Spontaneous modulation of superconducting phase in Kitaev ladder

TL;DR

This paper theoretically investigates a Kitaev ladder composed of two coupled Kitaev chains, revealing how competing Josephson couplings induce phase modulation, ground state degeneracy, and controllability via external fields.

Contribution

It introduces a novel model of a Kitaev ladder with competing Josephson couplings, demonstrating phase modulation and ground state degeneracy control.

Findings

Phase modulation of superconducting order parameter due to frustration.

Double degeneracy of ground states induced by phase modulation.

Manipulation of ground states using external electric and magnetic fields.

Abstract

We study theoretically the two Kitaev chains put in parallel, i.e., Kitaev ladder, coupled by Josephson junction. The $\pi$-junction between the Majorana bound states at the ends of the chains competes with the usual Josephson coupling along the chain, and this frustration leads to the modulation of the phase difference of the superconducting order parameter between the two chains. We show that this modulation gives the double degeneracy of the ground states, which can be manipulated by external electric and magnetic fields.