Effects of lattice fluctuations on Peierls distortion in a one-dimensional Holstein model

Abstract

The effects of quantum and thermal lattice fluctuations on the Peierls distortion are treated through an electron-phonon scattering function introduced in a unitary transformation, and the perturbation calculation is implemented by means of the Green's function method. The lattice-staggered ordering parameter for finite temperature, ${m}_{p}(T),$ and the Peierls transition temperature ${T}_{p},$ as functions of the phonon frequency and the electron-lattice coupling, have been calculated. Our main results are (1) a large ratio of the zero-temperature gap to ${T}_{p}$ agrees well with the experimental values for many Peierls systems; (2) the normalized ordering parameter ${m}_{p}{(T)/m}_{p}(0)$ as a function of the normalized temperature ${T/T}_{p}$ has been calculated, and although it deviates from the mean-field results, it agrees qualitatively with the experimental ones of $({\mathrm{TaSe}}_{4}{)}_{2}\mathrm{I}$ and ${\mathrm{K}}_{0.3}{\mathrm{MoO}}_{3};$ (3) the thermal lattice fluctuations may play an important role in suppressing the Peierls transition temperature even if the phonon frequency goes to zero.