Structure of mobility edges in a one-dimensional incommensurate model

Abstract

The localization of the Soukoulis-Economou model in one-dimensional incommensurate systems is studied by the use of multifractal analysis. In the case of ε n = 1.9[cos(2πωn) + 1 3cos(4πωn) ] and ω = lim l→∞ F l−1 F l , where F l is the generalized Fibonacci number satisflying the recursion relation F l = 8 F l−1 + F l−2 with F 0 = F 1 = 1, we have numerically found a hierarchical and selfsimilar structure of mobility edges. The results suggest the existence of an infinite number of mobility edges.