  Dirac/Weyl semimetals hosting linearly-dispersing bands have received recent
attention for potential thermoelectric applications, since their
ultrahigh-mobility carriers could generate large thermoelectric and Nernst
power factors. To optimize these efficiencies, the Fermi energy needs to be
chemically controlled in a wide range, which is generally difficult in bulk
materials because of disorder effects from the substituted ions. Here it is
shown that the Fermi energy is tunable across the Dirac point for layered
magnet EuMnBi$_2$ by partially substituting Gd$^{3+}$ for Eu$^{2+}$ in the
insulating block layer, which dopes electrons into the Dirac fermion layer
without degrading the mobility. Clear quantum oscillation observed even in the
doped samples allows us to quantitatively estimate the Fermi energy shift and
optimize the power factor (exceeding 100 $\mu$W/K$^2$cm at low temperatures) in
combination with the first-principles calculation. Furthermore, it is shown
that Nernst signal steeply increases with decreasing carrier density beyond a
simple theoretical prediction, which likely originates from the field-induced
gap reduction of the Dirac band due to the exchange interaction with the Eu
moments. Thus, the magnetic block layer provides high controllability for the
Dirac fermions in EuMnBi$_2$, which would make this series of materials an
appealing platform for novel transport phenomena.
