Green's Function Solution of the Wigner Transport Equation for Arbitrary Heat Sources in the Relaxation-Time Approximation

The Peierls formulation of the phonon Boltzmann transport equation in solids, while successful in describing transport in high thermal conductivity materials like silicon and diamond, fails to describe heat transport in low thermal conductivity materials like La₂Zr₂O₇ (LZO) and CsPbBr₃ (CPB). The Wigner formalism addresses this shortcoming by including interaction mechanisms that allow heat carriers to tunnel between different phonon branches, along with the usual particle-like scattering of phonons. We present a Green's function solution to the Wigner transport equation in the relaxation-time approximation that accepts arbitrary source terms. Using first-principles data, we study space- and frequency-effects of the thermal conductivity in LZO and CPB. Strikingly, we find that deviations from the bulk thermal diffusivity of LZO can be observed at experimentally accessible length scales near room temperature. Our open-source implementation is documented and openly available to the community.