Two-site Kitaev sweet spots evolving into topological islands

Arrays of quantum dots forming artificial Kitaev chains provide a versatile platform for realizing and probing Majorana-bound states (MBSs). In short chains, such as the two-site case, these zero-energy excitations — often called Poor Man’s Majoranas (PMMs) — appear only under finely tuned conditions. We investigate how these states evolve as the number of sites increases by combining the Bogoliubov-de Gennes formalism with scattering matrix and Green’s function approaches. Our results show that the discrete sweet spots of short chains broaden into extended “topological islands,” where MBSs become increasingly robust to parameter variations and disorder. A spinful model under finite magnetic fields exhibits similar behavior, with zero-energy plateaus emerging for long chains (N ≥ 20). We further show that conductance measurements through a side-coupled quantum dot [1, 2] can directly reveal the non-Abelian character of the MBSs [3]. This work demonstrates how increasing the chain length relaxes the stringent tuning required to obtain PMMs, bridging the gap between few-site realizations and fully developed Majorana modes.

[1] E. Vernek, P. H. Penteado, A. C. Seridonio, and J. C. Egues, Phys. Rev. B 89, 165314 (2014).

[2] D. A. Ruiz-Tijerina, E. Vernek, L. G. G. V. Dias da Silva, and J. C. Egues, Phys. Rev. B 91, 115435 (2015). 

[3] R. A. Dourado, J. C. Egues, and P. H. Penteado, arXiv: 2501.19376v1.