The easily accessible experimental signatures of Majorana modes are ambiguous and only probe topology indirectly: for example, quasi-Majorana states mimic most properties of Majoranas. Establishing a correspondence between an experiment and a theoretical model known to be topological resolves this ambiguity. Here we demonstrate that already theoretically determining whether a finite system is topological is by itself ambiguous. In particular, we show that the scattering topological invariant -- a probe of topology most closely related to transport signatures of Majoranas -- has multiple biases in finite systems. For example, we identify that quasi-Majorana states also mimic the scattering invariant of Majorana zero modes in intermediate-sized systems. We expect that the bias due to finite size effects is universal, and advocate that the analysis of topology in finite systems should be accompanied by a comparison with the thermodynamic limit. Our results are directly relevant to the applications of the topological gap protocol.
@article{arxiv.2504.01069,
title = {Identifying biases of the Majorana scattering invariant},
author = {Isidora Araya Day and Antonio L. R. Manesco and Michael Wimmer and Anton R. Akhmerov},
journal= {arXiv preprint arXiv:2504.01069},
year = {2025}
}