Lattice thermal conductivity of ZrSe2 based on the anharmonic phonon approach and on-the-fly machine learning force fields

Abstract

The lattice thermal conductivity (LTC) of ZrSe$_2$, a typical layered transition metal disulfide, has been calculated using a hybrid approach that combines force field molecular dynamics (MD) simulation and Boltzmann transport equation (BTE). In this approach, the phonon quasiparticle picture of each normal mode can be obtained directly by the velocity autocorrelation function and its power spectrum projected in $q$-space. By employing the retarded one phonon Green's function method, the phonon quasiparticle frequency and lifetime of each independent normal mode are effectively determined. On-the-fly machine learning force fields combine the precision of quantum mechanics and the scale of classical MD to analyze sizable supercells with long-wavelength phonons. This yields accurate LTC by using sufficient $q$-samples in the Brillouin zone, which cannot be achieved at the \emph{ab initio} molecular dynamics scale. The convergent LTC tensor of bulk and monolayer ZrSe$_2$ decays faster with increasing temperature than the well-known $\frac{1}{T}$ scale, which is typically observed when considering only three-phonon scattering. The phonon lifetime and mean free path exhibit significant dependence on temperature. MD simulations encompass all orders of anharmonic effects, thereby enabling an accurate description of anharmonic interactions between phonons at finite temperatures. Moreover, this approach respects the contribution of each normal mode to the LTC based on the BTE, which facilitates the quantitative analysis of phonon anharmonic properties and the role of specific normal modes.