Abstract
The electronic density of states (DOS) for a one-electron potential having twelve icosahedrally arranged plane-wave components is analyzed via the pseudo-Jones zone approach. The analysis reveals topological band-structure differences, which allow the icosahedral structure to have a gap in the electronic DOS, while an analogous simple monatomic bcc structure cannot. The analytical results are confirmed via numerical calculations for the rational-approximant structures, which also reveal a surprising effect, the presence of band-tail states at either the valence or conduction-band edge.
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