A brief overview is given of the studies of high-temperature interface superconductivity based on atomic-layer-by-layer molecular beam epitaxy (ALL-MBE). A number of difficult materials science and physics questions have been tackled, frequently at the expense of some technical tour de force, and sometimes even by introducing new techniques. ALL-MBE is especially suitable to address questions related to surface and interface physics. Using this technique, it has been demonstrated that high-temperature superconductivity can occur in a single copper oxide layer—the thinnest superconductor known. It has been shown that interface superconductivity in cuprates is a genuine electronic effect—it arises from charge transfer (electron depletion and accumulation) across the interface driven by the difference in chemical potentials rather than from cation diffusion and mixing. We have also understood the nature of the superconductor–insulator phase transition as a function of doping. However, a few important questions, such as the mechanism of interfacial enhancement of the critical temperature, are still outstanding.
1. Introduction: atomic-layer-by-layer molecular beam epitaxy
For the last 20 years, atomic-layer-by-layer molecular beam epitaxy (ALL-MBE) has been applied to the fabrication of high-temperature superconductor heterostructures and devices. ALL-MBE enables a precise control of the growth, it makes it possible to study layers that are just a few atoms thick and it provides heterostructures with atomically smooth interfaces. Certain procedures separate this technique from standard MBE. In this case, the sources' shutters are sequenced in such a way that the proper number of atoms is placed on the substrate at the right time. This way, the stoichiometry at the surface is always controlled. This procedure requires a very accurate control of the deposition rates. In order to provide feedback from the deposition and follow the deposition process, a number of in situ characterization techniques are needed. As will be shown, some of them are common, such as reflection high-energy electron diffraction (RHEED), but others were devised out of necessity in order to provide information that was lacking. The capabilities of this technique enable the study of very specific questions related to interfaces and surfaces. A number of the questions to be studied were anticipated  while others posed themselves subsequently as the field developed.
The technical basis of ALL-MBE work at Brookhaven National Laboratory is a unique multi-chamber ultra-high vacuum (UHV) system, consisting of a synthesis chamber, a processing chamber and a transfer chamber with two load-locks on both sides. The main growth chamber (figure 1) is equipped with 16 thermal effusion (Knudsen cell) sources. Each source is placed in a separate arm that can be isolated by a gate valve and pumped down by a dedicated turbo-molecular pump. This configuration allows replenishing or replacing each source while keeping UHV in the growth chamber, as well as venting the main chamber while keeping the sources at stand-by temperatures. Each source arm also contains a pneumatic, computer-control shutter. An ozone generator provides an O2 : O3 mixture that is distilled by condensation to deliver pure ozone to the growing film surface through four nozzles placed symmetrically around the substrate to ensure uniformity. The manipulator can host a single 3′′ wafer or up to a 4×4 array of 1×1 cm2 substrates. The samples are heated by four quartz lamps that can be adjusted separately to guarantee temperature homogeneity in the substrates.
A separate motorized manipulator hosting a scanning quartz-crystal rate monitor allows for mapping the deposition rate from each source. The fluxes are also monitored during growth in real time by means of atomic absorption spectroscopy. These measurements provide feedback to the computer that controls the shuttering intervals. The system also hosts in situ characterization tools such as an RHEED system, an optical pyrometer to measure the substrate temperature, and a time-of-flight ion scattering and recoil spectroscopy (TOF-ISARS) system. The TOF-ISARS system sends a beam of monochromatic (10 keV) K+ ions to impinge on the film surface, ejecting some of the ions from the film. These ions are mass-analysed using four detectors located at different angles, including a mass spectroscopy of recoiled ions analyzer. It is a highly surface-sensitive tool that provides information on the chemical composition of the sample in real time during film growth.
A processing chamber is placed inside an adjacent class-1000 clean room. It allows in situ micro-fabrication steps (evaporation, Ar-ion milling and ozone plasma treatments). The two chambers are connected by a UHV transfer chamber so that the samples can be transferred between them without being exposed to the atmosphere.
