Spectral decomposition of thermal conductivity: Comparing velocity decomposition methods in homogeneous molecular dynamics simulations

The design of new applications, especially those based on heterogeneous\nintegration, must rely on detailed knowledge of material properties, such as\nthermal conductivity (TC). To this end, multiple methods have been developed to\nstudy TC as a function of vibrational frequency. Here, we compare three\nspectral TC methods based on velocity decomposition in homogenous molecular\ndynamics simulations: Green-Kubo modal analysis (GKMA), the spectral heat\ncurrent (SHC) method, and a method we propose called homogeneous nonequilibrium\nmodal analysis (HNEMA). First, we derive a convenient per-atom virial\nexpression for systems described by general many-body potentials, enabling\ncompact representations of the heat current, each velocity decomposition\nmethod, and other related quantities. Next, we evaluate each method by\ncalculating the spectral TC for carbon nanotubes, graphene, and silicon. We\nshow that each method qualitatively agrees except at optical phonon\nfrequencies, where a combination of mismatched eigenvectors and a large density\nof states produces artificial TC peaks for modal analysis methods. Our\ncalculations also show that the HNEMA and SHC methods converge much faster than\nthe GKMA method, with the SHC method being the most computationally efficient.\nFinally, we demonstrate that our single-GPU modal analysis implementation in\nGPUMD (Graphics Processing Units Molecular Dynamics) is over 1000 times faster\nthan the existing LAMMPS (Large-scale Atomic/Molecular Massively Parallel\nSimulator) implementation on one CPU.\n