Implementation of merged topological edge states in square-root topological circuits

Merging topological edge states (TESs) holds great significance as it offers higher Q factors compared to isolated edge states. Here, we introduce a mirror-stacking method for constructing the merged topological edge states (MTESs) within the bilayer square-root Su–Schrieffer–Heeger (SSH) model. This method enables the Hamiltonian of the bilayer model to be decomposed into two mutually independent subspaces. The TESs in the subspaces can be tuned through interlayer coupling strength. When TESs from two subspaces overlap, it leads to the emergence of MTESs. In addition, we have successfully realized MTESs in a mirror-stacked square-root SSH circuit. Our results clearly demonstrate that the MTESs exhibit superior energy localization and higher Q factors compared to isolated edge states. The findings of this paper may enhance our understanding of topological edge states and square-root SSH model, potentially paving the way for the development of devices featuring strong robustness and enhanced Q factors.