2. Interface superconductivity
The first reports of interface superconductivity in high-temperature superconductivity (HTS) samples date back to several conferences in 2000 and 2001; the results were eventually published in 2002 . In that experiment, a heterostructure consisting of a 5 unit cell (UC) thick oxygen-doped La2CuO4+δ (S′) layer grown on top of a 15 UC thick layer of La1.85Sr0.15CuO4 (S) was shown to have Tc=51.5 K (figure 2). This was about 10 K higher than what was observed by the same group in any single-phase La2−xSrxCuO4 film, specifically including those made of the above two constituent materials (S or S′). The result was not broadly noticed, though, since the work reported  focused on a different subject (the effects on Tc of the epitaxial strain and the oxygen intake).
HTS at the interface between metallic La1.55Sr0.45CuO4 (M) and insulating La2CuO4 (I) layers was the focus of a more recent study . Superconductivity was observed with Tc≈15 K in I–M bilayers, and with Tc≈30 K in M–I bilayers. By growing a set of samples with different top-layer thickness, Gozar et al.  showed that superconductivity was confined within about 2 UC from the interface. The results, reproduced in figure 3, show that the critical temperature saturates when the top-layer thickness reaches or exceeds 2 UC.
Several experiments were performed in order to clarify the origin of superconductivity in these heterostructures, i.e. to discern whether this was an electronic effect or rather the outcome of ion interdiffusion between the two layers. The task was rather challenging, since it required measurement of the depth profiles of chemical composition and of mobile carrier density with atomic resolution. The first results were obtained by in situ RHEED and TOF-ISARS characterization during the film growth. The intensity of the RHEED specular spot showed pronounced oscillations, indicating an atomically smooth surface. Whenever the deposition was changed from M to I or vice versa, the amplitude and the shape of the RHEED oscillations changed within about 0.5 UC, indicating an abrupt interface between the two layers. TOF-ISARS data shown in figure 4 confirmed the RHEED observations by setting an upper limit of diffusion of Sr into La2CuO4 to 1 UC. Subsequently, electron energy-loss spectroscopy using a scanning transmission electron microscope confirmed this upper limit.
Once the limit for Sr interdiffusion was set, the question was how to quantify the charge transfer across the interface. As is well known, if the chemical potential of the constituent materials is different when they are separated, once they are brought in contact, the carriers redistribute across the interface in such a way that the chemical potential equalizes. In 2003, it was shown by Bozovic et al.  that no charge redistribution occurs between La1.85Sr0.15CuO4 and La2CuO4. The measurement in M–I bilayers was performed by Smadici et al.  using a novel synchrotron-based technique, resonant soft X-ray scattering. They measured a superlattice that consisted of 15 periods, each containing 1 UC of I and 2 UC of M. Again, none of the constituents were superconducting but the superlattice showed Tc≈38 K. The analysis of the data showed that the holes were not bound to the Sr2+ ions; they redistributed between the layers, generating a carrier concentration of about 0.15 holes/Cu in the middle of La2CO4 layers. The carrier interdiffusion was modelled by Loktev & Pogorelov  by solving the Poisson equation for the system.
The crystal structure of these bilayers was studied by X-ray diffraction measurements by Butko et al.  and yielded a surprising result. For both types of bilayers, M–I and I–M, the top layer grew pseudomorphic over the bottom layer. However, in both cases, the volume of the UC of the top layer was the same as the volume of the bottom layer, i.e. the c-axis lattice parameter of the top layer also matched the one of the bottom layer. This unconventional effect was investigated theoretically by Butko et al.  and Radovic et al. , who attributed it to strong Coulomb interaction between the layers, poorly screened in the c-axis direction.
However, traditional X-ray diffraction only provides accurate values of the lattice parameters, but does not present a direct measurement of the position of atoms within the UC. For this, another novel synchrotron-based X-ray phase-retrieval technique was employed, coherent Bragg-rod analysis (COBRA) . The measured diffraction intensities, and the fact that the complex structure factors vary continuously along the substrate-defined Bragg rods, are used to determine the diffraction phases and the complex structure factors. The latter are then Fourier transformed to obtain the three-dimensional electron density of the film and of the substrate, which in turn determines the atomic positions, with sub-ångström resolution.
