Green-Kubo formalism for thermal conductivity with Slater-Koster tight binding

The Green-Kubo formalism is a formally exact method to determine lattice thermal conductivity of materials from heat-flux autocorrelation functions. However, evaluating heat flux in the context of electronic-structure-based molecular dynamics is nontrivial, hindering the formalism's wider application. Here we present an exact expression of heat flux for Slater-Koster tight binding (TB). This expression takes full advantage of the local orbitals and is straightforward to implement in various TB approaches. Using local orbitals, the present approach is computationally efficient and thus opens an alternative avenue to determine the thermal conductivity of a broad class of materials, especially for those complex systems unsuitable for more expensive ab initio simulations.