  The interface between the two complex oxides LaAlO3 and SrTiO3 has remarkable
properties that can be locally reconfigured between conducting and insulating
states using a conductive atomic force microscope. Prior investigations of
sketched quantum dot devices revealed a phase in which electrons form pairs,
implying a strongly attractive electron-electron interaction. Here, we show
that these devices with strong electron-electron interactions can exhibit a
gate-tunable transition from a pair-tunneling regime to a single-electron
(Andreev bound state) tunneling regime where the interactions become repulsive.
The electron-electron interaction sign change is associated with a Lifshitz
transition where the dxz and dyz bands start to become occupied. This
electronically tunable electron-electron interaction, combined with the
nanoscale reconfigurability of this system, provides an interesting starting
point towards solid-state quantum simulation.
