Quantum transport of nanoscale Hall crosses*

Quantized Hall resistance in 2D electron systems arises due to edge modes. However, quantum transport in the extreme 1D limit is not as well understood, because quasi-1D semiconductor devices are highly susceptible to localization from disorder. Highly ballistic electron waveguides can now be routinely created at the LaAlO3/SrTiO3 (LAO/STO) interface using conductive atomic force microscopy lithography. These channels exhibit quantized ballistic conduction which is associated with lateral and vertical confinement within the waveguide. In this work, we investigate the transport characteristics of nanoscale Hall crosses. By creating transverse voltage probing leads inside the gated region of the waveguide, we can explore the interplay between confinement potential and magnetic field, and potentially investigate the transition between 1D waveguide modes and 2D edge states.