Metallic–insulator Phase Transitions in the Power-Law Modulated Harper Model

In this work we investigate the transport properties of non-relativistic quantum particles on incommensurate multilayered structures with the thicknesses wn of the layers following a power-law modulated Harper model given by wn=w0|cos(πanν)|. For the normal incidence case, which means an one-dimensional system, we obtained that for a specific range of energy, it is possible to see a metallic–insulator transition with the exponent ν. A metallic phase is supported for ν<1. We also obtained that for the specific value ν=1 there is an alternation between metallic and insulator phases as we change the disorder strength w0. When we integrate out all incidence angles, which means a two-dimensional system, the metallic–insulator transition can be seen for much larger range of energy compared to the normal incidence case.