Phononic Topological States in 1D Quasicrystals

• Main Authors: Silva, J. R. M, Vasconcelos, M. S, Anselmo, D. H. A. L, Mello, V. D
• Format: Journal Article
• Language: English
• Published: 02-04-2019
• Subjects: Physics - Disordered Systems and Neural Networks; Physics - Mesoscale and Nanoscale Physics
• DOI: 10.48550/arxiv.1902.02006

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-Andr\'e 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.