Crystalline solids exhibiting glasslike (ultralow) thermal conductivity have received substantial attention, owing to their significance in fundamental physics and practical applications like thermal insulation and thermoelectric devices. Conventionally, achieving this desirable, intrinsically thermal insulating behavior requires heavy atoms and complex lattice structures, limiting the search space for material design. Here, we reported the coexistence of anomalous positive temperature dependence alongside a moderate conductivity magnitude in hexagonal α-graphyne, despite its remarkably light atoms and simple lattice. Using first-principles anharmonic lattice dynamics and the unified thermal transport theory, we reveal that, at room temperature, the predicted thermal conductivity contributed by wavelike phonons (${\kappa }_{\mathrm{c}}$) is 5.7 W/mK, being comparable to the 8.6 W/mK contributed by particlelike phonons (${\kappa }_{\mathrm{p}}$), deviating from the established transport understandings in α-graphyne based on particlelike phonon transport. As temperature increases from 400 to 800 K, the ${\kappa }_{\mathrm{c}}$ component dominates thermal transport, driving an anomalous increase in total thermal conductivity (${\kappa }_{\mathrm{l}}={\kappa }_{\mathrm{c}}+{\kappa }_{\mathrm{p}}$) with temperature. Further analyses reveal that, driven by strong four-phonon anharmonicity, the high scattering rates of phonon modes near 13 and 62 THz bridge the frequency gap between nondegenerate eigenstates (with large frequency discrepancy), enabling robust interband tunneling. This work highlights the importance of wavelike tunneling and quartic anharmonicity in describing thermal transport in α-graphyne and opens a new avenue for overcoming conventional thermal conductivity barriers.

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• Phonons
• Thermal conductivity
• Carbon-based materials
• Monolayer films
• Boltzmann theory
• Density functional calculations