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

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