Manipulation of helical states revealed by crossed Andreev reflection

Abstract

The edge states of a quantum spin Hall insulator exhibit helical properties, which has generated significant interest in the field of spintronics. Although it is predicted theoretically that Rashba spin-orbit coupling can effectively regulate edge state spin, experimental characterization of this spin control remains challenging. Here, we propose utilizing crossed Andreev reflection to probe the efficiency of gate voltage control on edge state spin. We calculate the transport properties of the quantum spin Hall isolators-superconductor heterojunction by using non-equilibrium Green's function method. We find that the probabilities of crossed Andreev reflection, electron transmission, and non-local conductance all include the relative spin rotation angle $\theta$ caused by the Rashba spin-orbit coupling in the helical edge states. Notably, when the incident energy is close to the superconducting gap, the differential conductance $G_2\propto-\cos{\theta}$. Thus, the influence of Rashba spin-orbit coupling on edge state spin can be quantitatively characterized by crossed Andreev reflection, which provides a feasible scheme for experimental testing.