Quantum thermal transport in nanostructures

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 with 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 also briefly review the experimental status of the thermal transport measurements in nanostructures.PACS. 05.60.Gg quantum transport -44.10.+i heat conduction -65.80.+n thermal properties of small particles, nanocrystals, and nanotubes

Full-counting statistics of heat transport in harmonic junctions: Transient, steady states, and fluctuation theorems

“…For diffusive systems, the answer is given by Fourier's law [11][12][13] which is true only in the linear response regime, i.e., when the temperature difference between the baths is small. However for harmonic or ballistic systems, the heat current is given by a Landauer-like formula [3,7,10] which was first derived for electronic transport. Landauer formula on the contrary to the Fourier's law is true for arbitrary temperature differences between the leads.…”

Intrinsic anisotropy of thermal conductance in graphene nanoribbons

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