Inelastic electron tunneling in 2H-Ta$_x$Nb$_{1-x}$Se$_2$ evidenced by scanning tunneling spectroscopy

We report a detailed study of tunneling spectra measured on 2H-Ta$_x$Nb$_{1-x}$Se$_2$ ($x=0\sim 0.1$) single crystals using a low-temperature scanning tunneling microscope. The prominent gap-like feature unintelligible for a long time was found to be accompanied by some "in-gap" fine structures. By investigating the second-derivative spectra and their temperature and magnetic field dependencies, we were able to prove that inelastic electron tunneling is the origin of these features and obtain the Eliashberg function of 2H-Ta$_x$Nb$_{1-x}$Se$_2$ at atomic scale, providing a potential way to study the local Eliashberg function and phonon spectra of the related transition-metal dichalcogenides.