Imaging filamentary current flow near the metal-insulator transition in an oxide interface*

In systems near phase transitions, macroscopic properties often follow algebraic scaling laws, determined by the dimensionality and symmetries of the system. The emergence of such universal scaling implies that microscopic details are irrelevant. In my talk, I will discuss the scaling properties of the metal-insulator transition at the LaAlO₃/SrTiO₃ interface. Using scanning SQUID, we map the current flow at the interface close to the gate tunable transition. I will show that coupling between structural and electronic degrees of freedom modifies the filamentary, preventing a fractal with the expected universal dimension from forming. Our results open the door for engineering electronic transitions at the nanoscale.