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Strontium titanate (STO), apart from being a ubiquitous substrate for complex-oxide heterostructures, possesses a multitude of strongly-coupled electronic and mechanical properties. Surface acoustic wave (SAW) generation and detection offers insight into electromechanical couplings that are sensitive to quantum paraelectricity and other structural phase transitions. Propagating SAWs can interact with STO-based electronic nanostructures, in particular LaAlO$_3$/SrTiO$_3$ (LAO/STO). Here we report generation and detection of SAW within LAO/STO heterointerfaces at cryogenic temperatures ($T\ge$~2 K) using superconducting interdigitated transducers (IDTs). The temperature dependence shows an increase in the SAWs quality factor that saturates at $T\approx 8 $ K. The effect of backgate tuning on the SAW resonance frequency shows the possible acoustic coupling with the ferroelastic domain wall evolution. This method of generating SAWs provides a pathway towards dynamic tuning of ferroelastic domain structures, which are expected to influence electronic properties of complex-oxide nanostructures. Devices which incorporate SAWs may in turn help to elucidate the role of ferroelastic domain structures in mediating electronic behavior.

Strongly correlated electronic systems exhibit a wealth of unconventional behavior stemming from strong electron-electron interactions. The LaAlO$_3$/SrTiO$_3$ (LAO/STO) heterostructure supports rich and varied low-temperature transport characteristics including low-density superconductivity, and electron pairing without superconductivity for which the microscopic origins is still not understood. LAO/STO also exhibits inexplicable signatures of electronic nematicity via nonlinear and anomalous Hall effects. Nanoscale control over the conductivity of the LAO/STO interface enables mesoscopic experiments that can probe these effects and address their microscopic origins. Here we report a direct correlation between electron pairing without superconductivity, anomalous Hall effect and electronic nematicity in quasi-1D ballistic nanoscale LAO/STO Hall crosses. The characteristic magnetic field at which the Hall coefficient changes directly coincides with the depairing of non-superconducting pairs showing a strong correlation between the two distinct phenomena. Angle-dependent Hall measurements further reveal an onset of electronic nematicity that again coincides with the electron pairing transition, unveiling a rotational symmetry breaking due to the transition from paired to unpaired phases at the interface. The results presented here highlights the influence of preformed electron pairs on the transport properties of LAO/STO and provide evidence of the elusive pairing ''glue'' that gives rise to electron pairing in SrTiO$_3$-based systems., Comment: 10 Pages, 5 Figures, 1 Table

The quest to understand, design, and synthesize new forms of quantum matter guides much of contemporary research in condensed matter physics. One-dimensional (1D) electronic systems form the basis for some of the most interesting and exotic phases of quantum matter. The variety of experimentally-accessible ballistic 1D electronic systems is highly restricted, and furthermore these systems typically have few tuning parameters other than electric and magnetic fields. However, electron waveguides formed from two-dimensional (2D) LaAlO$_3$/SrTiO$_3$ heterointerfaces exhibit remarkable 1D properties, including ballistic multi-mode transport and strong attractive electron-electron interaction, but these systems conspicuously lack strong or tunable spin-orbit interactions. Here we describe a new class of quasi-1D nanostructures, based on LaAlO$_3$/SrTiO$_3$ electron waveguides, in which a sinusoidal transverse spatial modulation is imposed. Nanowires created with this "serpentine" modulation display unique dispersive features in the subband spectra, namely (1) a significant shift ($\sim$ 7 tesla) in the spin-dependent subband minima, and (2) fractional conductance plateaus, some of which are continuously tunable with a magnetic field. The first property can be understood as an engineered spin-orbit interaction associated with the periodic acceleration of electrons as they undulate through the nanowire (ballistically), while the second property signifies the presence of enhanced electron-electron scattering in this system due to the imposed periodic structure. The ability to engineer these interactions in quantum wires contributes to the tool set of a 1D solid-state quantum simulation platform.

