Nonequilibrium theory of scanning tunneling spectroscopy via adsorbate resonances: Nonmagnetic and Kondo impurities

Abstract

We report on a fully nonequilibrium theory of scanning tunneling microscopy (STM) through resonances induced by impurity atoms adsorbed on metal surfaces. The theory takes into account the effect of tunneling current and finite bias on the system, and is valid for arbitrary intra-adsorbate electron correlation strength. It is thus applicable to recent STM experiments on Kondo impurities. We discuss the finite-temperature effects and the consequences of atomic scale resolution of the STM for the spectral property of such systems. We find that the tip position affects the resonance line shapes in two ways. As a function of the distance from the surface, the line shapes vary due to the different extents of the adsorbate and metal wave functions into the vacuum. However, we do not expect large variations in line shapes unless tunneling into the tightly bound adsorbate states is considerable, or nonequilibrium effects are significant. As a function of the lateral tip position, line shapes should not change significantly on length scales of ${R}_{\ensuremath{\parallel}}<~10\AA{}$ under typical experimental conditions when the electrons tunnel into the perturbed bulk conduction states hybridized with the outer shell $\mathrm{sp}$ adsorbate orbitals. Tunneling into surfaces states on (111) surfaces of noble metals should be important for an observation of resonance at larger distances (>10 \AA{}), and oscillatory variations in the line shape should develop. This long-range behavior was not resolved in recent experiments with Kondo impurities. The temperature dependence of the Kondo resonance cannot be deduced directly from the differential conductance, as the thermal broadening of the tip Fermi surface produces qualitatively similar effects of comparable and larger magnitudes. A careful deconvolution is necessary to extract the temperature dependence of the Kondo resonance. The finite-bias current-induced nonequilibrium effects in tunneling through Kondo impurities should produce a characteristic broadening of the resonance in the case of strong hybridization of the discrete state with the STM tip.