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The quest to understand, design, and synthesize new forms of quantum matterguides much of contemporary research in condensed matter physics.One-dimensional (1D) electronic systems form the basis for some of the mostinteresting and exotic phases of quantum matter. The variety ofexperimentally-accessible ballistic 1D electronic systems is highly restricted,and furthermore these systems typically have few tuning parameters other thanelectric and magnetic fields. However, electron waveguides formed fromtwo-dimensional (2D) LaAlO$_3$/SrTiO$_3$ heterointerfaces exhibit remarkable 1Dproperties, including ballistic multi-mode transport and strong attractiveelectron-electron interaction, but these systems conspicuously lack strong ortunable spin-orbit interactions. Here we describe a new class of quasi-1Dnanostructures, based on LaAlO$_3$/SrTiO$_3$ electron waveguides, in which asinusoidal transverse spatial modulation is imposed. Nanowires created withthis "serpentine" modulation display unique dispersive features in the subbandspectra, namely (1) a significant shift ($\sim$ 7 tesla) in the spin-dependentsubband minima, and (2) fractional conductance plateaus, some of which arecontinuously tunable with a magnetic field. The first property can beunderstood as an engineered spin-orbit interaction associated with the periodicacceleration of electrons as they undulate through the nanowire(ballistically), while the second property signifies the presence of enhancedelectron-electron scattering in this system due to the imposed periodicstructure. The ability to engineer these interactions in quantum wirescontributes to the tool set of a 1D solid-state quantum simulation platform.

Engineered spin-orbit interactions in LaAlO$_3$/SrTiO$_3$-based 1D serpentine electron waveguides