Efficient Josephson diode effect on a two-dimensional topological insulator with asymmetric magnetization

The Josephson diode effect (JDE) is a nonreciprocal transport phenomenon in which, the oppositely flowing critical currents are asymmetric and has great potential for applications in superconducting electronic devices. In this study, we present a theoretical investigation of the JDE on the two helical edge states of a two-dimensional topological insulator with asymmetric magnetization on each edge. It is shown that for a single-edge Josephson junction, the optimal JDE efficiency is approximately $35%$, but for a double-edged Josephson junction with appropriate asymmetric magnetization on two edges, the JDE efficiency can be enhanced to around $68%$. The origin of this enhancement lies in the fact that the two individual magnetizations not only can independently affect the asymmetric critical currents of the single-edge Josephson junction but also can shift the current-phase relation of the junction.