Revisiting the Poor Man’s Majoranas: the spin–exchange induced spillover effect

We give a review on Poor Man's Majorana (PMM) modes, which are theoretically established in the minimal Kitaev chain implementation consisting of two grounded, spinless quantum dots (QDs) operating at the<i>sweet spot</i>condition, where electron cotunneling and crossed Andreev reflection amplitudes achieve precise balance. Particularly, we systematically review, within the Green's functions theoretical framework, the PMM hybridization dynamics under spin-exchange perturbations proposed by some of us in Sanches et al 2025 J. Phys.: Condens. Matter 37 205601, which demonstrates a characteristic spatial delocalization when subjected to an exchange coupling<i>J</i>mediated by a quantum spin<i>S</i>. This spin-exchange induced PMM spillover effect provides a spectroscopic protocol for determining the quantum statistics of<i>S</i>through the emergent multi-level structure in the proximal QD's density of states. Our principal theoretical result establishes that the exchange interaction generates2S+2(2S+1) satellite states symmetrically distributed about the zero-bias anomaly, serving as a definitive signature of bosonic (fermionic) spin statistics. As novelty, we demonstrate that multi-terminal environmental coupling induces significant suppression of the spin-exchange spillover mechanism. Under constrained variations of<i>J</i>, this effectively localizes the perturbed PMM within its host QD, preventing spatial hybridization with adjacent site. The absence of topological protection in this minimal Kitaev realization is strategically leveraged to: (i) develop a novel spectroscopic technique for quantum spin characterization through PMM hybridization signatures; (ii) propose the 'environmentally induced protection', an engineered dissipative spectral stabilization for PMMs against exchange fluctuations in multi-terminal architectures.