Steady-state charge transport via motion of charge-density waves (CDW’s) requires conversion between collective CDW conduction and quasiparticle conduction in the vicinity of current injection contacts. The conversion occurs via phase slip, in which CDW amplitude defects form and move in the presence of CDW strain so as to remove or add CDW phase fronts in a process analogous to phase slip in superconductors and superfluids. We have determined the spatial distribution of phase slip for the $T_{P_1}$ CDW in ${\mathrm{NbSe}}_3$ by measuring the spatial variation of the CDW current density $j_c\mathrm{}\left(x\right)\mathrm{}$. As the current contacts are approached, $j_c\mathrm{}\left(x\right)\mathrm{}$ decreases and the normal current $j_n\mathrm{}\left(x\right)\mathrm{}$ due to quasiparticle flow increases. The size of the region near each contact where appreciable phase slip occurs is less than $40\hspace{0.5em}\mu$m for $T$ near 120 K but grows to hundreds of micrometers at lower temperatures. The current and phase-slip profiles are asymmetric with respect to driving current direction, implying an asymmetry between phase front addition and removal. Analysis of these profiles yields the local relation between the phase-slip rate $r_{\mathrm{ps}}\mathrm{}\left(x\right)\mathrm{}$ and CDW strain $\epsilon \mathrm{}\left(x\right)\mathrm{}$. This relation is not unique, and for a given strain the phase-slip rate increases with increasing distance from the current electrode. These results are inconsistent with the predictions of models for phase slip via homogeneous defect nucleation, and provide evidence for amplitude defect motion. The presence of substantial amounts of phase slip at large distances from the current contacts explains the loss of coherence of the sliding CDW observed at lower temperatures, and suggests that predictions of phase-only models of CDW dynamics may be of very limited use in describing the sliding CDW in ${\mathrm{NbSe}}_3$.

• Received 24 November 1997

DOI:https://doi.org/10.1103/PhysRevB.57.12781