Spin-exchange induced spillover on poor man’s Majoranas in minimal Kitaev chains

The 'poor man's Majoranas' (PMMs) (Leijnse and Flensberg 2012<i>Phys. Rev. B</i><b>86</b>134528) devoid of topological protection can 'spill over' from one edge into another of the minimal Kitaev chain when perturbed electrostatically. As aftermath, this leads to a delocalized Majorana fermion (MF) at both the edges. Additionally, according to recent differential conductance measurements in a pair of superconducting and spinless quantum dots (QDs), such a PMM picture was brought to reality (Dvir<i>et al</i>2023<i>Nature</i><b>614</b>445; ten Haaf<i>et al</i>2024<i>Nature</i><b>630</b>329). Based on this scenario, we propose the spillover of the PMM when its QD is exchange coupled to a quantum spin<i>S</i>. We show that if this QD is perturbed by the exchange coupling<i>J</i>, solely the half2S+1(2S+2)of the fine structure stays explicit for a fermionic (bosonic)S.Concurrently, the other half squeezes itself as the delocalized MF zero-mode. Particularly, turning-off the superconductivity the multiplicity2S+1holds regardless the spin statistics. Meanwhile, the PMM spillover induced by<i>J</i>becomes a statistics dependent effect. Hence, our findings contribute to the comprehension of spin-phenomena interplay with superconductivity in minimal Kitaev chains, offering insights for future quantum computing devices hosting PMMs.