The dynamic Peierls instability

A mean-field model of a one-dimensional conductor is shown in the presence of a fixed total current to exhibit a dynamic charge-density-wave (CDW) solution which can propagate without Landau damping at a temperature higher than $T_c$, the transition temperature for the static instability. However, the free energy of the moving CDW state becomes less than that of the undistorted state with the same current at a temperature only below $T_c$. The phase transition at this lower temperature is first-order. There exists a critical current above which the free energy of the CDW state is always higher than that of the undistorted state.