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The charge density wave (CDW) or nematicity has been found to coexist withsuperconductivity in many systems. It is thus interesting that thesuperconducting transition temperature $T_c$ in the doped BaNi$_2$As$_2$ systemcan be enhanced up to six times as the CDW or nematicity in the undopedcompound is suppressed. Here we show that the transverse acoustic phonons ofBa$_{1-x}$Sr$_x$Ni$_2$As$_2$ are strongly damped in a wide doping range andover the whole $Q$ range, which excludes its origin from either CDW ornematicity. The damping of TA phonons can be understood as largeelectron-phonon coupling and possible strong hybridization between acoustic andoptical phonons as shown by the first-principle calculations. Thesuperconductivity can be quantitatively reproduced by the change ofelectron-phonon coupling constant calculated by the McMillan equation in theBCS framework, which suggests that no quantum fluctuations of any order isneeded to promote the superconductivity. On the contrary, the change of $T_c$in this system should be understood as the six-fold suppression ofsuperconductivity in undoped compounds.

Strong electron-phonon coupling in Ba$_{1-x}$Sr$_x$Ni$_2$As$_2$