Wavelike thermal phonons revealed by localization in graphene phononic crystals

The high Debye temperature and ultralong phonon mean free paths (MFPs) of graphene phononic crystals (GPnCs) enable wavelike phonon transport to manifest over extended length scales, making them an ideal platform for studying phonon localization. We employ machine-learning molecular dynamics to investigate thermal transport in periodic and aperiodic GPnCs. By combining homogeneous non-equilibrium molecular dynamics and non-equilibrium molecular dynamics, we directly extract the spectrally decomposed phonon MFP applicable to aperiodic structures. Spectral analysis establishes characteristic frequency (ωc≈10 THz) and length (Lc≈100 nm) scales for localization effects, and the nonlinear deviation in the 1/κ–1/L relationship (κ: thermal conductivity) indicates the presence of localized phonons. Lattice dynamics reveals that the increased fraction of low-participation-ratio modes and the absence of high-group-velocity modes in aperiodic graphene phononic crystals (ap-GPnC) uncover the microscopic origin of disorder-induced phonon localization. Elastic wave simulations further provide direct wave-field evidence of pronounced spatial localization of low-frequency phonons in ap-GPnC with increasing propagation distance.