Su-Schrieffer-Heeger quasicrystal: Topology, localization, and mobility edge

Abstract

In this paper we discussed the topological transition between trivial and nontrivial phases of a quasi-periodic (Aubry-André like) mechanical Su-Schrieffer-Heeger (SSH) model. We find that there exists a nontrivial boundary separating the two topological phases and an analytical expression for this boundary is found. We discuss the localization of the vibrational modes using the calculation of the inverse participation ratio (IPR) and access the localization nature of the states of the system. We find three different regimes: extended, localized, and critical, depending on the intensity of the Aubry-André spring. We further study the energy dependent mobility edge (ME) separating localized from extended eigenstates and find its analytical expression for both commensurate and incommensurate modulation wavelengths, thus enlarging the library of models possessing analytical expressions for the ME. Our results extend previous results for the theory of fermionic topological insulators and localization theory in quantum matter to the classical realm.

arXiv comment16 pages

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Cited by in corpus (5)

• Topological Anderson insulator phases in one dimensional quasi-periodic mechanical SSH chains
• Tensor network method for real-space topology in quasicrystal Chern mosaics
• Emergent topological phases in an extended Su-Schrieffer-Heeger model with Rashba spin-orbit interaction, higher order hopping and domain wall
• Disorder driven topological phase transitions in 1D mechanical quasicrystals
• Non-self-averaging topological Anderson insulator