Abstract
We report on a class of icosahedral aluminum–transition-metal (Al-TM) alloys with true semiconducting behavior. The existence of a semiconducting gap is found to depend critically on a particular kind of Al-TM ordering defined by a simple rule in the 6-dimensional superspace. Any deviation from this 6D order leads to the formation of strongly localized defect states in the gap. We show that by a judicious selection of transition metals to be alloyed with Al, we can find alloys with a semiconducting gap at the Fermi level for a hierarchy of approximants to a quasicrystal. As the electron/atom ratio placing the Fermi level into the gap is slightly different for each approximant, this suggests that the gap persists also in the quasiperiodic limit. Icosahedral Al-Pd-Re turns out to be a semiconductor with a band gap filled by the localized states.