Avalanches in vanadium sesquioxide nanodevices

The resistance versus temperature across the metal-insulator transition (MIT) of ${\mathrm{V}}_2{\mathrm{O}}_3$ nanodevices exhibits multiple discontinuous jumps. The jump sizes range over three orders of magnitude in resistance and their distribution follows a power law, implying that the MIT of ${\mathrm{V}}_2{\mathrm{O}}_3$ occurs through avalanches. While the maximum jump size depends on the device size, the power law exponent for ${\mathrm{V}}_2{\mathrm{O}}_3$ is independent of device geometry and different than the one found earlier in $\mathrm{V}{\mathrm{O}}_2$. A two-dimensional random percolation model exhibits a power law distribution different from the one found in ${\mathrm{V}}_2{\mathrm{O}}_3$. Instead, the model gives a similar exponent found in another vanadium oxide, $\mathrm{V}{\mathrm{O}}_2$. Our results suggest that the MITs of $\mathrm{V}{\mathrm{O}}_2$ and ${\mathrm{V}}_2{\mathrm{O}}_3$ are produced by different mechanisms.

Figure 1

The heating branches of five consecutive R-T measurements of a $1\times 2\mu {\mathrm{m}}^2{\mathrm{V}}_2{\mathrm{O}}_3$ device, as indicated by different colors. The main panel shows the temperature between 145 and 157.5 K. This range contains the largest jumps. (a) Scanning electron microscopy (SEM) image indicating the device length $(L=1\mu \mathrm{m})$ and width $(W=2\mu \mathrm{m})$. (b) The full hysteresis loop of the device. The red (blue) arrow indicates the heating (cooling) branches.

Figure 2

Average value of the maximum jumps vs device length. The red solid (blue open) circles are the average maximum jumps from the heating (cooling) branches of the R-T measurements for each device. The error bars correspond to the standard deviations of the maximum jumps. The black solid line is the linear fit of all the data points.

Figure 3

The black solid circles show the histogram of different jump sizes plotted on a log-log scale from the heating branches of the R-T measurements for a $1\times 2\mu {\mathrm{m}}^2$ device. The red solid line is a fit using the maximum likelihood method (MLM), showing a power law dependence. The exponent is $\alpha =2.22\pm 0.03$.

Figure 4

(a) R-T of a $1\times 2\mu {\mathrm{m}}^2$ device: simulation (thick blue solid line) and ${\mathrm{V}}_2{\mathrm{O}}_3$ (thin black solid line). (b) Comparison of the power law exponent of ${\mathrm{V}}_2{\mathrm{O}}_3$ (red circles), $\mathrm{V}{\mathrm{O}}_2$ (blue triangles), and the simulation (black squares). The solid (open) symbols are the exponents from the heating (cooling) branches of the R-T measurements. The error bars are the standard deviations given by $\sigma =\frac{\alpha }{\sqrt{N}}$ [26]. The dashed lines indicate the average exponent of different devices for ${\mathrm{V}}_2{\mathrm{O}}_3$ (red dashed line), $\mathrm{V}{\mathrm{O}}_2$ (blue dashed dotted line), and the simulation (black dashed dotted dotted line).