Momentum-dependent electron-phonon coupling in charge density wave systems

Many charge density wave (CDW) systems exhibit $q(T)$ electron-hole modulations continuously varying with $T$ and saturating upon cooling at an incommensurate value even if the maximum occurring in Lindhard response does not such a thermal shift. Using simple RPA argument we show that experimental can be understood electron-phonon coupling (EPC) $g(q)$, necessary to set coupled electronic structural modulations, is momentum dependent. In this analysis, sense of variation depends sign $\frac{\ensuremath{\partial}g(q)}{\ensuremath{\partial}q}$ its amplitude controlled by coherence length (or CDW rigidity) modulation direction. This model quantitatively accounts for dependence one-dimensional (1D) system ${\mathrm{K}}_{0.3}\mathrm{Mo}{\mathrm{O}}_{3}$ (blue bronze) both ground state pretransitional fluctuation regime. We suggest general analysis extended account observed other 1D 2D as transition metal di- trichalcogenides well lanthanide rare-earth tritellurides. detailed low frequency phonon spectrum blue bronze, then propose new scenario $q$ dependent EPC, where $g(q)$ due momentum-dependent hybridization between critical branch bearing Kohn anomaly low-lying branches. allows obtaining agreement deduced from $q(T)$. Finally, similar effects could also relevant exhibiting thermally modulation.