Dimensionality dependence of mode-locking dynamics in charge-density-wave transport.

Abstract

We estimate the widths of the harmonic mode-locked steps observed on the dc I-V characteristic of charge-density-wave (CDW) conductors when ac and dc voltages are applied together using the classical deformable medium model. For weakly pinned CDW's in the high-velocity limit, \ensuremath{\delta}${\mathit{E}}_{\mathit{p}/1}$/${\mathit{E}}_{\mathit{T}}$ =2\ensuremath{\Vert}${\mathit{J}}_{\mathit{p}}$(${\mathrm{\ensuremath{\omega}}}_{\mathit{c}0}$${\mathit{E}}_{\mathit{a}\mathit{c}}$/${\mathrm{\ensuremath{\omega}}}_{\mathit{a}\mathit{c}}$${\mathit{E}}_{\mathit{T}}$)${\mathrm{\ensuremath{\Vert}}}^{4/(4\mathrm{\ensuremath{-}}\mathit{D})}$ where \ensuremath{\delta}${\mathit{E}}_{\mathit{p}/1}$ is the width in electric field of the p/1 step and D is the effective dimension of the pinning. An analytic argument suggests that the phase deformations are much larger in the mode-locked state than in the normal sliding state. They are largest for ac amplitudes that yield maxima in the step width. On the p/1 step the time-averaged phase-phase correlation length is predicted to vary as \ensuremath{\delta}${\mathit{E}}_{\mathit{p}/1}^{\mathrm{\ensuremath{-}}1/2}$. These analytic estimates are supported by numerical simulations. Measurements of the step width variation with ac amplitude and frequency for ${\mathrm{NbSe}}_{3}$ crystals whose static pinning is two dimensional (2D) are consistent with the 2D step width prediction.