In this method, X-rays impinge on the sample at a very shallow angle, which makes the technique highly surface sensitive. For this reason, COBRA is most effective for epitaxial films that are just few unit cells thick and that have atomically smooth surfaces. Fortunately, ALL-MBE-grown films easily meet these requirements, making the two techniques a potent combination.
The COBRA results showed that in M–I bilayers, the copper-to-apical-oxygen distance R(Cu–OA) increases by as much as 0.45 Å towards the surface of the sample. This is not only surprising but also potentially quite exciting, because it is known that the variations in R(Cu–OA) strongly affect Tc in cuprates [10–13]. According to theory , for R(Cu–OA)≈2.85 Å as found near the surface in M–I bilayers, one would expect Tc≈80–90 K if only these layers were optimally doped. If this were right, one would have a recipe to double the critical temperature in HTS films.
Up to this point, it was established that in M–I heterostructures, superconductivity occurs in a layer within La2CuO4, no more than 1–2 UC thick, and doped to nearly optimum level by a combination of Sr diffusion and electron depletion. The state-of-the-art was pushed to the next level by Logvenov et al.  who performed a conceptually simple experiment that at the same time showed the extraordinary capabilities of ALL-MBE. A series of M–I bilayers was synthesized with each layer 3 UC thick; i.e. each heterostructure contained exactly 12 CuO2 planes, as illustrated in figure 5. Here, we have labelled the CuO2 planes within La1.56Sr0.44CuO4 from N=−6 (the one closest to the substrate) to N=−1, and within La2CuO4 from N=1 to N=6 (the one closest to the surface). In each of these heterostructures, δ-doping was performed in a different copper oxide plane, by replacing 3 per cent of Cu by Zn. Clearly, atomic-layer-by-layer synthesis capability has been critical for this task. Zn was chosen because it is known to suppress Tc and the superfluid carrier density ns significantly, without affecting the carrier density [15–18]. Logvenov et al. verified that in single-phase, superconducting La1.85Sr0.15CuO4 and La2CuO4+δ films, doping by 3 per cent Zn reduced Tc by a factor of 2 and ns by a factor of 4–5.
The results obtained in the experiment with M–I bilayers are summarized in figure 6: Tc remained unchanged at approximately 30 K in almost all the films. The only exceptions were those in which Zn δ-doping was carried out in the second CuO2 plane counting from the nominal geometric M–I interface towards the surface of the sample (N=2), in which case a drop to Tc≈18 K was observed. In the same films, mutual inductance measurements showed that ns also decreased, by a factor of 4–5. Both results clearly showed that in these M–I bilayers, superconductivity actually occurs in a single CuO2 plane inside La2CuO4.
3. Interface-enhanced superconductivity
In the above example, interface superconductivity appeared in heterostructures where both constituents are non-superconductive. It can also happen that one or even both constituents are superconducting themselves, but the interfacial layer has an even higher Tc and thus can be detected and differentiated. We will refer to this latter case as interface-enhanced superconductivity. In cuprates, the first reported example was the one reproduced in figure 2, i.e. an La1.85Sr0.15CuO4–La2CuO4+δ (S–S′) heterostructure with Tc=51.5 K, about 25 per cent higher than in either constituent material . More recently, Gozar et al.  showed similar critical temperature enhancement in M–S′ bilayers (figure 3). Measurements of the temperature dependence of the critical current density (jc) showed that in both cases, superconductivity with the highest critical temperature was confined to a layer 1 UC thick, whereas the critical temperature in the rest of the structure remained below 40 K.
