Calculation of Conduction Spectra in Quantum Dot Composed of Penrose Lattice

Conductance through finite two-dimensional Penrose lattices (PLs) are calculated as a function of gate voltage. To investigate effects of lattice defects and lattice vibrations, three types of PLs are taken into account; (A) PL without lattice defects, (B) PL with lattice defects, and (C) PL with lattice vibrations, which is applied the electric field across the conductor. When energy levels of PL coincides with the chemical potential of the electrodes with increasing gate voltage, electron transfer through PL takes place. However, electron transfer is forbidden at certain states; These states have confined states, which have multiple-degeneracy in their electronic states. In addition, the states are localized due to interference of their wave-functions though the wave-function of each state is extended. We would like to point out that rigidity of confined states with respect to lattice defects and lattice vibrations