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The time-honored Allen-Feldman theory of heat transport in glasses isgenerally assumed to predict a finite value for the thermal conductivity, evenif it neglects the anharmonic broadening of vibrational normal modes. Wedemonstrate that the harmonic approximation predicts that the bulk latticethermal conductivity of harmonic solids inevitably diverges at any temperature,irrespective of configurational disorder, and that its ability to represent theheat-transport properties observed experimentally in most glasses is implicitlydue to finite-size effects. Our theoretical analysis is thoroughly benchmarkedagainst careful numerical simulations. Our findings thus reveal that a properaccount of anharmonic effects is indispensable to predict a finite value forthe bulk thermal conductivity in any solid material, be it crystalline orglassy.

Unearthing the foundational role of anharmonicity in heat transport in glasses