The European Physical Journal B

, Volume 62, Issue 4, pp 381–404

Quantum thermal transport in nanostructures


DOI: 10.1140/epjb/e2008-00195-8

Cite this article as:
Wang, JS., Wang, J. & Lü, J. Eur. Phys. J. B (2008) 62: 381. doi:10.1140/epjb/e2008-00195-8


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.


05.60.Gg quantum transport 44.10.+i Heat conduction 65.80.+n Thermal properties of small particles, nanocrystals, and nanotubes 

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008

Authors and Affiliations

  1. 1.Center for Computational Science and Engineering and Department of PhysicsNational University of SingaporeSingaporeSingapore
  2. 2.College of Physical Science and Technology, Yangzhou UniversityYangzhouP.R. China