Valence fluctuations and electric reconstruction in the extended Anderson model on the two-dimensional Penrose lattice

We study the extended Anderson model on the two-dimensional Penrose lattice, combining the real-space dynamical mean-field theory with the noncrossing approximation. It is found that the Coulomb repulsion between localized and conduction electrons does not induce a valence transition, but the crossover between the Kondo and mixed valence states is in contrast to the conventional periodic system. In the mixed-valence region close to the crossover, nontrivial valence distributions appear, characteristic of the Penrose lattice, demonstrating that the mixed-valence state coexists with local Kondo states in certain sites. The electric reconstruction in the mixed valence region is also addressed.