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

The 'poor man's Majoranas' (PMMs) (Leijnse and Flensberg 2012Phys. Rev. B86134528) 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 (Dviret al2023Nature614445; ten Haafet al2024Nature630329). Based on this scenario, we propose the spillover of the PMM when its QD is exchange coupled to a quantum spinS. We show that if this QD is perturbed by the exchange couplingJ, 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 byJbecomes 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.