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The existence of fractionally quantized topological corner states serves as akey indicator for two-dimensional second-order topological insulators (SOTIs),yet has not been experimentally observed in realistic materials. Here, based oneffective model analysis and symmetry arguments, we propose a strategy forachieving SOTI phases with in-gap corner states in two dimensional systems withantiferromagnetic (AFM) order. We uncover by a minimum lattice model that theband topology originates from the interplay between intrinsic spin-orbitalcoupling and interlayer AFM exchange interactions. Using first principlescalculations, we show that the 2D AFM SOTI phases can be realized in(MnBi$_2$Te$_4$)(Bi$_2$Te$_3$)$_{m}$ films. Moreover, we demonstrate that thenontrivial corner states are linked to rotation topological invariants underthree-fold rotation symmetry $C_3$, resulting in $C_3$-symmetric SOTIs withcorner charges fractionally quantized to $\frac{n}{3} \lvert e \rvert $ (mod$e$). Due to the great recent achievements in(MnBi$_2$Te$_4$)(Bi$_2$Te$_3$)$_{m}$ systems, our results providing reliablematerial candidates for experimentally accessible AFM higher-order bandtopology would draw intense attentions.

Design of Antiferromagnetic Second-order Band Topology with Rotation Topological Invariants in Two Dimensions