Self-energy corrections to zone-edge acoustic phonons in monolayer and bilayer ${\mathrm{WS}}_2$

The self-energy corrections to phonons have mostly been observed for modes with zone-center ($q=0$) wave vectors. Here, we investigated the self-energy corrections to phonons in ionic-liquid-gated semiconductors, i.e., monolayer and bilayer ${\mathrm{WS}}_2$, experimentally. Apart from the previously observed $A_{1g}\left(\Gamma \right)$ mode renormalization by Raman spectroscopy, we additionally discovered that the zone-edge longitudinal acoustic (LA($M$)) phonon also softened under finite electron doping. This observed renormalization effect arises from the LA($M$) phonon-assisted electron scattering between the $K$ and $Q$ valleys in the conduction bands, indicating the nonadiabatic self-energy corrections dominate, different from the $A_{1g}\left(\Gamma \right)$ mode. The self-energy corrections of the two modes both depend on layer configurations. Our findings suggest that ${\mathrm{WS}}_2$ and other similar two-dimensional materials are intriguing playgrounds to study the electron-phonon interactions and valley-related physics.