Fermion parity of phases supporting multiple Majorana modes in a superconducting nanowire
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 6, pp. 820-829.

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The fermion parity of the ground state is determined in various topological phases of the semiconducting nanowire under external magnetic field with proximity-induced superconductivity and strong spin-orbit interaction. Electron hopping as well as spin-flip hopping due to spin-orbit coupling and superconducting pairings in the second coordination sphere are taken into account. The connection between the fermion parity and the parity of the BDI topological invariant is shown. The formation of topological phases with three and four pairs of Majorana modes has been demonstrated.
Keywords: Fermion parity, superconducting nanowire, topological invariant, topological phase diagram.
Mots-clés : Majorana modes
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Alexander Gamov; Anton O. Zlotnikov. Fermion parity of phases supporting multiple Majorana modes in a superconducting nanowire. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 6, pp. 820-829. http://geodesic.mathdoc.fr/item/JSFU_2023_16_6_a12/

[1] C.Nayak, S.H.Simon, A.Stern, M.Freedman, S.Das Sarma, “Non-Abelian Anyons and Topological Quantum Computation”, Rev. Mod. Phys., 80 (2008), 1083–1159

[2] J.Alicea, Y.Oreg, G.Refael, F. von Oppen, M.P.A.Fishser, “Non-Abelian statistics and topological quantum information processing in 1D wire networks”, Nature Physics, 7 (1038), 412–417 | DOI

[3] T.Karzig, F.Pientka, G.Rafael, F.von Oppen, “Shortcuts of non-Abelian braidings”, Phys. Rev. B, 91 (2011) | DOI

[4] F.Harper, A Pushp, R.Roy, “Majorana braiding in realistic nanowire Y-junctions and tuning forks”, Phys. Rev. Res., 1 (2019) | DOI

[5] M.T.Deng, S.Vaitiekenas, E.B.Hansen, J.Danon, M.Leijnse, K.Flensberg, J.Nygard, P.Krogstrup, C.M. Marcus, “Majorana bound state in a coupled quantum-dot hybrid-nanowire system”, Science, 354 (2016), 1557–1562 | DOI

[6] Microsoft Quantum et al., “InAs-Al Hybrid Devices Passing the Topological Gap Protocol”, Phys. Rev. B, 107 (2023), 245423 | DOI

[7] J.D.Sau, R.M.Lutchyn, S.Tewari, S.D.Sarma, “Generic New Platform for Topological Quantum Computation Using Semiconductor Heterostructures”, Phys. Rev. Lett., 104 (2010), 040502 | DOI

[8] R.M.Lutchyn, J.D.Sau, S.Das Sarma, “Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures”, Phys. Rev. Lett., 105 (2010), 077001 | DOI

[9] Y.Oreg, G.Refael, F. von Oppen, “Helical Liquids and Majorana Bound States in Quantum Wires”, Phys. Rev. Lett., 105 (2010), 177002 | DOI

[10] A.Yu.Kitaev, “Unpaired Majorana fermions in quantum wires”, Phys. Usp., 44 (2001), 131–136

[11] C.-X.Liu, J.D.Sau, T.D.Stanescu, S.D.Sarma, “Andreev bound states versus Majorana bound states in quantum dot-nanowire-superconductor hybrid structures: Trivial versus topological zero-bias conductance peaks”, Phys. Rev. B, 96 (2017), 075161 | DOI

[12] S.Das Sarma, “In Search of Majorana”, Nat. Phys., 19 (2023), 165–170 | DOI

[13] S.Ryu, A.P.Schnyder, A.Furusaki, A.W.W.Ludwig, “Topological Insulators and Superconductors: Tenfold Way and Dimensional Hierarchy”, New J. Phys., 12 (2010), 065010 | DOI

[14] S.Tewari, J.D.Sau, “Topological Invariants for Spin-Orbit Coupled Superconductor Nanowires”, Phys. Rev. Lett., 109 (2012), 150408 | DOI

[15] Y. Niu, S.B.Chung, C.-H.Hsu, I.Mandal, S.Raghu, S.Chakravarty, “Majorana zero modes in a quantum Ising chain with longer ranged interactions”, Phys. Rev. B, 85 (2012), 035110 | DOI

[16] C.L.M. Wong, K.T.Law, “Majorana Kramers Doublets in dx2-y2-Wave Superconductors with Rashba Spin-Orbit Coupling”, Phys. Rev. B, 86 (2012), 184516 | DOI

[17] S.V.Aksenov, A.O.Zlotnikov, M.S.Shustin, “Strong Coulomb interactions in the problem of Majorana modes in a wire of the non-trivial topological class BDI”, Phys. Rev. B, 101 (2020), 125431 | DOI

[18] A.A.Bespalov, “Tuning the Topological state of a helical atom chain via a Josepson phase”, Phys. Rev. B, 106 (2022), 134503 | DOI

[19] H.Wu, S.Wu, L.Zhou, “Floquet Topological Superconductors with Many Majorana Edge Modes: Topological Invariants, Entanglement Spectrum and Bulk-Edge Correspondence”, New J. Phys., 25 (2023), 083042 | DOI

[20] N.Read, D.Green, “Paired States of Fermions in Two Dimensions with Breaking of Parity and Time-Reversal Symmetries and the Fractional Quantum Hall Effect”, Phys. Rev. B, 61 (2000), 10267 | DOI

[21] V.V.Val'kov, M.S.Shustin, S.V.Aksenov, A.O.Zlotnikov, A.D.Fedoseev, V.A.Mitskan, M.Yu.Kagan, “Topological superconductivity and Majorana states in low-dimensional systems”, Phys. Usp., 65 (2022), 2–39 | DOI

[22] V.V.Val'kov, V.A.Mitskan, M.S.Shustin, “Ground-State Fermion Parity and Caloric Properties of a Superconducting Nanowire”, J. Exp. Theor. Phys., 129 (2019), 426–437 | DOI