Josephson effects between the Kitaev ladder superconductors

TL;DR

This paper explores the complex Josephson effects in Kitaev ladder superconductors, revealing controllable fractional, 0, and π junction behaviors influenced by inter-chain coupling and phase differences.

Contribution

It provides a theoretical analysis of Josephson effects in Kitaev ladder systems, highlighting the tunability of junction properties through system parameters.

Findings

Observation of fractional Josephson effect controlled by system parameters

Identification of 0 and π junction behaviors in the ladder system

Demonstration of tunable Josephson effects via transverse hopping and phase differences

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 $\theta$ between these two ladder systems as well as the phase difference $\phi$ 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 $\theta$, $\phi$, and also a transverse hopping $t_{\perp}$ in the ladders. We find that, by controlling $t_{\perp}$ and $\phi$, the junction exhibits not only the fractional Josephson effect for the phase difference $\theta$, but also the usual 0-junction and even $\pi$-junction properties.