Interstitial Electronic Localization

TL;DR

This paper models how electrons localize in the interstitial regions of a crystalline array of impenetrable spheres, revealing band narrowing and density changes as the sphere radius increases relative to the Wigner-Seitz radius.

Contribution

It introduces a simplified quantum model to study interstitial electron localization in crystalline arrays, with potential applications to understanding compressed alkali metals.

Findings

Electrons tend to localize in interstitial regions as the ratio r_c/r_s increases.

The relative band-width decreases monotonically with increasing r_c/r_s.

The model captures band narrowing and density maxima in interstitial regions.

Abstract

We investigate the ground-state properties of a collection of \textit{N} non-interacting electrons in a macroscopic volume $\Omega$ also containing a crystalline array of \textit{N} spheres of radius $r_c$ each taken as largely impenetrable to electrons and with proximity of neighboring excluding regions playing a key physical role. The sole parameter of this quantum system is the ratio $r_c/r_s$, where $r_s$ is the Wigner- Seitz radius. Two lattices (FCC and BCC) are selected to illustrate the behavior of the system as a function of $r_c/r_s$. As this ratio increases valence electrons localize in the interstitial regions and the relative band-width $\epsilon_F/\epsilon_F^0$ is found to decrease monotonically for both. The system is motivated by the behavior of the alkali metals at significant compression. It accounts for band narrowing, leads to electronic densities with interstitially centered maxima, and can be taken as a model which clearly may be improved upon by perturbation and other methods.