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We investigate van der Waals (vdW) heterostructures made of germanene,stanene or silicene with hexagonal Boron Nitride (h-BN). The intriguingtopological properties of these buckled honeycomb materials can be maintainedand further engineered in the heterostructures, where the competition betweenthe substrate effect and external electric fields can be used to control thetunable topological phase transitions. Using such heterostructures as buildingblocks, various vdW topological domain walls (DW) are designed, along whichthere exist valley polarized quantum spin Hall edge states orvalley-contrasting edge states which are protected by valley(spin)- resolvedtopological charges and can be tailored by the patterning of theheterojunctions and by external fields.

van der Waals Heterostructures of Germanene, Stanene and Silicene with Hexagonal Boron Nitride and Their Topological Domain Walls