Towards a unifying description of Andreev, Majorana, quasi-Majorana, and Shockley states*

Majorana bound states can be, in principle, realized in the nontrivial phase of proximized nanowires with strong spin-orbit coupling or magnetic atom chains deposited on a conventional superconductor. In these 1D systems, zero-energy Majorana edge modes localize at the domain walls between topologically distinct phases, similar to the case of Jackiw-Rebbi solitons, which are solutions of the Majorana-Dirac equation on an inhomogeneous background. On the other hand, topologically trivial Andreev states below the particle-hole gap, sometimes called quasi-Majorana states, can originate from disorder or spatial inhomogeneities. Distinguishing between Majorana and Andreev states is an ongoing challenge that generated intense debate in the scientific community. Indeed, there is a continuous crossover between topologically nontrivial Majorana and topologically trivial Andreev states induced by smooth inhomogeneities, and this crossover can occur without closing the bulk gap [1]. This Majorana/Andreev crossover is driven by field inhomogeneities with a length scale comparable to the nanowire length and larger than the Majorana localization length. Here, we describe nontrivial Majorana bound states, Andreev bound states induced by spatial inhomogeneities and disorder, Shockley states, and Jackiw-Rebbi solitons in a unifying framework, introducing a characteristic length scale that can unambiguously distinguish between different regimes [2].

[1] Marra, Nigro, J. Phys.: Condens. Matter 34 124001 (2022), arXiv:2112.00757

[2] Marra, Nigro, in preparation