Lattice thermal conductivity varies enormously across materials — from diamond at ~2,000 W/mK to glasses below 1. Predicting which materials conduct heat well requires understanding phonon scattering, which requires understanding anharmonicity, which requires solving the full lattice dynamics problem. This is computationally expensive. A simpler descriptor would help.
The phonon band center — the frequency-weighted average of the phonon density of states — turns out to capture most of the relevant physics. Higher phonon band center means lighter atoms, stiffer bonds, and less anharmonic scattering. The descriptor correlates inversely with the Grüneisen parameter (which measures how much phonon frequencies shift under compression, the standard metric of anharmonicity) and directly with lattice thermal conductivity across multiple material classes.
What makes this work is the compression. The full phonon spectrum contains thousands of modes with individual frequencies, lifetimes, and group velocities. The band center collapses all of that into one number — a center of mass in frequency space. That this single number predicts thermal conductivity means that the details of the spectrum matter less than its overall position on the frequency axis. Materials with high-frequency phonons (light, stiff) conduct heat well. Materials with low-frequency phonons (heavy, soft) don't. The spectrum's shape, its gaps, its fine structure — these refine the prediction but don't determine it. The zeroth-order physics is in the mean.
This is a reminder that not all properties require detailed models. Some are controlled by a single moment of the underlying distribution. The phonon band center is to thermal conductivity what the center of mass is to rigid body dynamics: the point where complexity collapses into a single predictive coordinate.
(arXiv:2603.18791)