Sketched ferroelectric single-electron transistor*

Oxide heterostructures formed from ultrathin layers of LaAlO$_{3}$ grown on TiO$_{2}$-terminated SrTiO$_{3}$, combined with a reversible nanoscale patterning technique, provide a versatile platform for nanoscale control at the single-electron limit. Here we demonstrate the creation and characterization of ``sketched'' single-electron transistors made from ultrasmall (1-2 nm) quantum dots. Shell filling from N=0 up to N=2 electrons by single-electron tunneling is observed. Resonant tunneling can be controlled in a deterministic and non-volatile fashion by altering the ferroelectric polarization within the SrTiO$_{3}$ tunnel barrier. These single-electron devices may find use as nanoscale hybrid piezoelectric/charge sensors, and as elemental building blocks for solid-state quantum computation and quantum simulation platforms.