Symmetry origin of phonon-like modes in ideal noncrystals

Ascertain whether the phonon-like vibrational modes observed in two-dimensional ideal noncrystals are Goldstone modes arising from the breaking of a subtle symmetry, and, if so, identify the specific symmetry—such as long-range correlated structure along the coherent paths—that is broken.

Background

The authors show that INC exhibit vibrational density of states consistent with Debye scaling, and real-space visualizations reveal plane-wave-like phonon modes, despite the absence of apparent translational or rotational symmetry breaking.

They explicitly state uncertainty about the symmetry responsible for these phonon-like modes and suggest correlated coherent paths as a candidate, calling for theoretical validation.