Electronic transport in multidimensional Fibonacci lattices

In this article, the Kubo-Greenwood formula is used to investigate the electronic transport behaviour in macroscopic systems by means of an exact renormalization method. The convolution technique is employed in the analysis of two-dimensional Fibonacci lattices. The dc electrical conductance spectra of multidimensional systems exhibit a quantized behaviour 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. 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. Finally, the ac conductance along periodic and quasiperiodic directions is compared with the optical conductivity measured in decagonal quasicrystals.