摘要：The narrow quantum spin Hall (QSH) insulator is characterized by interedge coupling, which could feature exotic transport phenomena, and thus serves as the key element for topological superconducting electronic devices. Herein, we theoretically explore possible Josephson π states in a QSH insulator strip touching on two s-wave superconductors in the presence of the interedge coupling. It is shown that the interedge coupling could give rise to a 0 - π transition modulated by the gate voltage, originating from an additional π phase difference caused by the interedge backscattering. The 0 - π transition in turn can manifest the helical spin texture of the edge states. A considerable residual value of the supercurrent at the 0 - π transition point is always exhibited, suggesting a very efficient performance of the device as a supercurrent switch. Moreover, the region of coexisting 0 and π states is found fairly large, which can be used to improve accuracy in the design of a π superconducting quantum interference device.
