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.
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.