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, 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
Mot 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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     title = {Testing the formation of {Majorana} states using {Majorana} polarization},
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     pages = {349--357},
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     doi = {10.1016/j.crhy.2017.09.005},
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Cristina Bena. Testing the formation of Majorana states using Majorana polarization. Comptes Rendus. Physique, 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/

Bibliographie
Cité par

[1] E. Majorana Teoria simmetrica dell'elettrone e del positrone, Nuovo Cimento (1924–1942), Volume 14 (2008) no. 4, p. 171 | DOI

[2] A.Y. Kitaev Unpaired Majorana fermions in quantum wires, Phys. Usp., Volume 44 (2001) no. 10S, p. 131 http://stacks.iop.org/1063-7869/44/i=10S/a=S29 (URL)

[3] J. Alicea New directions in the pursuit of Majorana fermions in solid state systems, Rep. Prog. Phys., Volume 75 (2012) no. 7 http://stacks.iop.org/0034-4885/75/i=7/a=076501 (URL)

[4] A.P. Mackenzie; Y. Maeno The superconductivity of ${Sr}_{2} {RuO}_{4}$ and the physics of spin-triplet pairing, Rev. Mod. Phys., Volume 75 (2003), pp. 657-712 https://link.aps.org/doi/10.1103/RevModPhys.75.657 (URL) | DOI

[5] S. Nadj-Perge; I.K. Drozdov; B.A. Bernevig; A. Yazdani Proposal for realizing Majorana fermions in chains of magnetic atoms on a superconductor, Phys. Rev. B, Volume 88 (2013) http://link.aps.org/doi/10.1103/PhysRevB.88.020407 (URL) | DOI

[6] H.A. Nilsson; P. Caroff; C. Thelander; M. Larsson; J.B. Wagner; L.-E. Wernersson; L. Samuelson; H.Q. Xu Giant, level-dependent g factors in InSb nanowire quantum dots, Nano Lett., Volume 9 (2009) no. 9, pp. 3151-3156 (pMID: 19736971) | DOI

[7] R.M. Lutchyn; J.D. Sau; S. Das Sarma Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures, Phys. Rev. Lett., Volume 105 (2010) http://link.aps.org/doi/10.1103/PhysRevLett.105.077001 (URL) | DOI

[8] Y. Oreg; G. Refael; F. von Oppen Helical liquids and Majorana bound states in quantum wires, Phys. Rev. Lett., Volume 105 (2010) http://link.aps.org/doi/10.1103/PhysRevLett.105.177002 | DOI

[9] V. Mourik; K. Zuo; S.M. Frolov; S.R. Plissard; E.P.A.M. Bakkers; L.P. Kouwenhoven Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices, Science, Volume 336 (2012) no. 6084, pp. 1003-1007 http://science.sciencemag.org/content/336/6084/1003 (URL) | DOI

[10] M.T. Deng; C.L. Yu; G.Y. Huang; M. Larsson; P. Caroff; H.Q. Xu Anomalous zero-bias conductance peak in a Nb-InSb nanowire-nb hybrid device, Nano Lett., Volume 12 (2012) no. 12, pp. 6414-6419 (pMID: 23181691) | DOI

[11] A. Das; Y. Ronen; Y. Most; Y. Oreg; M. Heiblum; H. Shtrikman Zero-bias peaks and splitting in an Al-InAs nanowire topological superconductor as a signature of Majorana fermions, Nat. Phys., Volume 8 (2012) no. 12, pp. 887-895 | DOI

[12] E.J.H. Lee; X. Jiang; M. Houzet; R. Aguado; C.M. Lieber; S. De Franceschi Spin-resolved Andreev levels and parity crossings in hybrid superconductor-semiconductor nanostructures, Nat. Nanotechnol., Volume 9 (2014) no. 1, pp. 79-84 | DOI

[13] S. Nadj-Perge; I.K. Drozdov; J. Li; H. Chen; S. Jeon; J. Seo; A.H. MacDonald; B.A. Bernevig; A. Yazdani Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor, Science, Volume 346 (2014) no. 6209, pp. 602-607 http://science.sciencemag.org/content/346/6209/602.full.pdf http://science.sciencemag.org/content/346/6209/602 | DOI

[14] N. Sedlmayr; C. Bena Visualizing Majorana bound states in one and two dimensions using the generalized Majorana polarization, Phys. Rev. B, Volume 92 (2015) http://link.aps.org/doi/10.1103/PhysRevB.92.115115 (URL) | DOI

[15] D. Sticlet; C. Bena; P. Simon Spin and Majorana polarization in topological superconducting wires, Phys. Rev. Lett., Volume 108 (2012) http://link.aps.org/doi/10.1103/PhysRevLett.108.096802 (URL) | DOI

[16] D. Chevallier; D. Sticlet; P. Simon; C. Bena Mutation of Andreev into Majorana bound states in long superconductor-normal and superconductor-normal-superconductor junctions, Phys. Rev. B, Volume 85 (2012) https://link.aps.org/doi/10.1103/PhysRevB.85.235307 (URL) | DOI

[17] MatQ http://www.icmm.csic.es/sanjose/MathQ/MathQ.html

[18] N. Sedlmayr; J.M. Aguiar-Hualde; C. Bena Majorana bound states in open quasi-one-dimensional and two-dimensional systems with transverse Rashba coupling, Phys. Rev. B, Volume 93 (2016) http://link.aps.org/doi/10.1103/PhysRevB.93.155425 (URL) | DOI

[19] A.C. Potter; P.A. Lee Multichannel generalization of Kitaev's Majorana end states and a practical route to realize them in thin films, Phys. Rev. Lett., Volume 105 (2010) http://link.aps.org/doi/10.1103/PhysRevLett.105.227003 (URL) | DOI

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