Heat Transport in Insulators from Ab Initio Green-Kubo Theory

  • Stefano BaroniEmail author
  • Riccardo Bertossa
  • Loris Ercole
  • Federico Grasselli
  • Aris Marcolongo
Living reference work entry


The Green-Kubo theory of thermal transport has long be considered incompatible with modern simulation methods based on electronic-structure theory, because it is based on such concepts as energy density and current, which are ill-defined at the quantum-mechanical level. Besides, experience with classical simulations indicates that the estimate of heat-transport coefficients requires analysing molecular trajectories that are more than one order of magnitude longer than deemed feasible using ab initio molecular dynamics. In this paper we report on recent theoretical advances that are allowing one to overcome these two obstacles. First, a general gauge invariance principle has been established, stating that thermal conductivity is insensitive to many details of the microscopic expression for the energy density and current from which it is derived, thus permitting to establish a rigorous expression for the energy flux from Density-Functional Theory, from which the conductivity can be computed in practice. Second, a novel data analysis method based on the statistical theory of time series has been proposed, which allows one to considerably reduce the simulation time required to achieve a target accuracy on the computed conductivity. These concepts are illustrated in detail, starting from a pedagogical introduction to the Green-Kubo theory of linear response and transport, and demonstrated with a few applications done with both classical and quantum-mechanical simulation methods.



This work was supported in part by the MaX EU Centre of Excellence, grant no 676598. SB, LE, and FG are grateful to Davide Donadio for insightful discussions all over the Summer of 2017 and beyond.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Stefano Baroni
    • 1
    • 2
    Email author
  • Riccardo Bertossa
    • 3
  • Loris Ercole
    • 3
  • Federico Grasselli
    • 3
  • Aris Marcolongo
    • 4
    • 5
  1. 1.SISSA – Scuola Internazionale Superiore di Studi AvanzatiTriesteItaly
  2. 2.CNR Istituto Officina dei MaterialiTriesteItaly
  3. 3.SISSATriesteItaly
  4. 4.Cognitive Computing and Computational Sciences DepartmentIBM ResearchZürichSwitzerland
  5. 5.THEOS-MARVELÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland

Section editors and affiliations

  • Davide Donadio
    • 1
  1. 1.University of California, DavisDavisUSA

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