  We present systematic theoretical results on thermoelectric effects in
semimetals based on the variational method of the linearized Boltzmann
equation. Inelastic electron-hole scattering is known to play an important role
in the unusual transport of semimetals, including the broad $T^2$ temperature
dependence of the electrical resistivity and the strong violation of the
Wiedemann-Franz law. By treating the inelastic electron-hole scattering more
precisely beyond the relaxation time approximation, we show that the Seebeck
coefficient when compensated depends on the screening length of the Coulomb
interaction as well as the Lorenz ratio (the ratio of thermal to electric
conductivity due to electrons divided by temperature). It is found that
deviations from the compensation condition significantly increase the Seebeck
coefficient, along with crucial suppressions of the Lorenz ratio. The result
indicates that uncompensated semimetals with the electron-hole scattering have
high thermoelectric efficiency when the phonon contribution to thermal
conductivity is suppressed.
