Nearest Neighbor Tight Binding Models with an Exact Mobility Edge in One Dimension

Sriram Ganeshan, J. H. Pixley, and S. Das Sarma
Phys. Rev. Lett. 114, 146601 – Published 9 April 2015
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Abstract

We investigate localization properties in a family of deterministic (i.e., no disorder) nearest neighbor tight binding models with quasiperiodic on site modulation. We prove that this family is self-dual under a generalized duality transformation. The self-dual condition for this general model turns out to be a simple closed form function of the model parameters and energy. We introduce the typical density of states as an order parameter for localization in quasiperiodic systems. By direct calculations of the inverse participation ratio and the typical density of states we numerically verify that this self-dual line indeed defines a mobility edge in energy separating localized and extended states. Our model is a first example of a nearest neighbor tight binding model manifesting a mobility edge protected by a duality symmetry. We propose a realistic experimental scheme to realize our results in atomic optical lattices and photonic waveguides.

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  • Received 6 December 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.146601

© 2015 American Physical Society

Authors & Affiliations

Sriram Ganeshan, J. H. Pixley, and S. Das Sarma

  • Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA

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Issue

Vol. 114, Iss. 14 — 10 April 2015

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