Many-body theory for the lattice thermal conductivity of crystalline thermoelectrics

Thermoelectric materials provide a way to generate electricity in a safe, reliable and sustainable manner. A key property to maximize their efficiency is their lattice thermal conductivity. Modern methods to model this quantity for crystalline solids are either limited by their computational cost (molecular dynamics simulations) or by the quasiparticle approximation used in the Boltzmann transport equation (BTE), which is questionable for bad thermal conductors. We have developed a new methodology for the lattice thermal conductivity using many-body perturbation theory and Hardy's energy-flux operator to overcome these difficulties. It treats the thermal conductivity on a full quantum level, taking into account phonon-phonon correlations beyond the quasiparticle approximation, and is invariant with respect to the gauge choice for the heat flux operator. Importantly, it only requires the same computational cost as the BTE. The method provides a basis to include other effects, such as disorder and electron-phonon interactions and may be applied to the most thermally resistive crystals, such as tin-selenide. We thereby significantly extend the range of materials accessible for lattice thermal conductivity calculations via high-throughput calculations.