Convolution and renormalization techniques applied to the Kubo conductivity in quasiperiodic systems

The localization and transport properties in quasiperiodic systems are quite different from those in crystalline and in disordered materials. In this work, we study the electrical conduction in macroscopic Fibonacci lattices by using the Kubo–Greenwood formula and a single-band tight-binding model. This study is carried out by means of the convolution technique and a novel renormalization method, which allows iterative evaluation of the products of the Green’s function in an exact way. The results of the spectrally averaged conductance show a power-law decay as the length of the quasiperiodic systems increases along the applied electric field. This fact reveals the critical localization nature in quasicrystalline materials, contrary to the constant and exponencial decay behaviors found in the periodic and randomly disordered systems, respectively.