Antiferromagnetic topological insulators in heavy-fermion systems

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.