Testing the formation of Majorana states using Majorana polarization

Cristina Bena

doi:10.1016/j.crhy.2017.09.005

Prix Anatole-et-Suzanne-Abragam de l'Académie des sciences 2016

Testing the formation of Majorana states using Majorana polarization
[Étude de la formation d'états de Majorana en utilisant la polarisation de Majorana]

Cristina Bena ¹

¹ Institut de physique théorique, Université Paris-Saclay, CEA, CNRS, Orme des Merisiers, 91191 Gif-sur-Yvette, France

Comptes Rendus. Physique, 2016 Prizes of the French Academy of Sciences /Prix 2016 de l’Académie des sciences, Volume 18 (2017) no. 5-6, pp. 349-357.

Résumé
Abstract

Nous étudions la formation d'états de Majorana dans les supraconducteurs en utilisant la polarisation de Majorana, qui permet d'évaluer localement le caractère de Majorana d'un état donné. Nous introduisons la définition du vecteur de polarisation de Majorana et du critère correspondant permettant d'identifier un état de Majorana, et nous l'appliquons à certains cas simples, tels qu'un fil unidimensionnel à couplage spin-orbite, sujet à un champ magnétique de type Zeeman, et proximisé par un supraconducteur, ainsi qu'à une jonction NS junction faite d'un tel fil. Nous appliquons ce critère à des rubans et à des carrés soumis aux mêmes conditions physiques. Notre analyse démontre la nécessité qu'il y a à utiliser le paramètre d'ordre local de la polarisation de Majorana pour caractériser les états de Majorana, particulièrement dans les systèmes de taille finie.

We study the formation of Majorana states in superconductors using Majorana polarization, which can locally evaluate the Majorana character of a given state. We introduce the definition of the Majorana polarization vector and of the corresponding criterion to identify a Majorana state, and we apply it to some simple cases such as a one-dimensional wire with spin-orbit coupling, subject to a Zeeman magnetic field, and proximitized by a superconductor, as well as to an NS junction made with such a wire. We also apply this criterion to two-dimensional finite-size strips and squares subject to the same physical conditions. Our analysis demonstrates the necessity of using the Majorana polarization local order parameter to characterize the Majorana states, particularly in finite-size systems.

Publié le : 2017-05-01

DOI : 10.1016/j.crhy.2017.09.005

Keywords: Majorana fermions, Edge state, Topological superconductors
Mots-clés : Fermions de Majorana, États de bord, Supraconducteurs topologiques

Affiliations des auteurs :

Cristina Bena ¹

¹ Institut de physique théorique, Université Paris-Saclay, CEA, CNRS, Orme des Merisiers, 91191 Gif-sur-Yvette, France

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Cristina Bena. Testing the formation of Majorana states using Majorana polarization. Comptes Rendus. Physique, 2016 Prizes of the French Academy of Sciences /Prix 2016 de l’Académie des sciences, Volume 18 (2017) no. 5-6, pp. 349-357. doi : 10.1016/j.crhy.2017.09.005. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2017.09.005/

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