Electron-phonon coupling and phonon dynamics in single-layer NbSe$_2$ on graphene: the role of moir\'e phonons

The interplay between substrate interactions and electron-phonon coupling in two-dimensional (2D) materials presents a significant challenge in understanding and controlling their electronic properties. Here, we present a comparative study of the structural characteristics, phonon dynamics, and electron-phonon interactions in bulk and monolayer NbSe$_2$ on epitaxial bilayer graphene (BLG) using helium atom scattering (HAS). High-resolution helium diffraction reveals a (9x9)0$^{\circ}$ superstructure within the NbSe$_2$ monolayer, commensurate with the BLG lattice, while out-of-plane HAS diffraction spectra indicate a low-corrugated (3$\sqrt{3}$x3$\sqrt{3}$)30$^{\circ}$ substructure. By monitoring the thermal attenuation of the specular peak across a temperature range of 100 K to 300 K, we determined the electron-phonon coupling constant $\lambda_{HAS}$ as 0.76 for bulk 2H-NbSe$_2$. In contrast, the NbSe$_2$ monolayer on graphene exhibits a reduced $\lambda_{HAS}$ of 0.55, corresponding to a superconducting critical temperature (T$_C$) of 1.56 K according to the MacMillan formula, consistent with transport measurement findings. Inelastic HAS data provide, besides a set of dispersion curves of acoustic and lower optical phonons, a soft, dispersionless branch of phonons at 1.7 meV, attributed to the interface localized defects distributed with the superstructure period, and thus termed moir\'e phonons. Our data show that moir\'e phonons contribute significantly to the electron-phonon coupling in monolayer NbSe$_2$. These results highlight the crucial role of the BLG on the electron-phonon coupling in monolayer NbSe$_2$, attributed to enhanced charge transfer effects, providing valuable insights into substrate-dependent electronic interactions in 2D superconductors.