Renormalization approach to the electrical conductivity of quasiperiodic systems with defects

Based on the Kubo–Greenwood formula, a novel renormalization plus convolution method is developed to investigate impurity effects on the electrical conductivity of periodic and aperiodic systems. This method combines the convolution theorem with the real-space renormalization technique, being able to address multidimensional quasiperiodic systems with defects. In this paper, the electronic transport in mirror Fibonacci systems with site impurity is investigated in detail. The results show that the mirror symmetry in quasiperiodic systems induces a large number of transparent states in the dc conductivity spectra. Moreover, the introduction of symmetrically located impurities in mirror Fibonacci chains preserves many of these transparent states. Finally, impurity effects on the ac conductivity of quasiperiodic nanowires are also analyzed.