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We report Aharonov-Bohm (AB)-type quantum interference in simply-connected devices created at the LaAlO$_3$/SrTiO$_3$ interface using conductive-atomic force microscope (c-AFM) lithography. The oscillations are multi-periodic functions of magnetic field strength, and they exhibit a substantial magnetic hysteresis with frequencies that depends on the magnetic sweep direction. The oscillation amplitude for the lowest two frequencies approaches $e^2/h$, consistent with the theoretical maximum for the AB effect, and harmonics up to third order are observable. Broadband quasiperiodic behavior is reported in a fraction of simply-connected electron waveguide devices that exhibit magnetic asymmetries. Curiously, nanoscale ring devices that are multiply-connected lack signatures of AB quantum interference. The interference phenomena are associated with an inhomogeneous magnetic landscape within the LaAlO$_3$/SrTiO$_3$ nanostructures., Comment: 5 pages, 3 figures, Supplementary materials

The widely reported magnetoresistance oscillations in LaAlO3/SrTiO3 heterostructures have invariably been attributed to the Shubnikov-de Haas (SdH) effect, despite a pronounced inconsistency with low-field Hall resistance measurements. Here we report SdH-like resistance oscillations in quasi-1D electron waveguides created at the LaAlO3/SrTiO3 interface by conductive atomic force microscopy lithography. These oscillations can be directly attributed to magnetic depopulation of magnetoelectric subbands. Our results suggest that the SdH oscillations in 2D SrTiO3-based systems may originate from naturally forming quasi-1D channels., Comment: 16 pages, 4 figures

We examine superconductivity in LaAlO$_3$/SrTiO$_3$ channels in which the channel width transitions from the 1D to 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 phase are also independent of channel width. Collectively, these results indicate that electron pairing and superconductivity exist at the boundary of these channels and are 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., Comment: 13 pages, 5 figures

SrTiO$_3$-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$_3$/SrTiO$_3$ interface can support quantized ballistic transport of electrons and (non-superconducting) 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 $e^2/h$ plateau indicate a ballistic mean-free path $l_{MF}\sim$ 20 $\mu$m, more than two orders of magnitude larger than for 2D LaAlO$_3$/SrTiO$_3$ heterostructures. Non-superconducting electron pairs are found to be stable in magnetic fields as high as $B=11$ T, and propagate ballistically with conductance quantized at 2$e^2/h$. 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$_3$/SrTiO$_3$ system and offers a new platform for the study of strongly interacting 1D electronic systems., Comment: 35 pages, 10 figures

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 have revealed the existence of a strongly correlated phase in which electrons form spin-singlet pairs without becoming superconducting. Here we report evidence for micrometer-scale ballistic transport of electron pairs in quasi-one-dimensional (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 zero magnetic field). Above a critical magnetic field $B_p$, electron pairs unbind and conductance oscillations shift with magnetic field. These experimental observations extend the regime of ballistic electronic transport to strongly correlated phases., Comment: 5 pages, 3 figures; Also includes Supplemental Information

We demonstrate a current tunable Rashba spin orbit interaction in LaAlO3/SrTiO3 (LAO/STO) quasi two dimensional electron gas (2DEG) system. Anisotropic magnetoresistance (AMR) measurements are employed to detect and understand the current-induced Rashba field. The effective Rashba field scales with the current and a value of 2.35 T is observed for a dc-current of 200 uA. The results suggest that LAO/STO heterostructures can be considered for spin orbit torque based magnetization switching.