Why does a metal get an insulator? Consequences of unfilled bands on boron crystals

Abstract

A longstanding issue why boron crystals such as β-rhombohedral boron are insulator, while band calculations predict metals, has been solved. The issue is intimately related to another property of the crystal, namely breaking of stoichiometry. The presence of unfilled bands requires reconstruction of chemical bonds. Usually, for simple structures, the energy barrier is so high that the bond reconstruction rarely occurs. For large unit cells, the degree of internal freedom increases, and accordingly the chance to meet other energy minima in the atomic configuration increases. Such reconstructions of bonds take place when the valence requirement is fulfilled. This often occurs for boron crystals by breaking the stoichometry. This mechanism is described for various boron crystals in a step-by-step approach.