Würzburg ToCoTronics Colloquium

The search for Majorana particles [1] is important both for fundamental understanding and possible topological quantum computation [2]. Since Majorana particles are an equal superposition of particle and antiparticle, they are naturally sought in superconductors, in the form of Majorana zero modes (MZMs). From Kitaev’s seminal paper [3], the quest to engineer devices capable of hosting MZMs is still ongoing. The search for new compounds hosting robust MZMs however requires a deeper understanding of these states.

Fu and Kane [4] showed that a MZM can emerge in the vortex-core states of an s-wave superconductor on top of a three-dimensional strong topological insulator (TI).

We study a d + id superconductor placed on a TI (d+id + Dirac model) [5] and show that the vortex-core MZMs can carry a nontrivial angular momentum. This establishes new ‘flavors’ of Majorana modes, independent of the Chern number and classified with respect to the windings of the order parameter and underlying normal state.

Contextually, we discuss the topological protection of the MZM. The small bulk gap, quasiparticle poisoning by trivial in-gap states, and their huge localization length might in fact severely limit the stability of MZMs in the d+id + Dirac model, in contrast to earlier claims. Nevertheless, the possibility of having different flavors of MZMs – in the form of angular momentum or something else – can provide a unique path forward for the study of MZMs.

References:

[1] A. Yazdani, F. von Oppen, B. I. Halperin, and A. Yacoby, Science 380, eade0850 (2023).
[2] D. Aasen, M. Aghaee, Z. Alam, M. Andrzejczuk, A. Antipov, M. Astafev, L. Avilovas, A. Barzegar, B. Bauer, J. Becker, et al.,  Phys. Rev. Res. 7, 041002 (2025)
[3] A. Kitaev, Usp. Fiz. Nauk 17, 131 (2001).
[4] Liang Fu, and C. L. Kane, Phys. Rev. Lett. 100, 096407 (2008). 
[5] G. Venditti, C. Berthod, L. Rademaker, Phys. Rev. B 113 014502 (2026).