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 omega(a )of the layers following a power-law modulated Harper model given by omega(a)= omega(0)| cos(pi an(v))|. 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 v. A metallic phase is supported for v < 1. We also obtained that for the specific value v= 1 there is an alternation between metallic and insulator phases as we change the disorder strength w(0). 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.