dc conductivity in one-dimensional incommensurate systems

Abstract

Using the Landauer formula to calculate the conductivity of a one-dimensional system with incommensurate potentials, we have located the mobility edges and determined the metal-insulator phase diagram. Near the mobility edge the conductivity shows a superperiodic structure with predictable superperiods which are characteristic to the incommensurate potentials. We have obtained the critical exponent \ensuremath{\simeq}1 for the localization length on the insulating side, and the critical exponent \ensuremath{\simeq}0.5 for the conductivity on the metallic side. The validity of a simple scaling theory is checked.