Electronic Transmission Properties of Two—Dimensional Quasi—Lattice

In the framework of the tight binding model,the electronic transmission properties of two-dimensional Penrose lattices with free boundary conditions are studied using the generalized eigenfunction method (Phys.Rev.B 60(1999)13 444).The electronic transmission coefficients for Penrose lattices with different sizes and widths are calculated,and the result shows strong energy dependence because of the quasiperiodic structure and quantum coherent effect.Around the Fermi level E=0,there is an energy region with zero transmission amplitudes,which suggests that the studied systems are insulating.The spatial distributions of several typical electronic states with different transmission coefficients are plotted to display the propagation process.