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The Benalcazar-Bernevig-Hughes(BBH) model is one of the most representativehigher-order topological insulators with different bulk-edge correspondencecomparing conventional topological states. In this work, we propose to realizea couple-BBH model with glide reflection symmetry by coupling two topologicallydistinct BBH models. Such a system gives rise to intriguing properties beyondthe traditional BBH model. A topological phase transition from higher-ordertopological phase to a semimetal has been predicted in this system.Furthermore, the band crossing points and nodal ring protected by glidereflection symmetry has also been explored. Our work provides a viewpoint todemonstrate the versatile phenomena induced by the interplay betweenhigher-order topology and nonsymmorphic symmetries.

Higher-order topological insulator with glide reflection symmetry