General formula for the thermoelectric transport phenomena based on Fermi liquid theory: Thermoelectric power, Nernst coefficient, and thermal conductivity

On the basis of linear response transport theory, the general expressions for the thermoelectric transport coefficients, such as thermoelectric power $(S),$ Nernst coefficient (ν), and thermal conductivity (κ), are derived by using Fermi liquid theory. The obtained expression is exact for the most singular term in terms of 1/γₖ* (γₖ* being the quasiparticle damping rate). We utilize Ward identities for the heat velocity which is derived by the local energy conservation law. The derived expressions enable us to calculate various thermoelectric transport coefficients in a systematic way, within the framework of the conserving approximation of Baym and Kadanoff. Thus the present expressions are very useful for studying strongly correlated electrons such as high-Tc superconductors, organic metals, and heavy fermion systems, where the current vertex correction (VC) is expected to play important roles. By using the derived expression, we calculate the thermal conductivity κ in a free-dispersion model up to second order with respect to the on-site Coulomb potential U. We find that it is slightly enhanced due to the VC for the heat current, although the VC for electron current makes the conductivity (σ) of this system diverge, reflecting the absence of the umklapp process.