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Introduction Interface conduction and the exemplary LaAlO3/ SrTiO3 two-dimensional electron gas/liquid It is in use as artificial diamond, but for many scientists, it has the appeal of a complete jewelry shop: Strontium-titanate, SrTiO3, the perovskite crystal structure that looks deceptively simple, but which harbors tremendously rich physics, especially when electronically doped. In 1969, Marvin Cohen, the co-discoverer of superconductivity in oxygen-reduced SrTiO3,1 said, “If SrTiO3 had magnetic properties, a complete study of this material would require a thorough knowledge of all of solid state physics.”2 In their 1987 Physics Nobel lecture, J. Georg Bednorz and K. Alex Müller mention SrTiO3 together with LaAlO3 as key materials under study, leading to the discovery of high-temperature superconductivity in cuprate perovskites.3 Notably, these two electrically insulating materials marked the beginning, in 2004, of a new chapter in the research on oxides, now focusing on their interfaces. Akira Ohtomo and Harold Y. Hwang showed that the contact area between a LaAlO3 film and a SrTiO3 substrate, of which the top-most atomic layer was chemically prepared to be TiO2, is conducting.4 Meanwhile, many additional remarkable properties have been observed for the LaAlO3/SrTiO3 interface, and these even include magnetic effects. In addition, this field of research has expanded to include many other oxide interface combinations.

These developments raise the questions: What makes these oxide interfaces so special, and what could they have further in store? Before turning to these questions, it is useful to note that among scientists working in the field of oxide electronics, a distinction is made between “simple” and “complex” oxides. The former includes such materials as SiO2, TiO2, and ZnO, which have many interesting and useful properties—not really simple, by the way. Especially noteworthy in relation to interface conductance is research on two-dimensional electron gases (2DEGs) at the interface between ZnO and MgZnO, in which electron mobilities up to 700,000 cm2/Vs at temperatures below 1K have been reached.5 The observation of the fractional quantum Hall effect in these systems, requiring ultra-low defect densities, exemplifies the excellent quality of these interfaces. In many respects, the ZnO/MgZnO interfaces can be viewed as an oxide analogue to semiconductor 2DEGs such as GaAs/ AlGaAs with potentially very long spin coherence, of interest for spintronic (quantum) devices.5 The designation of “complex” oxides is used for materials comprising—next to the oxygen anion—two or more cationic elements. Canonical examples of these are the perovskite oxides with the generic crystal unit cell composition ABO3, in which A is typically an element from the alkaline earth or rareearth metal groups, and B is a (post-)transition metal element (Ti, V, Mn, Fe, Cu, Ru, Ir, Al, Bi). In their stoichiometric “parent compound” phase, many of the perovskites are insulating,

Hans Hilgenkamp, University of Twente, The Netherlands; H.Hilgenk