Application of renormalization and convolution methods to the Kubo-Greenwood formula in multidimensional Fibonacci systems

Based on the Kubo formalism, electronic transport in macroscopic quasiperiodic systems is studied by means of an efficient renormalization method, and the convolution technique is used in the analysis of two- and three-dimensional lattices. For the bond problem, we found a transparent state located at a center of self-similarity and its ac conductivity is qualitatively different from that observed in mixing Fibonacci chains. The conductance spectra of multidimensional systems exhibit a quantized behavior when the electric field is applied along a periodically arranged atomic direction, and it becomes a devil's stair if the perpendicular subspace of the system is quasiperiodic. Furthermore, the dc conductance maintains a constant value for small imaginary parts (eta) of the energy and decays when eta>eta(c), where eta(c) is proportional to the inverse of the system length. Finally, the spectrally averaged conductance shows a power-law decay as the system length grows, neither constant as in periodic systems nor exponential decays occurred in randomly disordered lattices, revealing the critical localization nature of the eigenstates in quasicrystals