Peierls transition in substitutionally disordered quasi-one-dimensional conductors

In this paper, the mean-field transition temperature of the Peierls transition is obtained for a quasi-one-dimensional binary substitutional alloy ${A}_{x}{B}_{1\ensuremath{-}x}$ as a function of the relative concentration $x$. The Peierls state is assumed to result from a soft-mode structural instability driven by the one-dimensional electronic system coupled to the intramolecular vibrational mode. We consider only diagonal disorder arising from fluctuations in the intrasite electron potential and electron-intramolecular vibrational-mode interaction. Its effect on the Peierls phase is evaluated using the coherent potential approximation for single dimers. The use of suitable approximations resulted in an analytic expression for the transition temperature. The transition temperature of a half-filled conduction-band system diluted with a substitutional impurity of a different valency is also studied.