Electronic properties of the Penrose lattice. II. Conductance at zero temperature

Abstract

The conductance of the Penrose lattice at zero temperature is studied by the multichannel Landauer formula and the recursion method of the site Green functions. We have investigated the dependence on the Fermi energy and the lattice size. The Fermi-energy dependence of the conductance studied for a system with up to 3571 sites exhibits singularly rapid and large conductance fluctuation. Analysis of system-size dependence of the fluctuations with respect to energy suggests the wave functions are critical. This critical behavior of the wave functions is more directly confirmed by the lattice length dependence, which shows power-law decays of conductance up to a system with about 1.32 million sites.