Appearance of Mobility Edge in Self-Dual Quasiperiodic Lattices

Within the framework of the Aubry-Andre model, one kind of self-dual quasiperiodic lattice, it is known that a sharp transition occurs from \emph{all} eigenstates being extended to \emph{all} being localized. The common perception for this type of quasiperiodic lattice is that the self-duality excludes the appearance of the mobility edge separating localized from extended states. In this work, we propose a multi-chromatic quasiperiodic lattice model retaining the self-duality identical to the Aubry-Andre model, and demonstrate numerically the occurrence of the localization-delocalization transition with definite mobility edges. This contrasts with the Aubry-Andre model. As a result, the diffusion of wave packet exhibits a transition from ballistic to diffusive motion, and back to ballistic motion. We point out that experimental realizations of the predicted transition can be accessed with light waves in photonic lattices and matter waves in optical lattices.