Second-order Band Topology in Antiferromagnetic (MnBi$_2$Te$_4$)(Bi$_2$Te$_3$)$_{m}$ Films

Abstract

The existence of fractionally quantized topological corner states serves as a key indicator for two-dimensional second-order topological insulators (SOTIs), yet has not been experimentally observed in realistic materials. Here, based on first-principles calculations and symmetry arguments, we propose a strategy for achieving SOTI phases with in-gap corner states in (MnBi$_2$Te$_4$)(Bi$_2$Te$_3$)$_{m}$ films with antiferromagnetic (AFM) order. Starting from the prototypical AFM MnBi$_2$Te$_4$ bilayer, we show by an effective lattice model that such SOTI phase originate from the interplay between intrinsic spin-orbital coupling and interlayer AFM exchange interactions. Furthermore, we demonstrate that the nontrivial corner states are linked to rotation topological invariants under three-fold rotation symmetry $C_3$, resulting in $C_3$-symmetric SOTIs with corner 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 reliable material candidates for experimentally accessible AFM higher-order band topology would draw intense attentions.Comment: 6 pages, 4 figure