Proliferation of metallic domains caused by inhomogeneous heating near the electrically-driven transition in VO${}_2$ nanobeams

We discuss the mechanisms behind the electrically driven insulator-metal transition in single crystalline VO${}_2$ nanobeams. Our DC and AC transport measurements and the versatile harmonic analysis method employed show that non-uniform Joule heating causes phase inhomogeneities to develop within the nanobeam and is responsible for driving the transition in VO${}_2$. A Poole-Frenkel like purely electric field induced transition is found to be absent and the role of percolation near and away from the electrically driven transition in VO${}_2$ is also identified. The results and the harmonic analysis can be generalized to many strongly correlated materials that exhibit electrically driven transitions.