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Our detailed Angle Resolved Photoemission Spectroscopy (ARPES) study of$2H$-TaS$_2$, a canonical incommensurate charge density wave (CDW) material,illustrates pronounced many-body renormalization in the system, which ismanifested by the presence of multiple kink structures in the electronicdispersions. Temperature-dependent measurements reveal that these kinkstructures persist even at temperatures higher than the charge density wavetransition temperature $\it{T}_{\text{cdw}}\,$ and the energy locations of thekinks are practically temperature-independent. Correlating kink energies withthe published Raman scattering data and the theoretically calculated phononspectrum of $2H$-TaS$_2$, we conclude phononic mechanism for these kinks. Wehave also detected momentum-anisotropy in the band renormalization, which inturn indicates momentum-dependence of the electron-phonon coupling of thesystem.

Spectroscopic signature of the $\mathbf{k}$-dependent electron-phonon coupling in $2H$-TaS$_2$