单原子层薄膜热传导性质的晶格动力学研究(I)——声子线宽和热传导系数公式
Lattice Dynamics Study on the Thermal Conduction Properties of Single Atomic Layer Films (I)—Formulas for Phonon Linewidth and Thermal Conductivity
摘要: 本文在运用晶格动力学和Hardy能量通量公式得到单原子层薄膜的晶格振动的频率、原子位移、原子动量、晶格振动能量，非和谐势能和能量通量等公式，在此基础上运用Green函数理论和Green-Kubo公式推导单原子层薄膜的声子谱线宽度公式和热传导系数公式，结果表明单原子层薄膜的热传导系数为所有声子的热传导系数之和，而单个声子的热传导系数与其速度、声子能量、声子寿命或自由程密切相关。
Abstract: The formulas for lattice vibration frequency, atomic displacement and momentum, lattice vibration energy, an harmonic potential energy and energy flux of lattice vibration in single atomic layer film are derived in this paper on the basis of the lattice dynamics theory, and then the formulas for phonon line width and thermal conductivity are derived with the aid of Green function theory and Green-Kubo formula. The result shows that the thermal conductivity of the film is the sum of contribution from every single phonon which is closely related to phonon’s velocity, energy and lifetime or free path.
文章引用：黄建平, 贺业鹏. 单原子层薄膜热传导性质的晶格动力学研究(I)——声子线宽和热传导系数公式[J]. 现代物理, 2020, 10(6): 140-145. https://doi.org/10.12677/MP.2020.106016

参考文献

[1] Koran, K. (2019) Structural, Chemical and Electrical Characterization of Organocyclotriphosphazene Derivatives and Their Graphene-Based Composites. Journal of Molecular Structure, 1179, 224-232. [Google Scholar] [CrossRef] 
[2] Tang, D., Wang, Q., Wang, Z., et al. (2018) Highly Sensitive Wearable Sensor Based on a Flexible Multi-Layer Graphene Film Antenna. Science Bulletin, 63, 574-579. [Google Scholar] [CrossRef] [PubMed]
[3] Xu, X., Pereira, L.F.C., Wang, Y., et al. (2014) Length-Dependent Thermal Conductivity in Suspended Single-Layer Graphene. Nature Communications, 5, Article ID: 3689. [Google Scholar] [CrossRef] [PubMed]
[4] Tang, Q. (2004) A Molecular Dynamics Simulation: The Effect of Finite Size on the Thermal Conductivity in a Single Crystal Silicon. Molecular Physics, 102, 1959-1964. [Google Scholar] [CrossRef] 
[5] Zhu, L. and Li, B. (2014) Low Thermal Conductivity in Ultrathin Carbon Nanotube. Scientific Reports, 4, Article ID: 4917. [Google Scholar] [CrossRef] [PubMed]
[6] Mazur, P. and Mara-dudin, A.A. (1981) Mean-Square Displacements of Atoms in Thin Crystal Films. Physical Review B, 24, 2296. [Google Scholar] [CrossRef] 
[7] Maradudin, A.A. and Fein, A.E. (1962) Scattering of Neutrons by An-harmonic Crystal. Physical Review, 128, 2589-2608. [Google Scholar] [CrossRef] 
[8] Semwal, B.S. and Sharma, P.K. (1972) Heat Conductivity of an Anhar-monic Crystal. Physical Review B, 5, 3909-3913. [Google Scholar] [CrossRef] 
[9] Turney, J.E., Landry, E.S., McGaughey, A.J.H., et al. (2009) Predicting Phonon Properties and Thermal Conductivity from Anharmonic Lattice Dynamics Calculations and Molecular Dynamics Simulations. Physics Review, 79, Article ID: 064301. [Google Scholar] [CrossRef] 
[10] Kubo, R. (1957) Statistical Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications in Magnetic and Conduction Problems. Journal of the Physical Society of Japan, 12, 570-586. [Google Scholar] [CrossRef] 
[11] Hardy, R.J. (1963) Energy Flux Operator for a Lattice. Physical Review, 132, 168-177. [Google Scholar] [CrossRef]