Density dependence of the electronic supershells in the homogeneous jellium model

TL;DR

This paper investigates how electronic shell and supershell structures in clusters depend on electron density using self-consistent calculations within a homogeneous jellium model, revealing a simple scaling relation for supernode positions.

Contribution

It provides a detailed analysis of density-dependent electronic shell structures in clusters and introduces a simple scaling law for supernode positions based on electron density.

Findings

Shell and supershell structures vary with electron density.

A simple scaling law relates supernode positions to electron density.

Results apply to clusters with up to 6000 valence electrons.

Abstract

We present the results of self-consistent calculations of the electronic shell and supershell structure for clusters having up to 6000 valence electrons. The ionic background is described in terms of a homogeneous jellium. The calculations were performed for a series of different electron densities, resembling Cs, Rb, K, Na, Li, Au, Cu, Tl, In, Ga, and Al, respectively. By analyzing the occupation of the energy levels at the Fermi energy as a function of cluster size, we show how the shell and supershell structure for a given density arises from the specific arrangement of energy levels. We investigate the electronic shells and supershells obtained for different electron densities. Using a scaling argument, we find a surprisingly simple dependence of the position of the supernodes on the electron density.