Majorana modes in quantum dots coupled via a floating superconducting island

TL;DR

This paper investigates how Majorana modes can be realized in a minimal quantum dot setup coupled via a floating superconducting island, analyzing the effects of charging energy and identifying conditions for Majorana sweet spots.

Contribution

It extends previous models by analyzing a two-quantum-dot system with a floating superconductor, deriving analytic conditions for Majorana sweet spots, and benchmarking with a microscopic model.

Findings

Majorana sweet spots exist even without charge-degeneracy tuning

Degeneracy involves states with a well-defined particle number

Analytic expressions for Majorana splitting are derived

Abstract

Majorana modes can be engineered in arrays where quantum dots (QDs) are coupled via grounded superconductors, effectively realizing an artificial Kitaev chain. Minimal Kitaev chains, composed by two QDs, can host fully-localized Majorana modes at discrete points in parameter space, known as Majorana sweet spots. Here, we extend previous works by theoretically investigating a setup with two QDs coupled via a floating superconducting island. We study the effects of the charging energy of the island and the properties of the resulting minimal Kitaev chain. We initially employ a minimal perturbative model, valid in the weak QD-island coupling regime, to derive analytic expressions for the Majorana sweet spots and the splitting of the ground state degeneracy as a function of tunable physical parameters. The conclusions from this perturbative approximation are then benchmarked using a microscopic model that explicitly describes the internal degrees of freedom of the island. Our work shows the existence of Majorana sweet spots, even when the island is not tuned at a charge-degeneracy point. In contrast to the Kitaev chains in grounded superconductors, these sweet spots involve a degeneracy between states with a well-defined number of particles.