Phononic Topological States in 1D Quasicrystals

Abstract

We theoretically analyze the spectrum of phonons of a one-dimensional quasiperiodic lattice. We simulate the quasicrystal from the classic system of spring-bound atoms with a force constant modulated by the Aubry-André model, so that its value is slightly different in each site of the lattice. From the equations of motion, we obtained the equivalent phonon spectrum of the Hofstadter butterfly, characterizing a multifractal. In this spectrum, we obtained the extended, critical and localized regimes, and we observed that the multifractal characteristic is sensitive to the number of atoms and the $\lambda$ parameter of our model. We also verified the presence of border states for phonons, where some modes in the system boundaries present vibrations. Through the measurement of localization of the individual displacements in each site, we verify the presence of a phase transition through the Inverse Participation Rate (IPR) for $\lambda =1.0$, where the system changes from extended to localized.

7 pages, 10 figures, submitted for Physical Review B

References in corpus (5)

• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Observation of topological valley modes in an elastic hexagonal lattice
• Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
• Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models

Cited by in corpus (2)

• Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices
• Topological effects of phonons in GaN and AlxGa1-xN: A potential perspective for tuning phonon transport