Diverse Manifestations of Electron-Phonon Coupling in a Kagome Superconductor

Recent angle-resolved photoemission spectroscopy (ARPES) experiments on a kagome metal CsV$_3$Sb$_5$ revealed distinct multimodal dispersion kinks and nodeless superconducting gaps across multiple electron bands. The prominent photoemission kinks suggest a definitive coupling between electrons and certain collective modes, yet the precise nature of this interaction and its connection to superconductivity remain to be established. Here, employing the state-of-the-art \textit{ab initio} many-body perturbation theory computation, we present direct evidence that electron-phonon ($e$-ph) coupling induces the multimodal photoemission kinks in CsV$_3$Sb$_5$, and profoundly, drives the nodeless $s$-wave superconductivity, showcasing the diverse manifestations of the $e$-ph coupling. Our calculations well capture the experimentally measured kinks and their fine structures, and reveal that vibrations from different atomic species dictate the multimodal behavior. Results from anisotropic $GW$-Eliashberg equations predict a phonon-mediated superconductivity with nodeless $s$-wave gaps, in excellent agreement with various ARPES and scanning tunneling spectroscopy measurements. Despite of the universal origin from the $e$-ph coupling, the contributions of several characteristic phonon vibrations vary in different phenomena, highlighting a versatile role of $e$-ph coupling in shaping the low-energy excitations of kagome metals.