  The topological and thermoelectric properties of (EuO)$_{n}$/(MgO)$_{m}$(001)
superlattices (SLs) are explored using density functional theory calculations
including a Hubbard $U$ term together with Boltzmann transport theory. In
(EuO)$_{1}$/(MgO)$_{3}$(001) SL at the lattice constant of MgO a sizable band
gap of 0.51 eV is opened by spin-orbit coupling (SOC) due to a band inversion
between occupied localized Eu $4f$ and $5d$ conduction electrons. This
inversion between bands of opposite parity is accompanied by a spin
reorientation in the spin-texture along the contour of band crossing
surrounding the $\Gamma$ point and leads to a Chern insulator with $C$=-1, also
confirmed by the single edge state. Moreover, this Chern insulating phase shows
promising thermoelectric properties, e.g. a Seebeck coefficient between 400 and
800 $\mu$VK$^{-1}$. A similar SOC-induced band inversion takes place also in
the ferromagnetic semimetallic (EuO)$_{2}$/(MgO)$_{2}$(001) SL. Despite the
vanishing band gap, it leads to a substantial anomalous Hall conductivity with
values up to -1.04 $e^{2}/h$ and somewhat lower thermoelectric properties. Both
systems emphasize the relation between non-trivial topological bands and
thermoelectricity also in systems with broken inversion symmetry.
