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 thesweet spotcondition, 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 couplingJmediated by a quantum spinS. This spin-exchange induced PMM spillover effect provides a spectroscopic protocol for determining the quantum statistics ofSthrough 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 ofJ, 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.