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Electric current has been experimentally demonstrated to be able to drive theinsulator-to-metal transition (IMT) in VO$_2$. The main mechanisms involved arebelieved to be the Joule heating effect and the strong electron-correlationeffect. These effects are often entangled with each other in experiments, whichcomplicates the understanding of the essential nature of the observations. Weformulate a phase-field model to investigate theoretically in mesoscale thepure correlation effect brought by the current on the IMT in VO$_2$, i.e., theisothermal process under the current. We find that a current with a largedensity ($\sim 10^1$ nA/nm$^2$) induces a few-nanosecond ultrafast switch inVO$_2$, in agreement with the experiment. The temperature-current phase diagramis further calculated, which reveals that the current may induce the M2 phaseat low temperatures. The current is also shown capable of driving domain wallsto move. Our work may assist related experiments and provide guidance to theengineering of VO$_2$-based electric switching devices.

Isothermal current-driven insulator-to-metal transition in VO$_\text{2}$ through strong correlation effect