Electrostatically tuned dimensional crossover in LaAlO₃/SrTiO₃ heterostructures

We report a gate-tunable dimensional crossover in sub-micrometer-scale channels created at the LaAlO₃/SrTiO₃ interface. Conducting channels of widths 10 nm and 200 nm are created using conducting atomic force microscope lithography. Under sufficient negative back-gate tuning, the orbital magnetoconductance of the 200 nm channel is strongly quenched, and residual signatures of low-field weak-antilocalization become strikingly similar to that of the 10 nm channel. The dimensional crossover for the 200 nm channel takes place near the conductance quantum G = 2e²/h. The ability to tune the dimensionality of narrow LaAlO₃/SrTiO₃ channels has implications for interpreting transport in a variety of gate-tunable oxide-heterostructure devices.