Low frequency noise behavior in mesoscopic charge density wave conductors of o-TaS$_{3}$ and NbSe$_{3}$*

In quasi-one dimensional materials, charge density waves (CDW) often form as a result of an instability of the Fermi surface below a critical temperature (T$_{P}$). In the presence of disorder, CDW is pinned. As a result, fully gaped materials like o-TaS$_{3}$ exhibit an insulator-like behavior below T$_{P}$ and partially gaped materials like NbSe$_{3}$ show mixed signatures of both CDW and ungapped quasi-particles. A sufficient dc electric field can depin and slide the CDW. CDW phase fluctuation and phase slippage in the pinned state can be detected as resistance noise in an appropriate frequency window. Herein, results from electrical transport and low frequency noise measurements on single crystalline o-TaS$_{3}$ nanoribbons will be presented and compared with results on single-crystalline NbSe$_{3}$ nanoribbons. Interesting features in the differential conductance measurements across the electric field-driven depinning transitions in the nanoscale samples are observed. The noise magnitude, in the CDW pinned state, shows a non-monotonic dependence on driving electric field in NbSe$_3$ whereas in o-TaS$_{3}$ a monotonic dependence is observed. Results will be discussed in light of the differences in these materials and any possible finite size effects.