Inelastic tunneling into multipolaronic bound states in single-layer MoS$_2$

Polarons are quasiparticles that arise from the interaction of electrons or holes with lattice vibrations. Though polarons are well-studied across multiple disciplines, experimental observations of polarons in two-dimensional crystals are sparse. We use scanning tunneling microscopy and spectroscopy to measure inelastic excitations of polaronic bound states emerging from coupling of non-polar zone-boundary phonons to Bloch electrons in n-doped metallic single-layer MoS$_2$. The latter is kept chemically pristine via contactless chemical doping. Tunneling into the vibrationally coupled polaronic states leads to a series of evenly spaced peaks in the differential conductance on either side of the Fermi level. Combining density functional (perturbation) theory with a recently developed ab initio electron-lattice downfolding technique, we show that the energy spacing stems from the longitudinal-acoustic phonon mode that flattens at the Brillouin zone edge and is responsible for the formation of stable multipolarons in metallic MoS$_2$.