Charge-density-wave pinning and finite-size effects inNbSe3

We present a detailed experimental study of the effects of finite crystal size, impurities, and temperature on the properties of charge-density waves (CDW’s) in ${\mathrm{NbSe}}_3$. Finite-size effects in ${\mathrm{NbSe}}_3$ are controlled by the crystal thickness t. They are large in crystals of ordinary thickness, and remain signficant in high-purity crystals having thicknesses approaching 0.1 mm. In sufficiently thick Ta- and Ti-doped crystals, the threshold electric field ${\mathit{E}}_{\mathit{T}}$ for CDW depinning is independent of thickness and varies with the residual resistance ratio ${\mathit{r}}_{\mathit{R}}$ as ${\mathit{E}}_{\mathit{T}}$∝${\mathit{r}}_{\mathit{R}}^{\mathrm{-}1.9}$ and ${\mathit{r}}_{\mathit{R}}^{\mathrm{-}1.4}$, respectively. In thin crystals, ${\mathit{E}}_{\mathit{T}}$ increases with decreasing thickness as ${\mathit{E}}_{\mathit{T}}$=K/t, where K is roughly proportional to the impurity concentration. ${\mathit{E}}_{\mathit{T}}$ is strongly temperature dependent. The fractional increase in ${\mathit{E}}_{\mathit{T}}$ as T→0 is independent of thickness but decreases rapidly with increasing impurity concentration. The divergence of ${\mathit{E}}_{\mathit{T}}$ near ${\mathit{T}}_{\mathit{P}2}$=59 K is described by ${\mathit{E}}_{\mathit{T}}$∝(1-${\mathit{R}}_{\mathit{H}}$/${\mathit{R}}_{\mathit{L}}$ ${)}^{\mathrm{-}0.95}$, where ${\mathit{R}}_{\mathit{H}}$ and ${\mathit{R}}_{\mathit{L}}$ are the high-field and low-field resistances, respectively. In extremely thin crystals (t<0.1 μm) near ${\mathit{T}}_{\mathit{P}2}$, the sharp threshold vanishes and nonlinear conduction occurs at arbitrarily small fields.