One-dimensional Kronig-Penney superlattices at the LaAlO$_3$/SrTiO$_3$ interface

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.