Importance of quadratic dispersion in acoustic flexural phonons for thermal transport of two-dimensional materials

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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 $\ensuremath{\alpha}$-nitrophosphorene to highlight its role on thermal conductivity predictions. Our results show that the predicted $\ensuremath{\kappa}$ 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.