwang's seminal discovery of conductivity at the interface between LAO and STO, numerous papers have been devoted to the field. The present review did not attempt to present a comprehensive overview on the subject, but rather to underscore three key aspects of the electronic transport in this heterostructure. One of these aspects pertains to the origin of the two-dimensional electron liquid. Different scenarios have been advocated, based on polar catastrophe, intermixing, or vacancies. We discuss the 2DEL at the (001) interface and briefly at the in the 2DEL. In bulk STO, at low temperature, the lowest band is a combination of d x z /d y z orbitals near the gamma point. By contrast, the lowest sub-band has a d x y character in the 2DEL, a consequence of confinement. This impacts the band-filling sequence, when one gates the interface. When the d x z /d y z bands-which probe layers away from the interface and extend deep within the conducting sheet-start to be populated, transport evolves in a most spectacular way, as evidenced by measurements of the mobility, the interfacial spin-orbit contribution, and superconductivity. A third key aspect concerns the nature of the superconducting state that sets in when the interface is doped with electrons beyond a critical threshold. More specifically, how does it relate to the superconducting state that is observed in oxygen deficient bulk STO? We suggested that in the case of the 2DEL, Cooper pairing is established at a higher estimated 3D carrier concentration n 3D than in bulk STO, as a result of the "inversion" of the band filling sequence. Furthermore n 3D exhibits a non uniform variation with the gate voltage V g , such that it appears to decrease upon increasing V g beyond the top of the superconducting dome; overdoping the 2DEL is seen as increasing the oxygen content in oxygen deficient bulk STO (underdoping). Beyond these rather fundamental questions, many challenges more relating to technology issues are important. Let us mention a few of those. High mobility is a desirable attribute of a functional device and several ideas have been successfully pursued to obtain higher mobility samples. [69][70][71][72][73] For instance, reducing the growth temperature 74 or using special cappings of the LAO layer 75 allows mobilities of the order of 10 000 cm 2 /Vs to be reached at low temperature, these are associated with low carrier densities. The electronic structure and the control of superconductivity in such clean interfaces have yet to be determined.
Materials exhibiting giant thermopower are valuable as they may be used in the generation of electric power from thermal gradients. Very large thermopower with values of the Seebeck coefficient of up to 30 000 µV/K and giant oscillations of the Seebeck coefficient were observed as electrons were progressively removed from the LAO/STO interface. 76 The giant oscillations are understood as a signature of localized states found as the conduction band is being emptied.
Spin injection, a first step towards the fabrication of a spin field-effect transistor, has been successfully realized at the LAO/STO interface. 77,78 In these devices, spin-polarized electrons tunnel from a Co film, deposited onto the LAO layer, across the LAO tunnel barrier into the 2DEL. The spin population was probed using the Hanle effect, a measure of the junction resistance upon magnetic field sweep. A long-term goal would be to use the Rashba effect-that can itself be controlled by an electric field-to manipulate the spin of the conduction electrons along the channel between the source and the drain.
Taking advantage of the above properties for the purpose of engineering devices requires one to control the transfer of LAO/STO interfaces to other substrates. This has been tried with some success, for instance on silicon, 79 on LSAT and on NdGaO 3 . 80 It however turned out to be difficult to preserve metallicity down to low temperatures. In multilayer structures, recent efforts have attempted to explain why these do not always lead to conducting interfaces or why only a subset of the layers is metallic. Mixed termination and the quality of the STO films seem to be the critical parameters. 81 An interesting possibility in these multilayer systems consists of coupling superconducting layers in such a way as to trigger a 2D to 3D crossover.
Last but not least, nanostructures of LAO/STO interfaces can be realized. Electron beam lithography allows one to design small channels, 82,83 and steps at STO surfaces can be used to generate nanowires. 84 The properties of such small structures have been investigated and quantum phenomena such as quantum conductance fluctuations have been observed. A very exciting and promising tool in the design of nanoscale electronic structures and circuits is the atomic force microscope (AFM) with a conducting tip. Starting from a 3 unit cell thick LAO film-that is an insulating interface-one creates conducting regions with nanometer resolution. The AFM technique is described in Figure 6. Such a technique offers the possibility to realize nanoscale electronic structures and circuits. Demonstration of nanoscale transistors and other devices has been made. This technique should allow superconducting one-dimensional wires with interesting aspect ratios to be studied as well as other fascinating mesoscopic devices.
Finally, let us mention that while the present review focuses on the LAO/STO system there are many more interesting interface systems. For instance LaTiO 3 /STO (LTO/STO) 33 25 This thickness is below the threshold (4 unit cells) above which conductivity is observed. The technique uses the metallic tip of an atomic force microscope as a local source of electric field. Applying a bias between the tip and an electrode (for instance a gold layer in contact with the interface) and moving the tip away from the electrode induces locally, under the tip, a conducting area-the effect is non-volatile for some time. The width of the written conducting channel depends on the writing voltage and can be as small as a few nanometers. Panel (a) illustrates the writing process. The stability of the writing process might be linked to adsorbates that accumulate on the LAO surface while charges are transferred. 90 The process is indeed found to be sensitive to external parameters such as the humidity in the laboratory. (b) shows the design of a nanoscale transistor-a conducting path between two electrodes has been first drawn and then cut (scanning with the AFM tip perpendicular to the path and applying an opposite bias). 91 With negative bias applied to the side gate, the device is insulating (off-state) as can be seen from the drain current I D vs source-drain voltage V S D curve plotted on (c). Applying a positive voltage to the side gate allows conduction to be established, as can be seen from the linear I D -V S D curves (on-state). This technique can in principle allow the realization of complex circuits. Images taken from Refs. 25 and 91.
(GTO/STO). 85 Note that bulk LTO and GTO are Mott insulators. The LTO/STO heterostructure however displays properties very similar to those of LAO/STO. In the GTO/STO system, high mobile carrier densities are observed-corresponding to the densities expected for screening the GTO polar field-and multilayer structures with multiple conducting interfaces have been grown and studied. Several other exciting systems have been realized. 36 This flurry of novel conducting interfaces will certainly open new and interesting avenues for the investigation of low dimensional electron systems.

ACKNOWLEDGMENTS
S.G. and J.-M.T. thank Margherita Boselli, Alexandre Fête, Danfeng Li, Wei Liu, Jochen Mannhart, Davide Valentinis, Dirk van der Marel for illuminating discussions and valuable comments. This work was supported by the Swiss National Science Foundation-division II, by the