Josephson effects between the Kitaev ladder superconductors - Osamu Kanehira, Hiroki Tsuchiura (SciPost Physics Proceedings, 2023)
The two-leg ladder system consisting of the Kitaev chains is known to exhibit a richer phase diagram than that of the single chain. We theoretically investigate the variety of the Josephson effects between the ladder systems. We consider the Josephson phase difference $θ$ between these two ladder systems as well as the phase difference $φ$ between the parallel chains in each ladder system. The total energy of the junction at $T = 0$ is calculated by a numerical diagonalization method as functions of $θ$, $φ$, and also a transverse hopping $t_{\perp}$ in the ladders. We find that, by controlling $t_{\perp}$ and $φ$, the junction exhibits not only the fractional Josephson effect for the phase difference $θ$, but also the usual 0-junction and even $π$-junction properties.