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Quantum thermal transport in nanostructures

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  • J.-S. Wang
  • J. Wang
  • J. T. Lü

Abstract

In this colloquia review we discuss methods for thermal transport calculations for nanojunctions connected to two semi-infinite leads served as heat-baths. Our emphases are on fundamental quantum theory and atomistic models. We begin with an introduction of the Landauer formula for ballistic thermal transport and give its derivation from scattering wave point of view. Several methods (scattering boundary condition, mode-matching, Piccard and Caroli formulas) of calculating the phonon transmission coefficients are given. The nonequilibrium Green's function (NEGF) method is reviewed and the Caroli formula is derived. We also give iterative methods and an algorithm based on a generalized eigenvalue problem for the calculation of surface Green's functions, which are starting point for an NEGF calculation. A systematic exposition for the NEGF method is presented, starting from the fundamental definitions of the Green's functions, and ending with equations of motion for the contour ordered Green's functions and Feynman diagrammatic expansion. In the later part, we discuss the treatments of nonlinear effects in heat conduction, including a phenomenological expression for the transmission, NEGF for phonon-phonon interactions, molecular dynamics (generalized Langevin) with quantum heat-baths, and electron-phonon interactions. Some new results are also shown. We briefly review the experimental status of the thermal transport measurements in nanostructures. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008

Suggested Citation

  • J.-S. Wang & J. Wang & J. T. Lü, 2008. "Quantum thermal transport in nanostructures," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 62(4), pages 381-404, April.
    • Handle: RePEc:spr:eurphb:v:62:y:2008:i:4:p:381-404
    DOI: 10.1140/epjb/e2008-00195-8
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    Cited by:

    1. Qinshu Li & Fang Liu & Song Hu & Houfu Song & Susu Yang & Hailing Jiang & Tao Wang & Yee Kan Koh & Changying Zhao & Feiyu Kang & Junqiao Wu & Xiaokun Gu & Bo Sun & Xinqiang Wang, 2022. "Inelastic phonon transport across atomically sharp metal/semiconductor interfaces," Nature Communications, Nature, vol. 13(1), pages 1-7, December.
    2. Jianhua Zhou & Donghua Li, 2021. "The thermoelectric properties of four metastable graphene allotrope nanoribbons with nonalternant topology," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(8), pages 1-7, August.

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