Effects of impurities on charge-density waves: A mean-field calculation

The effect of substitutional impurities on systems that present a charge-density-wave (CDW) ground state induced by a Peierls distortion is studied within a mean-field approximation. The calculations have been performed for both one-dimensional and two-dimensional models. The results of the calculations indicate the following. (i) The presence of impurities weakens the CDW and eventually destroys it. (ii) A distinction is made between the two effects of doping that perturb the CDW, namely, the disorder and the shift of the band filling. (iii) In the case of disorder, the results are interpreted in terms of lack of coherence of the electronic states and the coherence length of the instability. (iv) The variations at $T=0\mathrm{}$ of the CDW order parameter with the impurity concentration follows a square-root law. (v) The CDW transition temperature is reduced by the presence of impurities showing a critical behavior. (vi) Substitutional impurities in commensurate CDW systems have a similar effect as magnetic impurities in superconducting materials and normal impurities in the excitonic insulator.