Harmonic vibrational excitations in graded elastic networks: transition from phonons to gradons

TL;DR

This paper investigates a transition in one-dimensional graded elastic chains where vibrational states shift from extended to localized, introducing a new type of localized mode called gradons that differ from traditional impurity modes.

Contribution

It identifies a novel localization transition in graded elastic networks and characterizes the unique properties of gradons, expanding understanding of vibrational modes in graded systems.

Findings

Transition occurs at the maximum frequency of the homogeneous chain

Gradons are localized modes with distinct profiles from impurity or Anderson modes

Results provide insights into macroscopic properties of graded materials

Abstract

We have identified a new type of transition from extended to localized vibrational states in one-dimensional graded elastic chains of coupled harmonic oscillators, in which the vibrating masses or nearest-coupling force constants vary linearly along the chain. We found that the delocalization transition occurs at the maximum frequency of the corresponding homogeneous chain, which is in a continuous single band. Although each state in the localized phase, called gradon, can be regarded as an impurity localized mode, the localization profile is clearly distinct from usual impurity modes or the Anderson localized modes. We also argue how gradons may affect the macroscopic properties of graded systems. Our results can provide insights into many analogous systems with graded characters.