  We calculate the thermoelectric response coefficients of three-dimensional
Dirac or Weyl semimetals as a function of magnetic field, temperature, and
Fermi energy. We focus in particular on the thermoelectric Hall coefficient
$\alpha_{xy}$ and the Seebeck coefficient $S_{xx}$, which are well-defined even
in the dissipationless limit. We contrast the behaviors of $\alpha_{xy}$ and
$S_{xx}$ with those of traditional Schr\"{o}dinger particle systems, such as
doped semiconductors. Strikingly, we find that for Dirac materials
$\alpha_{xy}$ acquires a constant, quantized value at sufficiently large
magnetic field, which is independent of the magnetic field or the Fermi energy,
and this leads to unprecedented growth in the thermopower and the
thermoelectric figure of merit. We further show that even relatively small
fields, such that $\omega_c \tau \sim 1$ (where $\omega_c$ is the cyclotron
frequency and $\tau$ is the scattering time), are sufficient to produce a more
than $100\%$ increase in the figure of merit.
