Solutions of the Peierls-Boltzmann transport equation using inputs from density functional theory calculations have been successful in predicting the thermal conductivity in a wide range of materials. In the case of two-dimensional (2D) materials, the accuracy of this method can depend highly on the shape of the dispersion curve for flexural phonon (ZA). As a universal feature, very recent theoretical studies have shown that the ZA branch of 2D materials is quadratic. However, many prior thermal conductivity studies and conclusions are based on a ZA branch with linear components. In this paper, we systematically study the impact of the long-wavelength dispersion of the ZA branch in graphene, silicene, and $\alpha$-nitrophosphorene to highlight its role on thermal conductivity predictions. Our results show that the predicted $\kappa$ value, its convergence and anisotropy, as well as phonon lifetimes and mean free path can change substantially even with small linear to pure quadratic corrections to the shape of the long-wavelength ZA branch. Also, having a pure quadratic ZA dispersion can improve the convergence speed and reduce uncertainty in this computational framework when different exchange-correlation functionals are used in the density functional theory calculations. Our findings may provide a helpful guideline for more accurate and efficient thermal conductivity estimation in mono- and few-layer 2D materials.

中文翻译：

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声弯曲声子二次色散对二维材料热传输的重要性

使用密度泛函理论计算输入的 Peierls-Boltzmann 传输方程的解已经成功地预测了各种材料的热导率。在二维 (2D) 材料的情况下，该方法的准确性在很大程度上取决于弯曲声子 (ZA) 的色散曲线的形状。作为一个普遍特征，最近的理论研究表明，二维材料的 ZA 分支是二次的。然而，许多先前的热导率研究和结论都是基于具有线性分量的 ZA 分支。在本文中，我们系统地研究了 ZA 支链在石墨烯、硅烯和$\alpha$-硝基磷烯以突出其在热导率预测中的作用。我们的结果表明，预测$\kappa$即使对长波长 ZA 分支的形状进行小的线性到纯二次校正，其收敛性和各向异性以及声子寿命和平均自由程也会发生显着变化。此外，当密度泛函理论计算中使用不同的交换相关函数时，具有纯二次 ZA 色散可以提高收敛速度并减少该计算框架中的不确定性。我们的发现可能为在单层和少层 2D 材料中更准确和有效地估计热导率提供有用的指导。