The paradigm of electrons interacting with a periodic lattice potential is central to solid-state physics. Semiconductor heterostructures and ultracold neutral atomic lattices capture many of the essential properties of 1D electronic systems. However, fully one-dimensional superlattices are highly challenging to fabricate in the solid state due to the inherently small length scales involved. Conductive atomic-force microscope (c-AFM) lithography has recently been demonstrated to create ballistic few-mode electron waveguides with highly quantized conductance and strongly attractive electron-electron interactions. Here we show that artificial Kronig-Penney-like superlattice potentials can be imposed on such waveguides, introducing a new superlattice spacing that can be made comparable to the mean separation between electrons. The imposed superlattice potential "fractures" the electronic subbands into a manifold of new subbands with magnetically-tunable fractional conductance (in units of $e^2/h$). The lowest $G=2e^2/h$ plateau, associated with ballistic transport of spin-singlet electron pairs, is stable against de-pairing up to the highest magnetic fields explored ($|B|=16$ T). A 1D model of the system suggests that an engineered spin-orbit interaction in the superlattice contributes to the enhanced pairing observed in the devices. These findings represent an important advance in the ability to design new families of quantum materials with emergent properties, and mark a milestone in the development of a solid-state 1D quantum simulation platform.

We report frictional drag measurements between two superconducting LaAlO$_3$/SrTiO$_3$ nanowires. In these experiments, current passing through one nanowire induces a voltage across a nearby electrically isolated nanowire. The frictional drag signal contains both symmetric and antisymmetric components. The antisymmetric component arises from the rectification of quantum shot noise in the drive nanowire by the broken symmetry in the drag nanowire. The symmetric component in the drag resistance is ascribed to rectification of thermal noise in the drive nanowire during superconducting-normal transition. The suppression of the symmetric component is observed when a normal nanowire is used as either a drag or drive nanowire with the other nanowire superconducting. The absence of symmetric drag resistance between a normal drag nanowire and a superconducting drive nanowire suggests a higher electron-hole asymmetry in the superconducting LaAlO$_3$/SrTiO$_3$ nanowire arising from the 1D nature of superconductivity at LaAlO$_3$/SrTiO$_3$ interface., Comment: 12 pages, 5 figures

Pristine, undoped graphene has a constant absorption of 2.3 % across the visible to near-infrared (VIS-NIR) region of the electromagnetic spectrum. Under certain conditions, such as nanostructuring and intense gating, graphene can interact more robustly with VIS-NIR light and exhibit a large nonlinear optical response. Here, we explore the optical properties of graphene/LaAlO$_3$/SrTiO$_3$ nanostructures, where nanojunctions formed at the LaAlO$_3$/SrTiO$_3$ interface enable large (~10$^8$ V/m) electric fields to be applied to graphene over a scale of ~10 nm. Upon illumination with ultrafast VIS-NIR light, graphene/LaAlO$_3$/SrTiO$_3$ nanostructures produce broadband THz emission as well as a sum-frequency generated (SFG) response. Strong spectrally sharp, gate-tunable extinction features (>99.99%) are observed in both the VIS-NIR and SFG regions alongside significant intensification of the nonlinear response. The observed gate-tunable strong graphene-light interaction and nonlinear optical response are of fundamental interest and open the way for future exploitation in graphene-based optical devices., Comment: 20 pages, 7 figures, supplementary information included

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 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 LaAlO$_3$/SrTiO$_3$ interface. The waveguide conductance follows a characteristic sequence within Pascal's triangle: $(1, 3, 6, 10, 15, ...)\cdot e^2/h$, where $e$ 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.

The properties of graphene depend sensitively on doping with respect to the charge-neutrality point (CNP). Tuning the CNP usually requires electrical gating or chemical doping. Here, we describe a technique to reversibly control the CNP in graphene with nanoscale precision, utilizing LaAlO$_3$/SrTiO$_3$ (LAO/STO) heterostructures and conductive atomic force microscope (c-AFM) lithography. The local electron density and resulting conductivity of the LAO/STO interface can be patterned with a conductive AFM tip, and placed within two nanometers of an active graphene device. The proximal LAO/STO nanostructures shift the position of graphene CNP by ~ $10^{12}$ cm$^{-2}$, and are also gateable. Here we use this effect to create reconfigurable edge states in graphene, which are probed using the quantum Hall effect. Quantized resistance plateaus at $h/e^2$ and $h/3e^2$ are observed in a split Hall device, demonstrating edge transport along the c-AFM written edge that depends on the polarity of both the magnetic field and direction of currents. This technique can be readily extended to other device geometries., Comment: 12 pages

