One-dimensional Kronig–Penney superlattices at the LaAlO3/SrTiO3 interface

Abstract

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

Spin-orbit-assisted electron pairing in one-dimensional waveguides

“…the LAO/STO interface, elaborating on the theory discussed in [23]. Our work suggests that heterostructures constitute an attractive platform for controlling collective spin states of electron pairs.…”

“…As mentioned in the introduction, recent transport experiments in a 1D modulated waveguide have shown signatures of SOC, both directly [22] and potentially through observation of spin-orbit enhanced electron pairing [23], which we present a description of in Sec. IV.…”

“…When they travel through the waveguide with a velocity v = v x e x where e i is a unit vector along i = x, y, z, they feel an electric field produced by the modulation. For a vertical modulation as in [23], it would have the form E eff ∝ E eff (x)e z . This would lead to an effective magnetic field B so ∝ v × E eff along y and then produce an energy shift of the form ∝ σ • B so .…”

“…In this specific scenario, we make the approximation that α v and α l describe the root-mean-square values of the varying parameters. Note finally that compared to the single-particle model presented in [23], our model is slightly more refined (as the vertically induced SOC reads ∝ α v σ y (p x − eBy) instead of ∝ α v σ y p x ) and is more general as it includes also laterally induced SOC. Since the Hamiltonian ( 9) is translationally invariant along x, we can make the replacement p x → hk x ≡ hk.…”

“…Driven by the long-term prospect of developing analog quantum simulators in the solid state, more recent experiments in LAO/STO interfaces have shown that by spatially modulating the AFM tip during the writing process, it is possible to create laterally undulating wires [22] and 1D Kronig-Penney-like superlattice structures [23]. Compared to straight waveguides [11], these devices exhibit stable fractional conductance plateaux and enhanced pairing of electrons.…”