In this work, authors used conductive atomic force microscope (c-AFM) lithography in which the conduction is controlled by surface protons that are distributed on the LAO surface. They have created two conducting channel with varying witdhs as 10 and 200nm on a LAO/STO heterostructures grown by pulsed-laser deposition. They designed the the devices in a way that two conducting channels connected in series with two leads and voltage probes. By using silver epoxy on the bottom of the STO substrate they created contacts for a back gate voltage. They investigated changes in the magnetotransport properties on the channels with different widths by varying back gate voltage and applied magnetic field. They measured the conductance for both narrow and wide channels and demonstarted the hysteresis of both channels with back gating. Saturation of the conductance at higher gate voltages was also shown. They were able to demonstrate dimensional crossover from 2d to 1D behavior with their magnetoconductance measurements.