Engineering mobility in quasiperiodic lattices with exact mobility edges

Abstract

We investigate the effect of an additional modulation parameter $\delta$ on the mobility properties of quasiperiodic lattices described by a generalized Ganeshan-Pixley-Das Sarma model with two on site modulation parameters. For the case with bounded quasiperiodic potential, we unveil the existence of self-duality relation, independent of $\delta$. By applying Avila's global theory, we analytically derive Lyapunov exponents in the whole parameter space, which enables us to determine mobility edges or anomalous mobility edges exactly. Our analytical results indicate that the mobility edge equation is described by two curves and their intersection with the spectrum gives the true mobility edge. Tuning the strength parameter $\delta$ can change the spectrum of the quasiperiodic lattice, and thus engineers the mobility of quasi-periodic systems, giving rise to completely extended, partially localized, and completely localized regions. For the case with unbounded quasiperiodic potential, we also obtain the analytical expression of the anomalous mobility edge, which separates localized states from critical states. By increasing the strength parameter $\delta$, we find that the critical states can be destroyed gradually and finally vanishes.

arXiv comment10 pages,6 figures

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• Hidden self-duality and exact mobility edges in quasiperiodic network models
• Exact non-Hermitian mobility edges and robust flat bands in two-dimensional Lieb lattices with imaginary quasiperiodic potentials
• Multifractal-enriched mobility edges and emergent quantum phases in Rydberg atomic arrays
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
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• Types of dynamical behavior in a quasiperiodic mosaic lattice
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• Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals
• Entanglement entropy as a probe of topological phase transitions
• Topological Anderson insulator and reentrant topological transitions in a mosaic trimer lattice
• Distinct reentrant transitions in a quasi-periodic Raman lattice