J. Phys. I France
Volume 2, Numéro 5, May 1992
Page(s) 725 - 740
DOI: 10.1051/jp1:1992176
J. Phys. I France 2 (1992) 725-740

Space-time distributions of solitons for the current conversion problem in charge density waves

S. Brazovskii and S. Matveenko

L.D. Landau Institute for theoretical Physics, Kosygina 2, Moscow, Russia

(Received 3 January 1992, accepted 17 January 1992)

Dissipative dynamics equations of Charge Density Waves (CDW) are derived for a homogeneous distribution of solitons and dislocations. Response functions for the CDW current and for the electric field are found for a spontaneous conversion process of electrons into solitons. A one- dimentional development of the injection current impulse is studied in details. The problem is investigated for a purely dissipative CDW regime and within a diffusion approximation for solitons. We find that first the nominal CDW current $j_\infty$, which is due to the CDW phase velocity $\beta_{\infty}=-\pi j_{\infty}$, and the electric field $E_{\infty} \propto j_{\infty}$ are established along the sample length in a very short time. Later on the diffusion front passes along with a constant velocity $b{\rm E}_{\infty}$, where b is a mobility of solitons. It is followed by the growth of the soliton concentration $\rho_{\rm s}$ and by the decrease of local coherent CDW current $j(x,t) \propto \beta(x,t)$. At largest time t they are related as $j(x,t) \propto \rho_{\rm s}^{-1} \propto t^{-1/3}$. The total electric current is nearly additive $J\approx j+2j_{\rm s}$ being almost constant. Also a stationary distribution is studied for generation of solitons at the presence of a constant CDW current. It is characterized by a step-like profile of the defects concentration.

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