Theoretical analysis of oscillatory terms in lattice heat-current time correlation functions and their contributions to thermal conductivity

Abstract

Lattice heat-current time correlation functions for insulators and semiconductors obtained using molecular dynamics (MD) simulations exhibit features of both pure exponential decay and oscillatory-exponential decay. For some materials the oscillatory terms contribute significantly to the lattice heat conductivity calculated from the correlation functions. However, the origin of the oscillatory terms is not well understood and their contribution to the heat conductivity is accounted for by fitting them to empirical functions. Here, a translationally invariant expression for the heat current in terms of creation and annihilation operators is derived. By using this full phonon-picture definition of the heat current and applying the relaxation-time approximation, we explain, at least in part, the origin of the oscillatory terms in the lattice heat-current correlation function. We discuss the relationship between the crystal Hamiltonian and the magnitude of the oscillatory terms. A solvable one-dimensional model is used to illustrate the potential importance of terms that are omitted in the commonly used phonon-picture expression for the heat current. While the derivations are fully quantum mechanical, classical-limit expressions are provided that enable direct contact with classical quantities obtainable from MD.

Many-body Green's function approach to lattice thermal transport

“…In the case of the Hardy current operator the present result correspond to the ones given in Ref. [25,26], but differ from more recent derivations [19,47]. We show that such a discrepancy originates from the procedure used to implement the limit of frequency-independent phonon lifetimes within the realtime Green's function, and we show that this affects only the description of interband effects.…”

“…As a result, these works have sparked interest in understanding how to describe accurately -and in a computationally affordable form -thermal transport. The most recent theoretical efforts [9,19,47,48] were thus motivated by a quantitative estimate of interband effects, but they actually led to a broader perspective about the microscopic description of heat transport, highlighting the failures of Peierls-Boltzmann formulation in complex crystals [9], where interband transitions emerge.…”

“…[9,10] the corresponding quantum operator for the heat current is not explicitly given, from the form of the matrix elements of phonon velocities presented in [9] one can already infer a different structure for it with respect to the one given by Hardy. A second apparent source of discrepancies between recent [19,47] and previous [25,26] works based on the Green-Kubo formalism concerns the implementation of interaction effects for phonons. Indeed, while the original papers [25,26] followed the standard route of implementing self-energy corrections in the frequency domain via a generalized phonon spectral function, in Ref.…”

“…Indeed, while the original papers [25,26] followed the standard route of implementing self-energy corrections in the frequency domain via a generalized phonon spectral function, in Ref. [19,47] the calculations are done in the time-domain, with approximated schemes needed to assign frequency-independent lifetimes to each phonon mode.…”

Assessment of Thermal Transport Properties of Group-III Nitrides: A Classical Molecular Dynamics Study with Transferable Tersoff-Type Interatomic Potentials

“…Since we try to produce pair potential parameters, calculated errors in optic phonons is acceptable up to the deviation of the longitudinal-transverse optic splitting effect. The noticeable difference in high-lying optic modes can be considered as the weakness of generated parameter set, however, the effect of these modes on lattice thermal conductivity is relatively less than the acoustic modes due to their low phonon group velocities [68,69]. On the other hand, one should consider the in-direct effect of optical modes due to phonon-phonon scattering.…”