Theoretical analysis of STM-derived lifetimes of excitations in the Shockley surface state band of Ag(111)

TL;DR

This paper provides a theoretical many-body analysis of electron-electron scattering decay rates in the Shockley surface state band of Ag(111), considering STM effects, and finds that STM-induced Stark shifts are small for these states.

Contribution

It offers a detailed GW approximation analysis of excitation lifetimes in Ag(111) surface states, including STM perturbations, which was not previously done.

Findings

Decay rate varies more rapidly with energy than for image potential states.

STM-induced Stark shifts are small under normal tunnelling conditions.

Previous STM-derived lifetimes for Shockley states are generally accurate without correction.

Abstract

We present a quantitative many-body analysis using the GW approximation of the decay rate $\Gamma$ due to electron-electron scattering of excitations in the Shockley surface state band of Ag(111), as measured using the scanning tunnelling microscope (STM). The calculations include the perturbing influence of the STM, which causes a Stark-shift of the surface state energy $E$ and concomitant increase in $\Gamma$. We find $\Gamma$ varies more rapidly with $E$ than recently found for image potential states, where the STM has been shown to significantly affect measured lifetimes. For the Shockley states, the Stark-shifts that occur under normal tunnelling conditions are relatively small and previous STM-derived lifetimes need not be corrected.