Influence of impurities on the thermodynamic properties of the charge density wave state

The basic equations that determine the thermodynamic properties of the condensed state of a charge density wave – the order parameter, energy gap, critical transition temperature – are obtained, together with an expression for the magnetic susceptibility. Allowance is made for the deviation from half-filling of the band, umklapp processes, and the influence of impurities. The obtained equations differ from the case of band half-filling, and also from the results of the theory of superconducting alloys with paramagnetic impurity. The limit of low impurity concentrations is considered. It is shown that with increasing impurity concentration there is a decrease in the Peierls transition temperature, which also depends strongly on the parameter $\mu$ that determines the deviation from band half-filling. At $T=0$, the paramagnetic susceptibility $\chi$ vanishes in the region of low impurity concentrations and increases with increasing temperature. The temperature dependence of $\chi$ in the case $\mu\ne0$ is very different from the half-filling case ($\mu=0$).