Fractal quantization of the electrical conductance in quasiperiodic systems

In this work, the Kubo-Greenwood formula is used to investigate the electronic transport in multidimensional macroscopic quasiperiodic lattices within the tight-binding model. This investigation is carried out by means of a novel renormalization method and the convolution technique. The dc electrical conductance of two-dimensional (2D) periodic systems shows uniform steps in units of 2e2/h, as observed in 2D electron-gas experiments, and a fractal distribution of these steps is found when the atoms in perpendicular direction to the applied electric field are quasiperiodically ordered. The spectral integral of these conductances presents a strong dependence on the imaginary part of energy in the Green's function, contrary to the case of density of states.