Interstitial Electronic Localization

Abstract

We investigate the ground-state properties of a collection of \textit{N} non-interacting electrons in a macroscopic volume $Ω$ 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 $ε_F/ε_F^0$ 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.