Electronic confinement by clusters in quasicrystals and approximants

Quasicrystals are characterised by a long range quasiperiodic order and the presence of many icosahedral clusters arranged in a hierarchical manner. In this paper we analyse the effect of these local environments on the electronic structure by considering a model of one atomic cluster embedded in a metallic matrix. This model leads to ‘cluster virtual bound states’, i.e. resonances of the wavefunction by clusters at different length scales. These states seem to be characteristic of the quasicrystalline local order and they are very sensitive to the geometry of the cluster.