Classical electricity analysis of the coupling mechanisms between admolecule vibrations and localized surface plasmons in STM for vibration detectability

The presence of a dynamic dipole moment in the gap between the tip of a scanning tunneling microscope (STM) and a substrate, both of which are made of metal, produces a large dynamic dipole moment via the creation of localized surface plasmons (LSPLs). With regard to the vibration-induced structures that have been experimentally observed in STM light emission spectra, we have incorporated the effect of the phonon vibrations of an admolecule below the STM tip into the local response theory, and we have evaluated the enhancement of the dynamic dipole involving phonon vibrations. Our analysis shows how effectively this vibration becomes coupled with the LSPLs. This was shown using three mechanisms that considered the vibrations of a dipole-active molecule and the vibrations of a charged molecule emitting and receiving tunneling electrons. In each of the mechanisms, phonon vibrations with angular frequency ωp shifted each LSPL resonance by ωp or by a multiple of ωp. The phonon effect was negligibly small when the position of the dipole-active molecule vibrated with ω_p, but it was largest and most detectable when the point charge corresponding to the admolecule at the surface of the tip vibrated with ω_p. It was found that a series of LSPL resonances with or without phonon-energy shifts can be characterized by a few dominant orders of multipole excitations, and these orders become higher as the resonance energy increases.