Josephson effects between the Kitaev ladder superconductors

Abstract

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 \thetaθ between these two ladder systems as well as the phase difference \phiϕ between the parallel chains in each ladder system. The total energy of the junction at T = 0T=0 is calculated by a numerical diagonalization method as functions of \thetaθ, \phiϕ, and also a transverse hopping t_{\perp}t⊥ in the ladders. We find that, by controlling t_{\perp}t⊥ and \phiϕ, the junction exhibits not only the fractional Josephson effect for the phase difference \thetaθ, but also the usual 0-junction and even \piπ-junction properties.