## Poster presentation

**Finite size quantization of mid-gap Majorana states of Rashba-nanowires**

__Nico Leumer__^{1,2}, Harald Schmid^{1,3}, Magdalena Marganska^{1}, Milena Grifoni^{1}

*
1 University of Regensburg
2 Donostia International Physics Center
3 Dahlem Center for Complex Quantum Systems, Freie Universität Berlin*

Propelled by new fabrication techniques, research on the rich physics of unconventional magnetic features, so called π-magnetism, of graphene derivatives developed into an attractive field [1,2]. The repulsion of former unpaired, localized electrons (pinned energetically close to the Fermi level) is the physical origin. Although these electrons may or may not manifest generally non-trivial topological character of the host material, the formation of edge states in magnetization noticed recently hints to it [3]. Within the literature and rather familiar to researchers of the Majorana community, terms such as “hybridization” or “spatial overlap” are frequently met. Concerning Majorana zero modes, these expressions describe the energy splitting away from zero to exponentially small energy states (w.r.t. the Fermi level) and their subsequent transformation into Majorana fermions residing at the system’s edges.

Although overlap arguments satisfy our most fundamental intuition, there is more beneath the surface as first meets the eye. Based on past experience [4,5], the “overlap” masks quite interesting finite size effects in allegiance with open boundary conditions. Similarities between the theoretical description of π-magnetism and Majorana fermions, hints at the same being true for the former as well.

In my contribution I will (shortly) motivate my reasoning. Turning to Majorana fermions, I will report on newest results on finite size effects on the mid-gap states imposed by open boundary conditions for the experimental relevant semi conducting Rashba nanowires and how the wave functions spatial profile impacts quantum transport. In the same way, we might expect interesting quantization effects for the lowest electron excitations in π-magnetism systems.

[1] D. G. de Oteyza and T. Frederiksen, J. Phys.: Condens. Matter 34 443001 (2022)

[2] S. Sengupta, T. Frederiksen and G. Giedke, Phys. Rev. B 107, 224433 (2023)

[3] R. Ortiz, G. Giedke and T. Frederiksen, Phys. Rev. B 107, L100416 (2023)

[4] N. Leumer et. al. 2020 J. Phys.: Condens. Matter 32 445502 (2020)

[5] N. Leumer et. al., Phys. Rev. B 103, 165432 (2021)