The X-ray diffraction experiments by Butko et al.  were extended also to M–S bilayers and revealed that the c-axis lattice constants of M–S and S–S′ bilayers were elongated by more than 0.5 per cent. Furthermore, a linear relation was noticed between the c-axis lattice parameters and the critical temperature of various heterostructures discussed here (figure 7). A similar relation was noticed by Sato et al.  for single-phase La2−xSrxCuO4 with 0<x<2 and by Locquet et al.  across various cuprate families.
A different mechanism for Tc enhancement in heterostructures has been proposed by Kivelson  and developed further by Berg et al.  and Goren & Altman . It is based on the hypothesis that interface-enhanced superconductivity could arise from the proximity effect between a material with strong pairing but low phase stiffness and a material with weak pairing but strong phase stiffness. Some experimental support for this scenario was found in overdoped/underdoped La2−xSrxCuO4 bilayers by Yuli et al. , but a subsequent study by Koren & Millo  did not reproduce the initial experimental observations.
In summary, it has been shown that Tc can be enhanced significantly in certain cuprate heterostructures, but the mechanism of this interface enhancement is still unclear.
4. Electrolyte–superconductor field-effect transistor
In the above two examples, interface superconductivity was generated in a ‘passive’ way, by just placing two materials with different chemical potentials together. It is also possible to generate it in an ‘active’ way, where one also applies bias voltage between the two materials. To maintain the potential difference, one of these should be an insulator. A typical device configuration is similar to that of the field-effect transistor (FET), with two electrodes (source and drain) for controlling the current flow and a third one (gate), separated by a thin insulator layer from the active channel, for controlling the perpendicular electric field. The first experiments with electrostatic doping of superconductors were performed by Glover & Sherrill  over 50 years ago, but they were able to induce only minute shifts in Tc, of the order of 10−4 K. The main difficulty they faced was the fact that the carrier density in available superconducting materials was 1022–1023 cm−3, several orders of magnitude higher than in typical semiconductors. The electric field is thus screened very efficiently; the thickness of the accumulation and depletion layers induced by the gate is determined by the electrostatic screening length, which is of the order of 1 Å. Thus, in order to induce a significant change in the carrier concentration, even in an extremely thin surface layer, the gate insulator has to sustain enormous electric fields.
A new phase in superconducting FET research began with the discovery of HTS in cuprates. It was realized before long that they are much more promising for several reasons: (i) Tc is much higher, (ii) the carrier density is significantly lower, as low as 1.5×1021 cm−3 in optimally doped La2−xSrxCuO4, and (iii) cuprates are quite anisotropic, with an extremely short coherence length in the c-axis direction, ξc≈1–2 Å. (Indeed, as shown in §2, HTS can be sustained in a single CuO2 layer.) In the last two decades, improvements in the techniques for deposition of HTS thin films have enabled a large increase in the tuning range [27–29]. However, apart from the need for atomically perfect ultrathin HTS films, for all-solid-state devices a serious limiting factor is the breakdown field of the gate insulator, typically less than about 107 V cm−1.
Another route, which has attracted much attention recently, is to work with solid–liquid interfaces. In this case, the gate insulator is replaced by an electrolyte or an ionic liquid (figure 8). When a voltage is applied to the gate, the mobile ions accumulate near the surfaces of the film and of the gate electrode. These ionic charges are compensated by electron accumulation or depletion inside the film and the gate electrode. The internal electric field inside this so-called Helmholtz double layer can exceed 108 V cm−1, with the induced surface charge density in the range of 1014–1015 cm−2. This should be enough to tune one CuO2 layer all the way from being completely undoped and insulating to optimally doped and superconducting with a high Tc, and even beyond, well into the overdoped regime. The caveat is that one needs an ultrathin cuprate film, a clean and atomically flat surface, and an electrolyte that is chemically compatible with the HTS material, so that there are no chemical reactions (nor electrochemical ion insertion or depletion).
