Impurity pinning of charge-density waves and spin-density waves

We reexamine the threshold electric field of the charge-density wave (CDW) within the Fukuyama-Lee-Rice model, where the temperature dependence of the effective Hamiltonian for the phase φ of the CDW is explicitly included. Our theory describes very well the temperature dependence of the threshold field in ${\mathrm{NbSe}}_3$ when the effects of the thermal fluctations of φ are included. An extension of the model for the spin-density wave predicts that the threshold electric field in the spin-density wave does not exhibit a divergence at T=$T_c$ but is almost constant for T≤0.5$T_c$ and slightly increases (∼33%) near T=$T_c$.