Semiconductor heterostructures provide an ideal platform for studying high-mobility, low-density electrons in reduced dimensions. The realization of superconductivity in heavily doped diamond, silicon, silicon carbide and germanium suggests that Cooper pairs eventually may be directly incorporated in semiconductor heterostructures, but these newly discovered superconductors are currently limited by their extremely large electronic disorder. Similarly, the electron mean free path in low-dimensional superconducting thin films is usually limited by interface scattering, in single-crystal or polycrystalline samples, or atomic-scale disorder, in amorphous materials, confining these examples to the extreme 'dirty limit'. Here we report the fabrication of a high-quality superconducting layer within a thin-film heterostructure based on SrTiO(3) (the first known superconducting semiconductor). By selectively doping a narrow region of SrTiO(3) with the electron-donor niobium, we form a superconductor that is two-dimensional, as probed by the anisotropy of the upper critical magnetic field. Unlike in previous examples, however, the electron mobility is high enough that the normal-state resistance exhibits Shubnikov-de Haas oscillations that scale with the perpendicular field, indicating two-dimensional states. These results suggest that delta-doped SrTiO(3) provides a model system in which to explore the quantum transport and interplay of both superconducting and normal electrons. They also demonstrate that high-quality complex oxide heterostructures can maintain electron coherence on the macroscopic scales probed by transport, as well as on the microscopic scales demonstrated previously.

The interface between the insulating oxides LaAlO 3 and SrTiO 3 exhibits a superconducting two-dimensional electron system that can be modulated by a gate voltage. While the conductivity has been probed extensively and gating of the superconducting critical temperature has been demonstrated, the question as to whether, and if so how, the gate tunes the superfluid density and superconducting order parameter needs to be answered. We present local magnetic susceptibility, related to the superfluid density, as a function of temperature, gate voltage, and location. We show that the temperature dependence of the superfluid density at different gate voltages collapses to a single curve that is characteristic of a full superconducting gap. Further, we show that the dipole moments observed in this system are not modulated by the gate voltage.

We demonstrate the formation of a two-dimensional electron gas (2DEG) at the (100) surface of the 5d transition-metal oxide KTaO3. From angle-resolved photoemission, we find that quantum confinement lifts the orbital degeneracy of the bulk band structure and leads to a 2DEG composed of ladders of subband states of both light and heavy carriers. Despite the strong spin-orbit coupling, we find no experimental signatures of a Rashba spin splitting, which has important implications for the interpretation of transport measurements in both KTaO3-and SrTiO3-based 2DEGs. The polar nature of the KTaO3(100) surface appears to help mediate formation of the 2DEG as compared to non-polar SrTiO3(100). Today's electronic devices largely rely on control of the conductivity of two-dimensional (2D) electron channels in semiconductor hosts. Creating such 2D electron gases (2DEGs) in oxides, which in bulk form generally show much larger and more diverse responses to external stimuli, holds the potential for devices with functionalities well beyond what we have experienced to date [1]. The prototypical example of an oxide 2DEG, formed when SrTiO 3 is interfaced to the polar surface of another perovskite oxide [2], has indeed proved a very rich system [3,4]. Recently, it was discovered that oxygen vacancies could mediate formation of a similar 2DEG at the bare surface of SrTiO 3 [5,6], providing an exciting opportunity for the realization of 2DEGs in more exotic parent materials than has been achieved via interface engineering.Of particular interest are 5d transition metal oxides (TMOs), whose large spin-orbit interactions offer the potential to incorporate the spintronic functionality sought in emerging schemes of semiconductor electronics [7][8][9] into all-oxide devices. Despite the extended nature of 5d atomic orbitals, the interplay of their large spinorbit interactions with even a modest Coulomb repulsion yields pronounced signatures of electron correlations in these materials, such as the formation of Mott insulating states [10][11][12] and possible correlated topological insulators [13,14], suggesting 5d TMOs could provide a novel and potentially very rich host for engineering of artificial 2D electron systems. Understanding the interplay of strong spin-orbit coupling, quantum confinement, and correlations within such a 2DEG is an essential step towards realizing their potential for practical applications. To date, this has been hampered by the difficulty of generating 2DEGs in 5d oxides via interface engineering.Here, we show that a 2DEG can be created at the (100) surface of the 5d perovskite KTaO 3 . Exploiting its surface-localized nature, we utilize angle-resolved photoemission (ARPES) to provide the first direct measurement of the subband structure of a 5d-oxide 2DEG. Our measurements, supported by model calculations, reveal an important role of multi-orbital physics in this system. Surprisingly, however, they do not show any significant Rashba spin-splitting of the 2DEG, which might naturally be expected.Single-crystal...