Effect of photoelectron mean free path on the photoemission cross section of noble metal Shockley states

Abstract

Every solid-state material has electrons at its surface with spatial and energetic distributions that depend on both the atomic elements that conforms it and its crystalline structure. These surface electrons can give rise to well defined surface states, such as Shockley states in the case of noble metals. The intensity of these vary with the photon energy as illustrated by its photoemission cross-section. By combining angle resolved photoemission (ARPES) experimental data with ab initio calculations we are able to understand the complex photoemission cross-section of the Shockley states of (111) terminated noble metals. The generally accepted final-state free-electron band picture based on the nearly-free-electron (NFE) model fails to reproduce the unprecedented fine details observed. Furthermore, the width of the photoemission cross-section curve has no straight relation to the wave function penetration depth, as often believed. Importantly, the differences observed in the photoemission cross-section at the L resonance between the two noble metals can be rationalized with the outgoing electrons mean free path, as calculated from the crystal band structure and the optical potential. The present results are particularly relevant for nanostructured systems, for example vicinal surfaces, where the resonant character of their surface states might be investigated through such kind of photoemission cross-section curves in particular, the question of whether the surface state changes into a surface resonance when increasing the density of steps at the surface, which is still controversial.