With the dimension of materials shrinking into nanoscale, there has been growing interest in the Kapitza resistance which inhibits overall thermal transport. In this work, using the non-equilibrium Green's function method, we systematically investigate the optimized interfacial couplers with various gradient materials for phonon transport across one-dimensional atomic hetero-junction models. Relative to the optimized homogenous couplers, the mass-graded or coupling-graded structures are found to be applicable to improve the interfacial thermal conductance of two lead materials with both mismatched impedance and mismatched cutoff frequencies. For the couplers with both geometric graded mass and geometric graded coupling, the interfacial thermal conductance can be maximum enhanced (nearly up to sixfold enhancement on interfacial thermal conductance compared to the optimized homogenous case). The underlying mechanism of phonon transport enhancement by the optimized coupler is investigated by the phonon transmission coefficient: on the one hand, this kind of coupler is able to maximally suppress the destructive interference for transmitted phonon waves; on the other hand, the constructive interference for the transmitted phonon is also largely improved. Our findings may offer guidance for advanced thermal interface materials design.

Interfacial thermal resistance (ITR, or Kapitza resistance) is the bottleneck that limits the further growth of density for integrated circuit. In this paper, we study the interfacial thermal coupling between two nonlinear systems by using a onedimensional FPUβ heterojunction model through molecular dynamics simulation. It is found that the ITR first decreases rapidly and then increases slowly with the increase of interface coupling coefficient (ICC). When the nonlinearity is weak, the optimal ICC can be explained by selfconsistent phonon theory and effective phonon theory. We also find a double scale behavior in heterojunctions. The study of optimal interfacial thermal coupling for two nonlinear systems has potential applications in reducing the ITR between real materials.

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In modern information technology, as integration density increases rapidly and the dimension of materials reduces to nanoscale, interfacial thermal transport (ITT) has attracted widespread attention of scientists. This review introduces the latest theoretical development in ITT through one-dimensional (1D) atomic junction model to address the thermal transport across an interface. With full consideration of the atomic structures in interfaces, people can apply the 1D atomic junction model to investigate many properties of ITT, such as interfacial (Kapitza) resistance, nonlinear interface, interfacial rectification, and phonon interference, and so on. For the ballistic ITT, both the scattering boundary method (SBM) and the non-equilibrium Green's function (NEGF) method can be applied, which are exact since atomic details of actual interfaces are considered. For interfacial coupling case, explicit analytical expression of transmission coefficient can be obtained and it is found that the thermal conductance maximizes at certain interfacial coupling (harmonic mean of the spring constants of the two leads) and the transmission coefficient is not a monotonic decreasing function of phonon frequency. With nonlinear interaction-phonon-phonon interaction or electron-phonon interaction at interface, the NEGF method provides an efficient way to study the ITT. It is found that at weak linear interfacial coupling, the nonlinearity can improve the ITT, but it depresses the ITT in the case of strong-linear coupling. In addition, the nonlinear interfacial coupling can induce thermal rectification effect. For interfacial materials case which can be simulated by a two-junction atomic chain, phonons show interference effect, and an optimized thermal coupler can be obtained by tuning its spring constant and atomic mass.