Metal-insulator transition in approximants to icosahedral Al-Pd-Re

The electronic structure of icosahedral Al-Pd-Re alloys has been calculated for a series of large approximants. For the 1/1 to 3/2 approximants with up to 2292 atoms/cell the electronic eigenstates have been calculated self-consistently via diagonalization of the Hamiltonian in a tight-binding linear-muffin-tin orbital representation. For the 5/3 and 8/5 approximants only the total and partial densities of states have been calculated using the real-space recursion method. The electronic structure of Al-Pd-Re differs from that of other icosahedral phases by (i) the appearance of a semiconducting gap for certain approximants and (ii) by a scaling behavior of the participation ratio of the states close to the Fermi level, indicating a possibly critical character of the eigenstates.