Designing XY and Dzyaloshinskii--Moriya couplings in Majorana Cooper pair boxes

TL;DR

This paper proposes a method to engineer various spin couplings, including XY and Dzyaloshinskii--Moriya interactions, in networks of Majorana Cooper pair boxes using RKKY interactions mediated by conduction electrons.

Contribution

It demonstrates how to realize and tune complex spin interactions in Majorana Cooper pair boxes, expanding their potential for quantum simulation.

Findings

Arbitrary spin couplings can be engineered in MCB networks.

XY and DM interactions are realizable and tunable via gate voltages.

MCBs serve as a versatile platform for quantum spin system design.

Abstract

We theoretically study how to design spin couplings in networks of Majorana Cooper pair boxes (MCBs) connected by multiple normal-metal leads. The inter-box interaction is generated by the conduction-electron-mediated Ruderman--Kittel--Kasuya--Yosida (RKKY) interaction. We show that the connectivity of Majoranas to the leads enables arbitrary types of couplings. As concrete examples, we show the realization of the XY exchange interaction and the Dzyaloshinskii--Moriya (DM) interaction, which are difficult to implement in previously proposed MCB-based schemes. The sign and magnitude of the couplings can be tuned continuously via gate-controlled tunneling amplitudes. These results establish MCBs as a versatile platform for engineered quantum spin systems.