First-principles Green-Kubo method for thermal conductivity calculations

We present a first-principles approach to calculate the phonon thermal conductivity based on the Green-Kubo formalism. In this approach, the density functional theory energy is distributed to each atom, and a two-step method in the molecular dynamics is introduced to avoid the atomic position $\mathbf{R}$ wrapping problem in a periodic system when the heat current is calculated. We show that this first-principles Green-Kubo approach is particularly suitable for disordered systems like amorphous and liquid, where the thermal conductivities are small due to strong phonon scattering but difficult to be calculated using anharmonic interaction energy. We have applied our method to liquid Ar, liquid Si, and amorphous Si. The calculated thermal conductivities agree well with previous theoretical and experimental results. We have also compared our method to previous works combining first-principles simulations with the Green-Kubo formalism.