Effects of surface roughness on the electronic shell structure of metal clusters.

Abstract

Electronic shell and supershell structures in spherical metal clusters with a rough surface are quantum mechanically investigated. Our nonperturbative approach involves a finite-depth step-walled spherical potential well with a sine-wave corrugation along the azimuthal and polar angular coordinates. The electronic structure is studied as a function of both the radial amplitude and the angular wavelength of the corrugation. When the spatial periods of the roughness are comparable to, or shorter than the Fermi wavelength, the shell structure related to the overall spherical symmetry survives, even in the case of a large radial corrugation amplitude. The weakening of the shell effects due to the loss of the spherical symmetry is rather minor and the electronic structure is essentially ruled by the spherical average of the rough potential, which has a soft surface profile. In consequence, the magic sizes (supershell beat locations) are slightly (noticeably) shifted towards larger sizes. These shifts depend strongly on the radial roughness amplitude. As far as the electronic structure is concerned, the results establish the equivalence between a fine-grained hard-walled rough potential and a spherical potential having a soft surface profile. Hence surface roughness could underlie partly the shift of the supershell nodes observed in trivalent metal experiments. When the wavelengths of the corrugation along the angular coordinates are large relative to the Fermi one the electronic density of states becomes quite smooth owing to the large level splitting and mixing effects. The supershell pattern and---to a lesser extent---the shell structure are considerably damped, and even may disappear. In consequence the size dependence of the shell-correction energy and of the ionization potential do not exhibit noticeable oscillations, except for small radial roughness amplitudes.