The quantum spin Hall (QSH) state, a kind of two-dimensional (2D) topological insulator [1][2][3][4][5], is characterized by the helical edge states, which are topologically protected by the time reversal symmetry. The spin-up and spin-down carriers of the same edge in the helical edge states run strictly toward opposite directions [2], indicating that the intraedge backscattering is thoroughly suppressed. Resultantly, the edge states have important applications in topological spintronic device and quantum information processing such as the promising creator and detector for entangled electron pairs [6,7]. Besides, though the edge-state conduction and the spin polarization of the edge current have been confirmed, a direct evidence for the helical spin texture of the edge states lacks enough. For a narrow QSH insulator, electron wave functions are confined within the strip width and overlap, thus such an effect makes
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.
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