Charge-density-wave glass state in quasi-one-dimensional conductors

Abstract

We have measured the real part \ensuremath{\epsilon}' and the imaginary part \ensuremath{\epsilon}'' of the dielectric susceptibility of the quasi-one-dimensional conductor ${\mathrm{TaS}}_{3}$ in its charge-density-wave (CDW) state in the wide frequency range f (${10}^{\mathrm{\ensuremath{-}}2}$--${10}^{7}$ Hz) in the low-temperature range (4.2--52 K). The frequency dependence of \ensuremath{\epsilon}'(\ensuremath{\omega},T) as well as \ensuremath{\epsilon}''(\ensuremath{\omega},T) show the lnf scaling and a crossover between a behavior corresponding to a Gaussian distribution of logarithms of relaxation time \ensuremath{\tau} at T\ensuremath{\ge}30 K and a frozen-in state with very wide \ensuremath{\tau} distribution at T\ensuremath{\le}24 K. The temperature dependences of \ensuremath{\epsilon}' measured at low frequencies (f\ensuremath{\le}${10}^{5}$ Hz) show maxima whose positions shift to low temperatures and whose amplitudes grow with decreasing frequency. The temperature dependences of \ensuremath{\tau} are characterized by two branches. With decreasing temperature the long-time branch of \ensuremath{\tau} diverges (\ensuremath{\alpha} relaxation) while the shorter-time branch shows a monotonous behavior, corresponding probably to the tunneling mechanism of CDW local motion (\ensuremath{\beta} relaxation). A qualitative model is suggested that describes the transition of CDW into the glass state with decreasing temperature and the main properties of this state.