Thermal fluctuations of the order parameter in charge-density waves

Incorporating the thermal fluctuations of the phase of charge-density-wave order parameter into the theory, we extend the Fukuyama-Lee-Rice theory to finite temperatures. We find the temperature dependence of the threshold field at low temperatures (e.g., T<(1/2)$T_c$) is given by &, where $T_0$ is a material constant independent of the impurity concentration. Furthermore, we find the characteristic Lee-Rice correlation length depends on the temperature as &. The former prediction describes quite well the observed temperature dependence of the threshold field $E_T$(T) at low temperatures of ${\mathrm{NbSe}}_3$, orthorhombic and monoclinic ${\mathrm{TaS}}_3$, and (${\mathrm{TaSe}}_4$ ${)}_2$I. Furthermore, the present theory describes qualitatively both the observed pressure dependence of $E_T$(0) and $T_0$ orthorhombic ${\mathrm{TaS}}_3$ and (${\mathrm{TaSe}}_4$ ${)}_2$I.