Universal correlation between boson peak and quasi-localized modes in solids

The low-temperature specific heat capacity C_ph of ideal crystals can be effectively described by the classical Debye T³ law. However, in amorphous solids and defective crystals, the reduced phonon heat capacity, C_ph/T³, consistently deviates from the Debye model, exhibiting the well-known non-Debye excess anomaly, namely the boson peak (BP). In this work, we systematically study the low-temperature heat capacity C_p across a wide range of solids, finding that C_p can be accurately described by the soft potential model. The C_ph/T³ of these solids begins to deviate from the Debye prediction near the characteristic temperature T_C and displays a pronounced excess hump at T_BP, which is the characteristic temperature of BP. We find that the reduced BP in both glasses and crystals exhibits a universal behavior, which can be described by an empirical function Δ*. Furthermore, a linear correlation between T_C and T_BP is observed among solids regardless of their topology, which reveals a universal connection between the BP and quasilocalized modes in solids. The result provides experimental support for the soft potential model, which may underpin the explanation of low-temperature anomalies and the formation of the BP in solids.