Calculation of statistical entropic measures in a model of solids

TL;DR

This paper calculates statistical entropic measures in a 1D crystalline solid model, revealing extremal values at half-filled bands, which correlate with high conductivity in real metals.

Contribution

It introduces a method to compute statistical complexity and Fisher-Shannon information in a simplified solid-state model, linking these measures to electronic properties.

Findings

Extremal entropic measures occur at half-filled bands.

High conductivity correlates with these extremal values.

The model captures key electronic features of monovalent metals.

Abstract

In this work, a one-dimensional model of crystalline solids based on the Dirac comb limit of the Kronig-Penney model is considered. From the wave functions of the valence electrons, we calculate a statistical measure of complexity and the Fisher-Shannon information for the lower energy electronic bands appearing in the system. All these magnitudes present an extremal value for the case of solids having half-filled bands, a configuration where in general a high conductivity is attained in real solids, such as it happens with the monovalent metals.