Josephson current controlled by Fermi-arc surface states of Weyl semimetals

In this paper, the supercurrent of the superconductor (SC)–Weyl semimetal–SC Josephson junction hybrid system is studied based on the Landauer-Büttiker formula combined with the nonequilibrium Green's method. According to the different edge states, the Fermi arcs are divided into three regions: the symmetric, topological, and insulated regions, which are defined by the azimuthal angle $\theta$ and the transverse momentum $k_z$. Here, $\theta$ is the azimuthal angle between the symmetry axis of the Fermi arcs and the normal of the Josephson junction. It is found that the supercurrent is suppressed in the symmetric region. In the topological region, the supercurrent increases with increasing $\theta$. The supercurrent is almost zero in the insulated region due to the presence of the energy gap. The total supercurrent summed over all $k_z$ channels increases and then decreases with increasing $\theta$, that is, $\theta$ can control the value of the supercurrent. In addition, the magnetic field and the azimuthal angle $\theta$ can adjust the phase transition of the Josephson junction, allowing it to be a 0, $\pi$, or ${\phi }_0$ junction. These properties provide research ideas for controlling the value of the supercurrent and the Josephson junction phase transition and play an important role in the development and application of superconducting electronic devices.