  The cooperation of electronic correlation and spin-orbit coupling can
stabilize magnetic topological insulators which host novel quantum phenomena
such as the quantum anomalous Hall state also known as Chern insulator (CI).
Here, we investigate the existence of magnetic topological insulators with
antiferromagnetic (AF) order in heavy-fermion materials. Our analysis relies on
the half-filled Kane-Mele-Kondo (KMK) model with the AF Kondo interaction
$J_{\rm K}$ coupling the spin of itinerant electrons with a $S=1/2$ localized
spin at each lattice site. We consider the N\'eel AF ordering with the local
magnetization not only perpendicular ($z$-AF ordering) but also parallel
($xy$-AF ordering) to the honeycomb plane. We show that in the absence of an
energy offset between the two sublattices of the honeycomb structure the system
is always topologically trivial. There is a transition from the trivial $xy$-AF
insulator ($xy$-AFI) to the trivial Kondo insulator (KI) upon increasing
$J_{\rm K}$. We unveil that an alternating sublattice potential can lead to the
stabilization of the $z$-AFCI and the $z$-AF quantum spin Hall insulator
($z$-AFQSHI). We address the charge excitations in the bulk as well as at the
edges of the KMK model. We provide a systematic comparison between the size of
the charge gap in the AFCI in heavy-fermion materials and the size of the
charge gap in the AFCI in transition-metal compounds. Our findings can guide
the future experimental studies searching for AF topological insulators in
novel class of systems which can survive up to higher temperatures.
