Non-Conventional Critical Behavior and Q-dependent Electron-Phonon Coupling Induced Phonon Softening in the CDW Superconductor LaPt2Si2

This paper reports the first experimental observation of phonons and their softening on single crystalline LaPt$_2$Si$_2$ via inelastic neutron scattering. From the temperature dependence of the phonon frequency in close proximity to the charge-density wave (CDW) $q$-vector, we obtain a CDW transition temperature of T$_{CDW}$ = 230 K and a critical exponent $\beta$ = 0.28 $\pm$ 0.03. This value is suggestive of a non-conventional critical behavior for the CDW phase transition in LaPt$_2$Si$_2$, compatible with a scenario of CDW discommensuration (DC). The DC would be caused by the existence of two CDWs in this material, propagating separately in the non equivalent (Si1-Pt2-Si1) and (Pt1-Si2-Pt1) layers respectively, with transition temperatures T$_{CDW-1}$ = 230 K and T$_{CDW-2}$ = 110 K. A strong $q$-dependence of the electron-phonon coupling has been identified as the driving mechanism for the CDW transition at T$_{CDW-1}$ = 230 K while a CDW with 3-dimensional character, and Fermi surface quasi-nesting as a driving mechanism, is suggested for the transition at T$_{CDW-2}$ = 110 K. Our results clarify some aspects of the CDW transition in LaPt$_2$Si$_2$, which have been so far misinterpreted by both theoretical predictions and experimental observations, and give direct insight into its actual temperature dependence.