Machine learning interatomic potentials as efficient tools for obtaining reasonable phonon dispersions and accurate thermal conductivity: A case study of typical two-dimensional materials

The accurate description of phonon dispersion of two-dimensional (2D) materials demonstrates significance in many research fields of condensed matter physics. In this paper, we systematically calculate the phonon spectra and transport properties of six representative 2D materials (encompassing single-element and binary compounds with flat, buckled, and puckered backbone geometries) by means of density functional theory (DFT) and two machine learning interatomic potentials [MLIPs, on-the-fly machine learning potential (FMLP), and moment tensor potential (MTP)]. The results show that the acoustic out-of-plane flexural (ZA) dispersion of the 2D materials are always and easily exhibiting non-quadratic dispersion phenomena near the center of the Brillouin zone by using the pure DFT calculation method. This phenomenon contradicts physics and reflects intuitively from the non-zero group velocity at Gamma point. However, no matter which MLIP (FMLP/MTP) the calculation is based on, it could solve such behavior perfectly, where the ZA mode conforms to the quadratic dispersion relationship in the long-wavelength limit. Our results further demonstrate that compared to the pure DFT calculation, the FMLP and MTP method could quickly and relatively accurately obtain the lattice thermal conductivities of graphene, silicene, phosphorene, SiC, MoS2, and GeS. The findings presented in this work provide a solution about the pseudophysical phenomenon of ZA dispersions in 2D materials with the pure DFT calculation, which will greatly facilitate research areas such as phonon thermal transport, flexural mechanics, and electron-acoustic coupling.