Resistance noise spectroscopy across the thermally and electrically driven metal-insulator transitions in VO$_2$ nanobeams*

Vanadium dioxide (VO$_2$) is a strongly correlated material that exhibits a sharp thermally driven metal-insulator transition at $T_c\sim$ 340 K. The transition can also be triggered by a DC voltage in the insulating phase with a threshold ($V_{th}$) behavior. The mechanisms behind these transitions are hotly discussed and resistance noise spectroscopy is a suitable tool to delineate different transport mechanisms in correlated systems. We present results from a systematic study of the low frequency (1 mHz $<$ f $<$ 10 Hz) noise behavior in VO$_2$ nanobeams across the thermally and electrically driven transitions. In the thermal transition, the power spectral density (PSD) of the resistance noise is unchanged as we approach $T_c$ from 300 K and an abrupt drop in the magnitude is seen above $T_c$ and it remains unchanged till 400 K. However, the noise behavior in the electrically driven case is distinctly different: as the voltage is ramped from zero, the PSD gradually increases by an order of magnitude before reaching $V_{th}$ and an abrupt increase is seen at $V_{th}$. The noise magnitude decreases above $V_{th}$, approaching the $V=0$ value. The individual roles of percolation, Joule heating and signatures of correlated behavior will be discussed.