Exactly Solvable Mobility Edges for Phonons in One-DimensionalQuasiperiodic Chains

Mobility edges, which demarcate the boundary between extended and localized states, are fundamental to understanding the physics of localization in condensed matter systems. Systems exhibiting exact mobility edges are rare, and the localization properties of phonons have received limited prior investigation. In this work, we reveal analytical mobility edges in one-dimensional quasiperiodic-modulated spring-mass chains. The mobility edges are exactly solved and numerically validated through the eigenfrequency spectra, inverse/normalized participation ratios, and lattice wave dynamics. Our research demonstrates the Anderson localization transition in phonon systems, paving the way for experimental observations of phonon localization.