Scaling properties of wave functions and transport coefficients in quasicrystals

Electronic wave functions and transport properties are presented in realistic crystalline approximants of decagonal Al-Cu-Co alloy, up to 4414 atoms in a unit cell. The system-size dependence of the participation ratio of wave functions shows that the wave functions of eigenstates show a power-law decay on average. The finite-size scaling analysis indicates that the diffusion constant decreases slowly with increasing system size, as a power of the system size. The scaling properties of the diffusion constant are discussed in connection with the spikiness of the density of states.