Thermodynamic properties of charge-density waves

Low-temperature thermodynamic properties of linear-chain compounds exhibiting charge-density waves (CDW) are examined theoretically within a mean-field theory. A result for the spin susceptibility χ is obtained which agrees with the clear-cut available data on ${\mathrm{K}}_{0.3}$ ${\mathrm{MoO}}_3$ for T<0.9$T_P$, where $T_P$ is the Peierls transition temperature. The influence of ordinary impurities on the order parameter Δ, the half-gap ${\Omega }_G$, and spin susceptibility χ is calculated. Numerical results are obtained for Δ and ${\Omega }_G$ as a function of the impurity concentration x. Substantial difference is found between the lattice distortion parameter Δ and the half-gap ${\Omega }_G$ even for relatively small impurity concentration x, which is directly accessible to experimental verification. Beyond a critical concentration $x_c^{\mathcal{’}}$, the excitation spectrum of CDW condensate does not exhibit a gap. The order parameter also yields the transition temperature as a function of x, in agreement with earlier results of Patton and Sham and with recent experiments on ${\mathrm{TaS}}_3$ doped with Nb and Se impurities. Impurities are found to enhance spin susceptibility. However, the susceptibility at zero temperature remains zero for all concentrations, except in the gapless regime.