Linking the thermal-conductivity plateau to the <i>Cp</i> / <i>T</i> 3 hump in amorphous and complex disordered solids

We investigate the relationship between the low-temperature thermal conductivity plateau and the hump in reduced heat capacity (Cp/T3) in a range of disordered solids, including polymers, glasses, and complex crystalline materials. Using a unified framework that separates particle-like propagation (Peierls term) and wave-like coherence contributions, we analyze experimental data to extract characteristic temperatures associated with each contribution. Our results demonstrate that the temperature of the Cp/T3 hump Tmax correlates systematically with the onset of the thermal-conductivity plateau and the crossover between particle-like and coherence-dominated transport. Normalized scaling of the particle-like contribution reveals a universal behavior across chemically and structurally diverse systems. These findings provide clear evidence of a direct link between the thermal-conductivity plateau and low-temperature heat capacity anomalies, establishing Tmax it as a robust characteristic parameter for predicting thermal transport in disordered solids.