Classification of quasione-dimensional Peierls–Frehlich conductors

The limits of the spectrum of a single-gap potential that extremalizes the Peierls-Frbhlieh thermodynamic functional are calculated as functions of the temperature. Analysis of the obtained results leads to a classification of quasione-dimensional conductors as a function of the dimensionless number $\varkappa=(\hbar^2\mu/2m)^{1/2}\hbar\omega/\lambda^2$, where $\mu$ is the chemical potential, $\omega$ is the frequency of acoustic phonons, and $\lambda$ is the electron-phonon coupling constant. If $\varkappa>\varkappa_c$ a quasione-dimensional conductor is a conductor with charge density waves; if $\varkappa<\varkappa_c$, a conductor of soliton (condenson) type. In accordance with analytic calculations, $\varkappa_c=0,1326$. For energies and temperatures corresponding to a singularity in the spectrum (forbidden band or discrete level) analytic expressions in good agreement with numerical calculations are obtained.