Dimensionality effects in AFM-written conducting structures

Combining the properties of oxides with low dimensionality leads to the emergence of complex phenomena. The two-dimensional electron system confined at the interface between $LaAlO_{3}$ and $SrTiO_{3}$ is a perfect playground to explore these effects. On top of the electrons out-of-plane confinement at the interface, introducing an in-plane confinement is also possible. Among the different options, the AFM-writing method is very promising. By applying a bias to the tip of an atomic force microscope and by scanning the surface of $LaAlO_{3}$, electrons can be transferred at the interface in nanoscale regions. We showed that the conducting wires defined using this technique can have a width of $\sim$10 nm and that their physical properties are very sensitive to the tip bias and the air humidity of the writing environment. We present here a systematic study of the transport properties of a series of AFM-written electronic devices with lateral dimension progressively reduced. Above the superconducting phase the system is not, strictly speaking, in a 1D regime but dimensionality effects should be observable. Once in the superconducting phase, we expect a stronger effect as the coherence length is comparable or larger than the lateral size of the written nanostructures.