Karyn Le Hur : Majorana Fermions, Superconductivity and Topological Correspondences

In this Talk, I show how protected Majorana fermions at zero energy can occur in s-wave superconducting wires as a result of the coupling with one magnetic impurity [1]. I introduce a general quantum field theory model generalizing the Jackiw-Rebbi model of topological interfaces to Majorana fermions. I show a correspondence onto the Kitaev p-wave superconducting wire [2] from the bulk and from local probes. I also show a correspondence onto the J1-J2 quantum spin model or the 1D quantum compass model [3], which is also optimistic for the realization and probes of Majorana fermions at zero energy. This talk then leads us to think about new solvable spin models from one to two dimensions [3] and to a new classification scheme for topological phases [4].

[1] Karyn Le Hur, Comptes Rendus Physique of Academie des Sciences 27 (2026), pp. 307-322; Karyn Le Hur, EuroPhysics Letters 49 (6), pp. 768-774 (2000).

[2] A. Kitaev, Uspekhi Fizicheskikh Nauk, 2001, Volume 171, supplement № 10, Pages 131–136

[3] K. Le Hur, F. Yang, M. Korolev, Phys. Rev. B 113, L121106 (2026); M. Korolev, F. Yang, E. Sorensen, K. Le Hur, in preparation; K. Le Hur, A. Soret, F. Yang, Phys. Rev. B 96, 205109 (2017); F. Yang, K. Plekhanov, K. Le Hur, Phys. Rev. Research 2, 013005 (2020)

[4] K. Le Hur, Physics Reports 1104, 1-42 (2025); K. Le Hur and A. Baldanza, Comptes Rendus Physique of Academie des Sciences, 27 (2026), pp. 323-351; F. Del Pozo, L. Herviou, O. Dmytruk, K. Le Hur, Phys. Rev. B 111, 075170 (2025); K. Le Hur, K. Narayanan, O. Manas Chambert, arXiv:2608.09415