Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models

2013/01/31 by Sriram Ganeshan, Kai Sun, S. Das Sarma · 2 citations
Physics and Astronomy · #cond-mat.mes-hall #quant-ph

paper · pdf · doi:10.1103/physrevlett.110.180403

published as Phys. Rev. Lett. 110, 180403 (2013) · 5 pages + 1 page supplementary material

arxiv created 2013/05/02 · arxiv updated 2013/05/03

Abstract

The Aubry-André or Harper (AAH) model has been the subject of extensive theoretical research in the context of quantum localization. Recently, it was shown that one-dimensional quasicrystals described by the incommensurate AAH model has a nontrivial topology. In this Letter, we show that the commensurate off-diagonal AAH model is topologically nontrivial in the gapless regime and supports zero-energy edge modes. Unlike the incommensurate case, the nontrivial topology in the off-diagonal AAH model is attributed to the topological properties of the one-dimensional Majorana chain. We discuss the feasibility of experimental observability of our predicted topological phase in the commensurate AAH model.

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• Fibonacci number systems and the localization criterion in the many-body Aubry-André model
• Divergent density of states and non-analytic Lyapunov exponent in one-dimensional slowly varying systems

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