Discontinuous behavior of the localization properties in a finite-length incommensurate potential with weak applied electric fields.

Abstract

Model calculations are performed for a tight-binding model with an incommensurate potential of finite length, in a weak electric field scrE, with site energies given by ${E}_{n}$=W cos(2n)-eascrEn (n=1,2,...,N). It is found that there is a discontinuous delocalizing behavior in that localization properties and the position of the localized wave function have sudden discontinuities as a function of the electric field, where the calculations are performed for values of W>${W}_{C}$, where ${W}_{C}$ is the value of W above which the states are localized in the absence of an external electric field. As W decreases, the discontinuities become more frequent, resulting in a ``noisy'' behavior near threshold.