Localization in one-dimensional incommensurate lattices beyond the Aubry-André model

Details Localization in one-dimensional incommensurate lattices beyond the Aubry-André model Localization in one-dimensional incommensurate lattices beyond the Aubry-André model

2009-07-01

arxiv.org/abs/0907.0252v1

Phys. Rev. A 80, 021603 (2009)

Physics

Quantum Physics

5 pages, 6 figures

Scientific paper

10.1103/PhysRevA.80.021603

Localization properties of particles in one-dimensional incommensurate lattices without interaction are investigated with models beyond the tight-binding Aubry-Andr\'e (AA) model. Based on a tight-binding t_1 - t_2 model with finite next-nearest-neighbor hopping t_2, we find the localization properties qualitatively different from those of the AA model, signaled by the appearance of mobility edges. We then further go beyond the tight-binding assumption and directly study the system based on the more fundamental single-particle Schr\"odinger equation. With this approach, we also observe the presence of mobility edges and localization properties dependent on incommensuration.

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