Strontium titanate (SrTiO3) is the first and best known superconducting semiconductor. It exhibits an extremely low carrier density threshold for superconductivity, and possesses a phase diagram similar to that of high-temperature superconductors--two factors that suggest an unconventional pairing mechanism. Despite sustained interest for 50 years, direct experimental insight into the nature of electron pairing in SrTiO3 has remained elusive. Here we perform transport experiments with nanowire-based single-electron transistors at the interface between SrTiO3 and a thin layer of lanthanum aluminate, LaAlO3. Electrostatic gating reveals a series of two-electron conductance resonances-paired electron states--that bifurcate above a critical pairing field Bp of about 1-4 tesla, an order of magnitude larger than the superconducting critical magnetic field. For magnetic fields below Bp, these resonances are insensitive to the applied magnetic field; for fields in excess of Bp, the resonances exhibit a linear Zeeman-like energy splitting. Electron pairing is stable at temperatures as high as 900 millikelvin, well above the superconducting transition temperature (about 300 millikelvin). These experiments demonstrate the existence of a robust electronic phase in which electrons pair without forming a superconducting state. Key experimental signatures are captured by a model involving an attractive Hubbard interaction that describes real-space electron pairing as a precursor to superconductivity.

SrTiO-based heterointerfaces support quasi-two-dimensional (2D) electron systems that are analogous to III-V semiconductor heterostructures, but also possess superconducting, magnetic, spintronic, ferroelectric, and ferroelastic degrees of freedom. Despite these rich properties, the relatively low mobilities of 2D complex-oxide interfaces appear to preclude ballistic transport in 1D. Here we show that the 2D LaAlO/SrTiO interface can support quantized ballistic transport of electrons and (nonsuperconducting) electron pairs within quasi-1D structures that are created using a well-established conductive atomic-force microscope (c-AFM) lithography technique. The nature of transport ranges from truly single-mode (1D) to three-dimensional (3D), depending on the applied magnetic field and gate voltage. Quantization of the lowest e/ h plateau indicate a ballistic mean-free path l ∼ 20 μm, more than 2 orders of magnitude larger than for 2D LaAlO/SrTiO heterostructures. Nonsuperconducting electron pairs are found to be stable in magnetic fields as high as B = 11 T and propagate ballistically with conductance quantized at 2 e/ h. Theories of one-dimensional (1D) transport of interacting electron systems depend crucially on the sign of the electron-electron interaction, which may help explain the highly ballistic transport behavior. The 1D geometry yields new insights into the electronic structure of the LaAlO/SrTiO system and offers a new platform for the study of strongly interacting 1D electronic systems.

The interface between the two complex oxides LaAlO 3 and SrTiO 3 has remarkable properties that can be locally reconfigured between conducting and insulating states using a conductive atomic force microscope. Prior investigations of "sketched" quantum dot devices revealed a phase in which electrons form pairs, implying a strongly attractive electron-electron interaction. Here, we show that these devices with strong electron-electron interactions can exhibit a gate-tunable transition from a pair-tunneling regime to a singleelectron (Andreev bound state) tunneling regime where the interactions become repulsive. The electronelectron interaction sign change is associated with a Lifshitz transition where the d xz and d yz bands start to become occupied. This electronically tunable electron-electron interaction, combined with the nanoscale reconfigurability of this system, provides an interesting starting point towards solid-state quantum simulation.

One-sentence summary:We report a sequence of quantized conductance plateaus that follows the third diagonal of Pascal's triangle. Abstract:The ability to create and investigate composite fermionic phases opens new avenues for the investigation of strongly correlated quantum matter. We report the experimental observation of a series of quantized conductance steps within strongly interacting electron waveguides formed at the LaAlO3/SrTiO3 interface. The waveguide conductance follows a characteristic sequence within Pascal's triangle: (1, 3, 6, 10, 15,…) ⋅ 2 /ℎ, where is the electron charge and ℎ is the Planck constant. The robustness of these steps with respect to magnetic field and gate voltage indicate the formation of a new family of degenerate quantum liquids formed from bound states of n = 2, 3, 4, … electrons. These experiments could provide solid-state analogues for a wide range of composite fermionic phases ranging from neutron stars to solid-state materials to quark-gluon plasmas.

High-mobility complex-oxide heterostructures and nanostructures offer new opportunities for extending the paradigm of quantum transport beyond the realm of traditional III-V or carbon-based materials. Recent quantum transport investigations with LaAlO_{3}/SrTiO_{3}-based quantum dots reveal the existence of a strongly correlated phase in which electrons form spin-singlet pairs without becoming superconducting. Here, we report evidence for the micrometer-scale ballistic transport of electron pairs in quasi-1D LaAlO_{3}/SrTiO_{3} nanowire cavities. In the paired phase, Fabry-Perot-like quantum interference is observed, in sync with conductance oscillations observed in the superconducting regime (at a zero magnetic field). Above a critical magnetic field B_{p}, the electron pairs unbind and the conductance oscillations shift with the magnetic field. These experimental observations extend the regime of ballistic electronic transport to strongly correlated phases.

We examine superconductivity in LaAlO_{3}/SrTiO_{3} channels with widths that transition from the 1D to the 2D regime. The superconducting critical current is independent of the channel width and increases approximately linearly with the number of parallel channels. Signatures of electron pairing outside of the superconducting regime are also found to be independent of the channel width. Collectively, these results indicate that superconductivity exists at the boundary of these channels and is absent within the interior region of the channels. The intrinsic 1D nature of superconductivity at the LaAlO_{3}/SrTiO_{3} interface imposes strong physical constraints on possible electron pairing mechanisms.

The LaAlO3/SrTiO3 system exhibits unusual magnetic and superconducting behavior arising from electron–electron interactions whose physical origin is not well understood. Quantum transport techniques, especially those involving mesoscopic geometries, can offer insight into these interactions. Here evidence for long‐range electron–electron interactions in LaAlO3/SrTiO3 nanowires, measured through the phenomenon of frictional drag, is reported, in which current passing through one nanowire induces a voltage across a nearby electrically isolated nanowire. Frictional drag mediated by the Coulomb interaction is predicted to decay exponentially with interwire separation, but with the LaAlO3/SrTiO3 nanowire system it is found to be nearly independent of separation. Frictional drag experiments performed with three parallel wires demonstrate long‐range frictional coupling even in the presence of an electrically grounded central wire. Collectively, these results provide evidence for a new long‐range non‐Coulombic electron–electron interaction unlike anything previously reported for semiconducting systems.

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