Theory of STM-induced enhancement of dynamic dipole moments on crystal surfaces

We present the theory of the enhancement of dynamic dipole moments on crystal surfaces, induced by the presence of a scanning tunneling microscope (STM) tip placed just above the dipole. We approximate the tip by a spherical object whose radius is large compared to its distance from the surface. The tip and substrate are described within the framework of local dielectric theory, and we ignore the role of retardation in the description of the substrate/dipole/tip complex. Within this picture, through use of bispherical coordinates, one may describe the total dipole moment of the complex through use of an expansion in terms of elementary functions. We obtain explicit results for two cases: (i) the dipole moment is normal to the surface and (ii) the dipole moment is parallel to the surface. Through numerical calculations, we find very substantial enhancements for case (i), when the tip/substrate separation is in the nanometer range, while for case (ii) the enhancements are modest. We comment on the implications of these results for the study of optical interactions experienced by atoms or molecules with dipole-active transitions, for entities on metal surfaces in the vicinity of STM probes.