Interplay between Coulomb blockade and Josephson effect in a topological superconductor-quantum dot device

TL;DR

This paper investigates the interplay of Coulomb blockade and Josephson effect in a topological superconductor-quantum dot device, revealing unique current-phase relations and $4\,\pi$-periodic Rabi oscillations immune to quasiparticle poisoning.

Contribution

It provides a detailed analysis of the Andreev spectrum and Josephson current in different tunneling regimes of a topological superconductor-quantum dot system, highlighting novel $4\pi$-periodic phenomena.

Findings

In the weak tunneling regime, the Andreev spectrum has two levels per fermion parity sector.

The Rabi oscillation frequency is $4\pi$-periodic and immune to quasiparticle poisoning.

Coulomb charging enhances backscattering effects at the interfaces.

Abstract

We study the behavior of a topological Josephson junction in which two topological superconductors are coupled through a quantum dot. We focus on the case with the bulk superconducting gap being the largest energy scale. Two parameter regimes are investigated: a weak tunneling between the dot and the superconductors, with the dot near its charge degeneracy point, and a strong tunneling regime in which the transmission between the dot and the superconductors is nearly perfect. We show that in the former situation, the Andreev spectrum for each sector with fixed fermion parity consists of only two levels, which gives rise to the nontrivial current-phase relation. Moreover, we study the Rabi oscillation between the two levels and indicates that the corresponding frequency is a $4\pi$-periodic function of the phase difference between the two superconductors, which is immune to the quasiparticle poisoning. In the latter case, we find that the Coulomb charging energy enhances the effect of backscattering at the interfaces between the dot and the superconductors. Both the temperature and the gate-voltage dependence of the critical Josephson current are examined.