Predicting lattice thermal conductivity from first principles requires solving the Boltzmann transport equation with full anharmonic phonon scattering rates --- a calculation that scales prohibitively across large material spaces. Mukherjee, Srivastava, and Singh bypass this with a single scalar: the phonon band center, defined as the spectral centroid of the phonon density of states weighted by frequency. This descriptor captures the essential physics of phonon scattering without computing scattering rates at all. It correlates inversely with the Gruneisen parameter --- the standard measure of anharmonicity --- and directly with lattice thermal conductivity across multiple material classes. Validated first on chalcopyrites and then against experimental data spanning structurally diverse compounds, the phonon band center distinguishes high-conductivity from low-conductivity materials using only harmonic phonon information.
The power of the descriptor lies in what it compresses. Anharmonicity is a many-body phenomenon: three-phonon and four-phonon scattering processes involve the full cubic and quartic force constants of the lattice. The phonon band center encodes none of this detail explicitly. Instead, it captures the consequence of anharmonicity --- the redistribution of spectral weight toward lower frequencies as bonds soften --- through the position of the spectral centroid. Low phonon band center means the spectrum is pulled downward, meaning the potential energy surface is shallow, meaning anharmonicity is strong, meaning thermal conductivity is low. The chain of causation runs through four levels of physics, but the descriptor measures only the endpoint. This works because the intermediate steps are monotonically related in the systems tested.
A descriptor that works is not the same as an explanation, but it reveals where the explanation lives. The phonon band center succeeds because anharmonicity's diverse microscopic mechanisms all produce the same macroscopic signature: spectral softening. When many causes converge to one observable, that observable becomes a reliable diagnostic regardless of which cause is active. The failure mode is equally clear: any mechanism that produces strong anharmonicity without spectral softening will break the descriptor. The centroid is a bet that the dominant channel is always the same. Knowing what the bet is makes it useful; knowing when it fails makes it honest.
(arXiv:2603.18791)