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Nernst effect beyond the relaxation-time approximation

Motivated by recent interest in the Nernst effect in cuprate superconductors, we calculate this magneto-thermo-electric effect for an arbitrary (anisotropic) quasiparticle dispersion relation and elastic scattering rate. The exact solution of the linearized Boltzmann equation is compared with the commonly used relaxation-time approximation. We find qualitative deficiencies of this approximation, to the extent that it can get the sign wrong of the Nernst coefficient. Ziman's improvement of the relaxation-time approximation, which becomes exact when the Fermi surface is isotropic, also cannot capture the combined effects of anisotropy in dispersion and scattering.