On the Peierls transition in a periodic potential

The properties of a one-dimensional conductor in the presence of an external periodic potential V_Q have been investigated. The low temperature gap is enhanced, the temperature dependence of the gap Δ(T) is smeared at T_PF, the Peierls transition temperature in the absence of V_Q, and hence there is no longer a real phase transition. We also relate the phase pinning frequency ω_ø to the size of V_Q.