Evidence for the weak coupling scenario of the Peierls transition in the blue bronze

Abstract

On the basis of first-principles DFT calculations the wave-vector and temperature dependencies of the Lindhard response function of the blue bronze ${\mathrm{K}}_{0.3}{\mathrm{MoO}}_{3}$ have been calculated. The ${k}_{F}^{I}+{k}_{F}^{II}$ interband component of the response, which is responsible for the Peierls instability, has been quantitatively analyzed. It is found that (i) the electron-hole coherence length of this response determines the length scale of the experimental intrachain CDW correlations, and (ii) the intrachain ${q}_{\ensuremath{\parallel}}$ dependence of such a response also determines the shape of the Kohn anomaly experimentally measured. These findings provide compelling evidence that the Peierls transition of the blue bronze ${\mathrm{K}}_{0.3}{\mathrm{MoO}}_{3}$ follows the weak electron-phonon coupling scenario in the adiabatic approximation, something that had not yet been proved on the basis of first-principles calculations for a real material. It is proposed that the CDW interchain coupling occurs through a Coulomb coupling between dipolar CDWs. The nature of the phonon mode leading to the dipolar nature of the CDWs is also discussed, and the relevance of these results to rationalize the CDW instabilities in other oxides and bronzes is pointed out. These findings are also contrasted with recent results for other CDW materials like chalcogenides and tellurides.