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Keywords:

  • Fano defects;
  • Kubo–Greenwood formula;
  • quasicrystals;
  • renormalization method

In this paper, we investigate the effects on the electrical conductivity originated by the inclusion of Fano defects (FDs) for periodic and quasiperiodic systems of macroscopic size. This study is developed using the extension of the methods of renormalization for the Kubo–Greenwood formula in real space within the tight-binding formalism. Within this formalism, the conductivity is determined in an exact form, without any other approximation. For periodic systems, we find the zeros of conductivity located at the eigenenergies of the coupled chain of inline image atoms, and transparent states at the eigenenergies of a chain of inline image atoms. These results are shown in both numerical and analytical way. Moreover, the position of the FD in the system does not alter the conductivity spectrum. On the other hand, for quasiperiodic systems, only some coupled chains preserve the transparent state; this was found both numerically and analytically. The case of two FDs attached to the system is also analyzed, founding a high dependence of the electrical conductivity on the distance between the FDs. Finally, this study is extended to two dimensions.