Characteristic length scales of the electrically induced insulator-to-metal transition

Some correlated materials display an insulator-to-metal transition as the temperature is increased. In most cases, this can also be induced electrically, resulting in volatile resistive switching due to formation of a conducting filament. While phenomenon has attracted much attention potential applications, many fundamental questions remain unaddressed. One them its characteristic lengths: What sets size these filaments, and how does impact properties? Here, we use combination wide-field scattering-type scanning near-field optical microscopies characterize filament ${\mathrm{NdNiO}}_{3}$ ${\mathrm{SmNiO}}_{3}$ thin films. We find clear trend: Smaller filaments increase current density, yielding sharper larger drop. With aid numerical simulations, discuss parameters controlling width and, hence, properties.