Low frequency resistance fluctuations in nanoribbons of charge density wave (CDW) conductor NbSe$_{3}$

We investigate finite size effects in the low-frequency (1 mHz $<$ f $<$ 10 Hz) resistance fluctuations of individual nanoribbons of single-crystalline NbSe$_{3}$ (cross sections of 10$^{4}$ nm$^{2})$ across the two CDW transitions ($\sim $ 59 K and $\sim $ 141 K). This ultra sensitive frequency-dependent study of the electrical noise is crucial in improving our understanding of the mechanisms that generate noise around CDW transitions. The power spectral density, S$_{R}$, of the resistance noise has a generic form, S$_{R} \quad \sim $ 1/f$^{\alpha }$, typical of a diffusive metallic conductor. Below the CDW transition at 59 K, where the CDW is pinned by disorder, S$_{R}$ (at 1 Hz) shows a non-monotonic behavior with a maximum magnitude around 45 K. A similar peak in S$_{R}$ is also observed at 125 K, below the second CDW transition. Also, it is well known that the CDW state can be depinned by an application of a high bias voltage or current and S$_{R}$ is measured as a function of current across the pinning-depinning of CDW. S$_{R}$ shows a complex, non-monotonic dependence and is extremely sensitive to temperature below the CDW transition. In contrast, S$_{R}$ is bias independent above the CDW transitions as expected from a metal. The implications of these noise behaviors in understanding the pinning and depinning of CDW in NbSe$_{3}$ will be discussed.