Exchange interaction between two quantum dots coupled through a superconducting island

TL;DR

This paper theoretically investigates how two quantum dots coupled via a superconducting island exhibit different spin alignments depending on particle number and superconductor bandwidth, revealing conditions for ferromagnetic or antiferromagnetic coupling.

Contribution

It provides a detailed analysis of spin interactions in a quantum dot-superconductor system, highlighting the impact of bandwidth and particle number on magnetic alignment, which informs design of quantum devices.

Findings

Antiferromagnetic alignment occurs at even particle number with negligible bandwidth.

Ferromagnetic alignment occurs at finite bandwidth for even particle number.

Odd particle number always results in ferromagnetic alignment.

Abstract

We present a theoretical study of a system consisting of a superconducting island and two quantum dots, a possible platform for building qubits and Cooper pair splitters, in the regime where each dot hosts a single electron and, hence, carries a magnetic moment. We focus on the case where the dots are coupled to overlapping superconductor states and we study whether the spins are ferromagnetically or antiferromagnetically aligned. We show that if the total number of particles is even, the spins align antiferromagnetically in the flatband limit, i.e., when the bandwidth of the superconductor is negligibly small, but ferromagnetically if the bandwidth is finite and above some value. If the total number of particles is odd, the alignment is ferromagnetic independently from the bandwidth. This implies that the results of the flatband limit are applicable only within restricted parameter regime for realistic superconducting qubit systems and that some care is required in applying simplified models to devices such as Cooper pair splitters.