Pioneering work in the field of electrolyte-based HTS-FET devices was in fact done in the 1990s by McDevitt and collaborators [30–39]. In their comprehensive studies, they reported detailed electrochemical characterization of the double-layer parameters. They have observed in YBa2Cu3O7−x reproducible and reversible shifts of Tc by more than 50 K—the record that until today no other group was able to come close to. It may be worth noting that the films they used were granular and had rough surfaces. It is thus possible that the main effect of the electric field was to introduce carriers into the otherwise underdoped and perhaps insulating grain boundaries, where the screening length would be much longer. This would greatly affect the Josephson coupling between the HTS grains. If this conjecture is right, then one could argue that the working principle of McDevitt's polypyrrole devices is not exactly the same as the one in current HTS-FET devices. McDevitt et al. also pioneered the work with fluid electrolytes. They used existing polymer electrolytes but also developed their own novel electrolytes that stayed liquid down to low temperature, allowing them to measure the changes in the device capacitance that occur at the superconducting transition.
Ironically, this work seems to have been way ahead of its time, and was somehow forgotten. The electrolyte FET technique was rediscovered two decades later, apparently independently, by Ueno et al. . Several other groups followed before long [41–43]. However, the comprehensive prior work by McDevitt's group was overlooked by everyone including the authors of this review; we are trying to remedy that blunder here. Ueno et al.  used KClO4 dissolved in polyethylene oxide as the gate electrolyte, and were able to induce superconductivity in SrTiO3. This stimulated work on other materials. Ye et al.  used an ionic liquid, N,N-diethyl-N-(2-methoxyethyl)-N-methylammonium bis(trifluoromethyl sulphonyl)imide, and were able to modulate the carrier density in ZrNCl by as much as 2.5×1015 cm−2. Cuprates were then tackled by several groups [41–43].
The main benefit from these studies was an advance in the understanding of superconductor–insulator (S–I) quantum phase transition that is driven by changing the doping level. In principle, the FET technique may enable a continuous, controlled and reversible way of changing the carrier concentration of a compound without adding disorder. However, great care should be taken that a proper ionic liquid is chosen so that there are no unwanted chemical reactions and/or ion intercalation. Bollinger et al.  used ALL-MBE to fabricate HTS-FET structures and study the S–I transition in La2−xSrxCuO4. Using ionic liquids, they induced large modulation in the carrier density, up to ±0.04 carriers per Cu, corresponding to shifts in Tc by up to 30 K (figure 9). The process was reversible and non-destructive. Hundreds of resistance versus temperature curves, recorded at different gate voltages, were shown to scale and collapse onto a single curve, as predicted for the S–I transition in two-dimensional systems. The critical values of carrier density and sheet resistance were xc≈0.06 and Rc≈6.5 kΩ, exactly the quantum resistance for pairs. This finding points to pair localization and quantum phase fluctuations as the mechanisms responsible for the S–I transition. Simultaneously and independently, very similar results were obtained by Goldman's group  in YBa2Cu3O7−δ as well, so chances are that this may be true for all HTS cuprates. A broader perspective on other studies of both disorder-driven and field-driven S–I quantum phase transitions is offered in several excellent reviews [45–47], and will thus be omitted here.
ALL-MBE has proved to be a powerful technique to grow atomically flat layers of complex oxides, including various HTS cuprate compounds, with high crystal quality. This, in turn, enables one to use highly surface-sensitive characterization techniques, such as COBRA, and obtain atomic-level information that would be very difficult to attain otherwise. Interface phenomena can thus be studied with an unprecedented accuracy. The key results obtained to date include significant enhancement of the critical temperature of superconductors at certain interfaces. New insights into the nature of S–I quantum phase transitions as a function of doping were obtained as well, with the potential to trigger an advance in understanding the mechanism of HTS in cuprates.
J.P. and C.P. were supported by the Prime Minister's Office, National Research Foundation, Singapore; I.B., G.L. and A.G. by the US Department of Energy, Basic Energy Sciences, Materials Sciences and Engineering Division; and A.T.B. by the Center for Emergent Superconductivity, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences.
One contribution of 10 to a Discussion Meeting Issue ‘The new science of oxide interfaces’.
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