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

Nanoscale control of the quasi-two-dimensional electron gas at the LaAlO3/SrTiO3 (LAO/STO) interface by a conductive probe tip has triggered the development of a number of electronic devices. While the spatial distribution of the conductance is crucial for such devices, it is challenging to directly visualize the local electrical properties at the buried interface. Here we demonstrate conductivity imaging of sketched nanostructures at the LAO/STO interface by microwave impedance microscopy (MIM) with a lateral resolution on the order of 100 nm. The sheet conductance extracted from the MIM data agrees with the transport measurement. The tip-induced insulator-to-metal transition is observed above a threshold voltage of +4 V. Our work paves the way to study emergent phenomena at oxide interfaces by probing nanoscale conductance distribution., Comment: 12 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

The LaAlO$_3$/SrTiO$_3$ 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 we report evidence for long-range electron-electron interactions in LaAlO$_3$/SrTiO$_3$ nanowires, measured through the phenomenon of frictional drag, 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 LaAlO$_3$/SrTiO$_3$ nanowire system it is found to be nearly independent of separation. Frictional drag experiments performed with three parallel wires demonstrates long-range frictional coupling even in the presence of an electrically grounded central wire. Collectively, these results provides evidence for a new long-range non-Coulombic electron-electron interaction unlike anything previously reported for semiconducting systems., Comment: 10 pages, 4 figures

The integration of graphene with complex-oxide heterostructures such as LaAlO$_3$/SrTiO$_3$ offers the opportunity to combine the multifunctional properties of an oxide interface with the electronic properties of graphene. The ability to control interface conduction through graphene and understanding how it affects the intrinsic properties of an oxide interface are critical to the technological development of novel multifunctional devices. Here we demonstrate several device archetypes in which electron transport at an oxide interface is modulated using a patterned graphene top gate. Nanoscale devices are fabricated at the oxide interface by conductive atomic force microscope (c-AFM) lithography, and transport measurements are performed as a function of the graphene gate voltage. Experiments are performed with devices written adjacent to or directly underneath the graphene gate. Unique capabilities of this approach include the ability to create highly flexible device configurations, the ability to modulate carrier density at the oxide interface, and the ability to control electron transport up to the single-electron-tunneling regime, while maintaining intrinsic transport properties of the oxide interface. Our results facilitate the design of a variety of nanoscale devices that combine unique transport properties of these two intimately coupled two-dimensional electron systems., Comment: 27 pages, 10 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

The transfer of graphene grown by chemical vapor deposition (CVD) using amorphous polymers represents a widely implemented method for graphene-based electronic device fabrication. However, the most commonly used polymer, poly(methyl methacrylate) (PMMA), leaves a residue on the graphene that limits the mobility. Here we report a method for graphene transfer and patterning that employs a perfluoropolymer---Hyflon---as a transfer handle and to protect graphene against contamination from photoresists or other polymers. CVD-grown graphene transferred this way onto LaAlO$_3$/SrTiO$_3$ heterostructures is atomically clean, with high mobility (~30,000 cm$^2$V$^{-1}$s$^{-1}$) near the Dirac point at 2 K and clear, quantized Hall and magneto-resistance. Local control of the LaAlO$_3$/SrTiO$_3$ interfacial metal-insulator transition---through the graphene---is preserved with this transfer method. The use of perfluoropolymers such as Hyflon with CVD-grown graphene and other 2D materials can readily be implemented with other polymers or photoresists., Comment: 6 pages, 4 figures

The interface between the two complex oxides LaAlO3 and SrTiO3 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 single-electron (Andreev bound state) tunneling regime where the interactions become repulsive. The electron-electron interaction sign change is associated with a Lifshitz transition where the dxz and dyz 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., Comment: 25 pages, 7 figures

The pseudospin quantum degree of freedom is one of the most remarkable properties of graphene that distinguishes it from ordinary two-dimensional metals and semiconductors. Pseudospin quantum interference leads to weak antilocalization (WAL) and is influenced strongly by point defects and thermal perturbations that break chirality and destroy phase coherence. Preserving and manipulating quantum transport properties up to room temperature is key to realizing practical pseudospin-based graphene devices. Here we report fabrication and transport characterization of graphene field-effect devices on a complex-oxide heterostructure, LaAlO3/SrTiO3. Signatures of WAL, a consequence of pseudospin quantum interference, persist up to room temperature. The LaAlO3/SrTiO3 substrate plays a critical role in suppressing short-range impurity scattering and electron-phonon coupling. The observation of quantum transport signatures at room temperature is unique to this system and presents new opportunities for the development of pseudospin-based devices and novel multifunctional devices that couple to the complex-oxide interface., Comment: 38 pages, 5 figures (Suppl. Info. 17 pages, 10 figures, 1 table)

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