Electronic transport of quasicrystals with random phason strain: The two-dimensional Penrose lattice

The electronic density of states, eigenstates, length dependence, and Fermi-energy dependence of the dc conductance in the two-dimensional Penrose lattice are calculated by using an exact diagonalization, Landauer formula and the forced oscillator method in finite size, zero-temperature systems with and without random phasons. Two typical behaviors of the conductance are found according to a choice of the Fermi energy. One is that the randomness decreases the localization length and decreases conductance. The other is that the randomness smears out the density of states and the channels for the electronic transport open, i.e., the conductance increases. Based on this observation, a plausible explanation for the abnormal transport properties in quasicrystals is proposed.