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Funding Information: National Natural Science Foundation of China Academy of Finland Funding Information: Z.F. acknowledges the supports from the National Natural Science Foundation of China (NSFC) (No. 11974059). Z.Z. and Y.C. are grateful for the research computing facilities offered by ITS, HKU. Y.W., H.D., and T.A.-N. acknowledge the support from the Academy of Finland Centre of Excellence program QTF (Project No. 312298) and the computational resources provided by Aalto Science-IT project and Finland's IT Center for Science (CSC). Publisher Copyright: © 2021 American Physical Society. We develop a neuroevolution-potential (NEP) framework for generating neural network-based machine-learning potentials. They are trained using an evolutionary strategy for performing large-scale molecular dynamics (MD) simulations. A descriptor of the atomic environment is constructed based on Chebyshev and Legendre polynomials. The method is implemented in graphic processing units within the open-source gpumd package, which can attain a computational speed over atom-step per second using one Nvidia Tesla V100. Furthermore, per-atom heat current is available in NEP, which paves the way for efficient and accurate MD simulations of heat transport in materials with strong phonon anharmonicity or spatial disorder, which usually cannot be accurately treated either with traditional empirical potentials or with perturbative methods.

Funding Information: Some of the computing for this project was performed on the Sherlock cluster at Stanford University. We would like to thank Stanford University and the Stanford Research Computing Center (SRCC) for providing computational resources and support that contributed to these results. This paper was also partially supported by ASCENT, one of the six centers in JUMP, a Semiconductor Research Corporation (SRC) program sponsored by DARPA. A.J.G. also acknowledges support from the Achievement Rewards for College Scientists (ARCS) Northern California Chapter. T.A-N. has been supported in part by the Academy of Finland through its QTF Center of Excellence (Project No. 312298). Z.F. has been supported by the National Natural Science Foundation of China (NSFC; No. 11974059). Publisher Copyright: © 2021 American Physical Society. The design of applications, especially those based on heterogeneous integration, must rely on detailed knowledge of material properties, such as thermal conductivity (TC). To this end, multiple methods have been developed to study TC as a function of vibrational frequency. Here, we compare three spectral TC methods based on velocity decomposition in homogenous molecular dynamics simulations: Green-Kubo modal analysis (GKMA), the spectral heat current (SHC) method, and a method we propose called homogeneous nonequilibrium modal analysis (HNEMA). First, we derive a convenient per-atom virial expression for systems described by general many-body potentials, enabling compact representations of the heat current, each velocity decomposition method, and other related quantities. Next, we evaluate each method by calculating the spectral TC for carbon nanotubes, graphene, and silicon. We show that each method qualitatively agrees except at optical phonon frequencies, where a combination of mismatched eigenvectors and a large density of states produces artificial TC peaks for modal analysis (MA) methods. Our calculations also show that the HNEMA and SHC methods converge much faster than the GKMA method, with the SHC method being the most computationally efficient. Finally, we demonstrate that our MA implementation in the Graphics Processing Units Molecular Dynamics code on a single graphics processing unit is over 1000 times faster than the existing implementation in the Large-scale Atomic/Molecular Massively Parallel Simulator code on one central processing unit.

Van der Waals heterostructures have exhibited interesting physical properties. In this paper, heat transfer in hybrid coplanar bilayer/monolayer (BL-ML) graphene, as a model layered van der Waals heterostructure, was studied using non-equilibrium molecular dynamics (MD) simulations. The temperature profile and inter- and intra-layer heat fluxes of the BL-ML graphene indicated that, there is no fully developed thermal equilibrium between layers and the drop in the average temperature profile at the step-like BL-ML interface is not attributable to the effect of Kapitza resistance. By increasing the length of the system up to 1 μm in the studied MD simulations, the thermally non-equilibrium region was reduced to a small area near the step-like interface. All MD results were compared to a continuum model and a good match was observed between the two approaches. Our results provide a useful understanding of heat transfer in nano- and micro-scale layered materials and van der Waals heterostructures.

Molecular dynamics (MD) simulations play an important role in studying heat transport in complex materials. The lattice thermal conductivity can be computed either using the Green-Kubo formula in equilibrium MD (EMD) simulations or using Fourier's law in nonequilibrium MD (NEMD) simulations. These two methods have not been systematically compared for materials with different dimensions and inconsistencies between them have been occasionally reported in the literature. Here we give an in-depth comparison of them in terms of heat transport in three allotropes of Si: three-dimensional bulk silicon, two-dimensional silicene, and quasi-one-dimensional silicon nanowire. By multiplying the correlation time in the Green-Kubo formula with an appropriate effective group velocity, we can express the running thermal conductivity in the EMD method as a function of an effective length and directly compare it to the length-dependent thermal conductivity in the NEMD method. We find that the two methods quantitatively agree with each other for all the systems studied, firmly establishing their equivalence in computing thermal conductivity.

Demands for engineering thermal transport properties are ever increasing for a wide range of modern micro-and nanodevices and materials-based energy technologies. In particular, there is a severe situation due to the rapid progress in the synthesis and processing of materials and devices with structural characteristic length on the nanometer scales, which are comparable or even smaller than the intrinsic length scales (such as mean free path and wavelength) of basic energy carriers (such as phonons, electrons, and photons). Although advanced approaches for controlling the electronic and photonic transport have been proposed in the past decades, progress on controlling lattice vibrations (i.e., the phonons) is still far behind. Gaps between the fundamental understandings of the behavior of the basic energy carriers at small scales and the technological demands still remain, particularly from a computer modeling point of view. Herewith, we give a perspective of the computational approaches for predicting the thermal transport properties of low-dimensional materials and nanostructures, which are mainly sorted into three categories: empirical molecular dynamics, anharmonic lattice dynamics based Boltzmann transport equation, and Landauer theory. The advantage and disadvantage of each method are discussed and some possible solutions are suggested. The discussion is focused on fully and accurately characterizing the mode-level phonon behavior, possible all-order phonon scattering process, and incorporation of realistic nanostructures. Moreover, emerging challenges of phonon coupling effects, such as electron-phonon, phonon-photon, and phonon-magnon coupling, are also discussed. We expect that this perspective will stimulate future research in computer modeling of micro-/nanoscale heat transfer beyond traditional phonons.

Two-dimensional materials have unusual phonon spectra due to the presence of flexural (out-of-plane) modes. Although molecular dynamics simulations have been extensively used to study heat transport in such materials, conventional formalisms treat the phonon dynamics isotropically. Here, we decompose the microscopic heat current in atomistic simulations into in-plane and out-of-plane components, corresponding to in-plane and out-of-plane phonon dynamics, respectively. This decomposition allows for direct computation of the corresponding thermal conductivity components in two-dimensional materials. We apply this decomposition to study heat transport in suspended graphene, using both equilibrium and nonequilibrium molecular dynamics simulations. We show that the flexural component is responsible for about two-thirds of the total thermal conductivity in unstrained graphene, and the acoustic flexural component is responsible for the logarithmic divergence of the conductivity when a sufficiently large tensile strain is applied.