Josephson Diode Effect for a Kitaev Ladder System

TL;DR

This paper demonstrates a geometry-induced Josephson diode effect in a Kitaev ladder system, where nonreciprocal supercurrent arises from phase differences and topology, enabling magnetic-field-free superconducting rectification.

Contribution

It introduces a novel geometry-based mechanism for Josephson diode effect in topological Kitaev ladders, linking symmetry breaking, topology, and transport properties.

Findings

Nonreciprocal Josephson current without magnetic fields or spin-orbit coupling.

Maximum diode efficiency occurs at intermediate interleg coupling.

Majorana modes influence the diode response and are identified via topological invariants.

Abstract

We study the Josephson diode effect realized purely by geometry in a Kitaev-ladder Josephson junction composed of two parallel spinless $p$-wave chains coupled by an interleg hopping $t_\perp$. The junction is governed by two phases: the superconducting phase difference across the weak link, $\theta$, and the leg-to-leg phase difference, $\phi$. For $\phi\notin \{0, \pi\}$ (mod $2\pi$), time-reversal symmetry is broken, and the absence of leg-exchange symmetry leads to a breakdown of the antisymmetry of the current-phase relation, yielding nonreciprocal Josephson transport without magnetic fields or spin-orbit coupling. By resolving transport into bonding and antibonding channels defined by $t_\perp$, it is shown that the leg phase acts as an effective phase shift for interband ($p_\nu/p_{-\nu}$) tunneling, whereas the same-band ($p_\nu/p_\nu$) contribution remains unshifted. These channels arise at different perturbative orders and, together with the $4\pi$-periodic Majorana channel that emerges near the topological transition, interfere to produce a pronounced diode response. The class-D Pfaffian invariant identifies the parameter regime where the ladder hosts Majorana zero modes. Bogoliubov-de Gennes calculations reveal a dome-like dependence of the diode efficiency $\eta$ on $t_\perp$: $\eta\to 0$ for $t_\perp\to 0$ and for large $t_\perp$, with a maximum at intermediate coupling that is tunable by $\phi$. The present results establish a field-free, geometry-based route to superconducting rectification in one-dimensional topological systems and specify symmetry and topology conditions for optimizing the effect in ladder and network devices.