Distorted structures in half-filled p-band materials

Many half-filled p-band materials form complex, semiconducting or semi-metallic crystallographic structures, which are commonly conceived of as distortions of simpler, higher-symmetry structures. This distortion is conventionally attributed to the energy gained by the opening of a band gap in the vicinity of the Fermi level, which was assumed to lower the overall energy of the lattice. Applying DFT calculations of the total energy and its component terms to both elemental and binary half-filled p-band materials, we show that the energy gain from distortion arises from the Coulombic interactions. Furthermore, we demonstrate that although the distortion is followed by an opening of a band gap, there may be other changes of the same order of magnitude in lower energy levels of the electrons. These results are demonstrated to apply both in the distortion parameter space of a specific phase and between different phases with different symmetries. It is therefore our conclusion that, in contrast to the prevailing concept, the metal-semiconductor or metal-semimetal transitions of such materials are the consequence of the distortion rather than its cause. This may suggest a more general mechanism of high-to-low symmetry transitions, relevant also to other distorted structures which do not demonstrate the same electronic transitions.