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.

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.

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. Here, we describe a family of quasi-1D nanostructures, based on LaAlO3/SrTiO3 electron waveguides, in which a sinusoidal transverse spatial modulation is imposed. These devices display unique dispersive features in the subband spectra, namely, a sizeable shift (∼7 T) in the spin-dependent subband minima, and fractional conductance plateaus. 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. The ability to engineer these interactions in quantum wires contributes to the tool set of a 1D solid-state quantum simulation platform.

Quantum materials (QMs) with strong correlation and nontrivial topology are indispensable to next-generation information and computing technologies. Exploitation of topological band structure is an ideal starting point to realize correlated topological QMs. Here, we report that strain-induced symmetry modification in correlated oxide SrNbO 3 thin films creates an emerging topological band structure. Dirac electrons in strained SrNbO 3 films reveal ultrahigh mobility ( max ≈ 100,000 cm 2 /Vs), exceptionally small effective mass (m* ~ 0.04m e ), and nonzero Berry phase. Strained SrNbO 3 films reach the extreme quantum limit, exhibiting a sign of fractional occupation of Landau levels and giant mass enhancement. Our results suggest that symmetry-modified SrNbO 3 is a rare example of correlated oxide Dirac semimetals, in which strong correlation of Dirac electrons leads to the realization of a novel correlated topological QM.

Semiconductor heterostructures [1] and ultracold neutral atomic lattices [2] capture many of the essential properties of onedimensional (1D) electronic systems. However, fully 1D 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 applied to an oxide interface can create ballistic few-mode electron waveguides with highly quantized conductance and strongly attractive electron-electron interactions [3]. 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. The lowest plateau, associated with ballistic transport of spin-singlet electron pairs [3], shows enhanced electron pairing, in some cases up to the highest magnetic fields explored. 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 are an advance in the ability to design new families of quantum materials with emergent properties and the development of solid-state 1D quantum simulation platforms.Quantum theory provides a unified framework for understanding the fundamental properties of matter.However, there are many quantum systems whose behavior is not well understood because the relevant equations are are not able to be solved using known approaches. The idea of "quantum simulation", first articulated by Feynman [4], aims to exploit the quantum-mechanical properties of materials to compute the properties of interest and gain insight into the quantum nature of matter. There are two main "flavors" of quantum simulation: one based upon the known efficiency of circuit-based quantum computers to solve the Schrödinger equation, and the other based on microscopic control over quantum systems to emulate a given Hamiltonian. The former approach is limited by the capabilities of present-day quantum computers. The latter approach has shown great promise using a variety of methods including ultracold atoms [2, 5, 6], spin systems from ion trap arrays [7]. superconducting Josephson junction arrays [8], photonic systems [9], and various solid-state approaches [1,10,11,12]. Platforms capable of quantum simulation of Hubbard models would be of enormous value in condensed matter physics and beyond.Complex oxides offer new opportunities to create a platform for quantum simulation in a solid-state

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A nanoscale cross, written at the LaAlO3/SrTiO3 interface using conductive AFM lithography, reveals an inhomogeneous electronic band structure.

Understanding and controlling the transport properties of interacting fermions is a key forefront in quantum physics across a variety of experimental platforms. Motivated by recent experiments in one-dimensional (1D) electron channels written on the LaAlO 3 /SrTiO 3 interface, we analyze how the presence of different forms of spin-orbit coupling (SOC) can enhance electron pairing in 1D waveguides. We first show how the intrinsic Rashba SOC felt by electrons at interfaces such as LaAlO 3 /SrTiO 3 can be reduced when they are confined in one dimension. Then, we discuss how SOC can be engineered, and show using a mean-field Hartree-Fock-Bogoliubov model that SOC can generate and enhance spin-singlet and -triplet electron pairing. Our results are consistent with two recent sets of experiments [Briggeman et al., Nat. Phys. 17, 782787 (2021); Sci. Adv. 6, eaba6337 (2020)] that are believed to engineer the forms of SOC investigated in this work, which suggests that metal-oxide heterostructures constitute attractive platforms to control the collective spin of electron bound states. However, our findings could also be applied to other experimental platforms involving spinful fermions with attractive interactions, such as cold atoms.