Malviya Nikhil, Ravichandran Navaneetha K
Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012, India.
J Phys Condens Matter. 2025 Jun 19;37(26). doi: 10.1088/1361-648X/ade219.
The Callaway approximation to the linearized Peierls-Boltzmann equation (LPBE) is often used to describe the steady-state and the transient phonon dynamics in ultrahigh thermal conductivity () materials, particularly under cryogenic conditions, due to its low computational cost relative to the full LPBE solution. However, the predictive capability of the Callaway approximation to the LPBE is not well-established, since a direct quantitative comparison with the full solution of LPBE from first-principles does not exist in the literature under these conditions. Here, we present a quantitative comparison of the steady-state and transient thermal transport predictions from the Callaway approximation and the full LPBE solution for 20 different semiconductor materials below 200 K. We find that the Callaway approximation successfully predicts the conventional Fourier-diffusive and the quasiballistic heat transfer regimes at temperatures where momentum-dissipative Umklapp processes (U-processes) are comparable or only slightly weaker than the momentum-conserving Normal processes (N-processes). As the temperature is further lowered, the U-processes become exceptionally weaker than the N-processes-a necessary condition for the unconventional hydrodynamic heat flow regime, and the Callaway model fails to closely approximate the full LPBE solution. Using quantitative comparisons of the predicted steady-stateand temporal temperature dynamics in a pump-probe experiment called the transient grating, we uncover a strong correlation between the failure of the Callaway approximation to the LPBE and the onset of phonon hydrodynamics, as the temperature is lowered. Our work provides guidelines to determine the applicability of the Callaway approximation to the LPBE to describe phonon dynamics at low temperatures.
对于线性化的派尔斯 - 玻尔兹曼方程（LPBE），卡拉韦近似法常用于描述超高热导率材料中的稳态和瞬态声子动力学，特别是在低温条件下，因为相对于完整的LPBE解，它的计算成本较低。然而，卡拉韦对LPBE的近似法的预测能力尚未得到充分确立，因为在这些条件下，文献中不存在与基于第一性原理的LPBE完整解的直接定量比较。在此，我们给出了卡拉韦近似法和完整LPBE解对20种不同半导体材料在200 K以下的稳态和瞬态热输运预测的定量比较。我们发现，在动量耗散的倒逆过程（U过程）与动量守恒的正规过程（N过程）相当或仅略弱于N过程的温度下，卡拉韦近似法成功地预测了传统的傅里叶扩散和准弹道热传递模式。随着温度进一步降低，U过程变得比N过程异常更弱——这是非常规流体动力学热流模式的必要条件，并且卡拉韦模型无法紧密逼近完整的LPBE解。通过在一个称为瞬态光栅的泵浦 - 探测实验中对预测的稳态和时间温度动力学进行定量比较，我们发现随着温度降低，卡拉韦对LPBE的近似法失效与声子流体动力学的出现之间存在很强的相关性。我们的工作为确定卡拉韦对LPBE的近似法在描述低温下声子动力学的适用性提供了指导。
