Electronic Transmission Properties of Two-Dimensional Quasi-lattice

In the framework of tight binding model, the electronic transmission properties of two-dimensional Penrose-lattices with free boundary condition are studied by using the generalized eigenfunction method Phys. Rev. B 60(1999)13444. The electronic transmission coefficients for Penrose lattices with different size and width are calculated, and the result shows strong energy dependence because of the quasi-periodic structure and quantum coherent effect. Around the Fermi level E = 0, there is an energy region with zero transmission amplidutes, which suggests that the studied systems are insulating. The spatial distributions of several typical electronic states with different transmission coefficient are plotted to display the propagation process.