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Extrinsic higher-order topological corner states in AB-stacked transition-metal dichalcogenides

Higher-order topological insulators (HOTIs) are a novel type of topological phases which supports $d$-dimensional topological boundary states in $D$-dimensional systems with $D-d>1$. In this work, we theoretically predict that interlayer couplings in AB-stacked bilayer transition-metal dichalcogenides (TMDs) lead to the emergence of extrinsic second-order topological phases, where corner states are induced by the band inversion of zigzag edge bands. We find that the systems feature a quantized multiband Berry phase defined for a zigzag nanoribbon geometry, unveiling the nontrivial topological properties of its two zigzag edges. With detailed investigation into the bilayer TMDs under different geometries, we find two types of boundary-obstructed corner states arising from different corner terminations of either the same type of or heterogeneous zigzag edges. The topological nature of these corner states and their degeneracy is further analyzed with both the crystalline symmetries of different geometries, and a topological phase transition of the Berry phase induced by a layer-dependent onsite energy.