Geodesic
Existence of Majorana bound states in a superconducting nanowire
Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 2, pp. 279-289
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We consider a nanowire with the $s$-wave superconducting order induced as a result of the proximity effect in the presence of the Zeeman field and the Rashba interaction. For a small superconducting gap and small momenta, we analytically prove the existence of Majorana bound states for a certain local change in the Zeeman field or the superconducting order and also obtain explicit expressions for the corresponding wave functions. We study the scattering of excited states with energies that are close to boundary gap points in the case of propagation through an impurity for local changes in the indicated system parameters near this impurity and show that the transmission probability is equal to unity.
Keywords: superconductivity, Majorana bound state, nanowire, impurity, Zeeman field, scattering problem. 
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Yu. P. Chuburin. Existence of Majorana bound states in a superconducting nanowire. Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 2, pp. 279-289. http://geodesic.mathdoc.fr/item/TMF_2018_197_2_a6/

[1] S. R. Elliot, M. Franz, “Colloquium: Majorana fermions in nuclear, particle, and solid-state physics”, Rev. Modern Phys., 87:1 (2015), 137–163, arXiv: 1403.4976 | DOI | MR

[2] M. Sato, S. Fujimoto, “Majorana fermions and topology in superconductors”, J. Phys. Soc. Japan, 85:7 (2016), 072001, 32 pp., arXiv: 1601.02726 | DOI

[3] J. Alicea, “New directions in the pursuit of Majorana fermions in solid state systems”, Rep. Progr. Phys., 75:7 (2012), 076501, 36 pp., arXiv: 1202.1293 | DOI

[4] S. Das Sarma, A. Nag, J. D. Sau, “How to infer non-Abelian statistics and topological visibility from tunneling conductance properties of realistic Majorana nanowires”, Phys. Rev. B, 94:3 (2016), 035143, 17 pp. | DOI

[5] J. D. Sau, E. Demler, “Bound states at impurities as a probe of topological superconductivity in nanowires”, Phys. Rev. B, 88:20 (2013), 205402, 6 pp. | DOI

[6] T. Karzig, G. Refael, F. von Oppen, “Boosting Majorana zero modes”, Phys. Rev. X, 3:4 (2013), 041017, 16 pp. | DOI

[7] S. Das Sarma, J. D. Sau, T. D. Stanescu, “Splitting of the zero-bias conductance peak as smoking gun evidence for the existence of the Majorana mode in a superconductor-semiconductor nanowire”, Phys. Rev. B, 86:22 (2012), 220506, 5 pp. | DOI

[8] C.-X. Liu, F. Setiawan, J. D. Sau, S. Das Sarma, “Phenomenology of soft gap, zero-bias peak, and zero-mode splitting in ideal Majorana nanowires”, Phys. Rev. B, 96:5 (2017), 054520, 18 pp., arXiv: 1706.04573 | DOI

[9] C. Moore, T. D. Stanescu, S. Tewari, “Two-terminal charge tunneling: disentangling Majorana zero modes from partially separated Andreev bound states in semiconductor-superconductor heterostructures”, Phys. Rev. B, 97:16 (2018), 165302, 14 pp., arXiv: 1611.07058 | DOI

[10] D. Chevallier, P. Simon, C. Bena, “From Andreev bound states to Majorana fermions in topological wires on superconducting substrates: a story of mutation”, Phys. Rev. B, 88:16 (2013), 165401, 6 pp. | DOI

[11] Yu. N. Demkov, V. N. Ostrovskii, Metod potentsialov nulevogo radiusa v atomnoi fizike, Izd-vo Leningr. gos. un-ta, L., 1975

[12] S. K. Adhikari, M. Casas, A. Puente, A. Rigo, M. Fortes, M. A. Solis, M. de Llano, A. A. Valladares, O. Rojo, “Linear to quadratic crossover of Cooper-pair dispersion relation”, Physica C, 351:4 (2001), 341–348, arXiv: cond-mat/0008478 | DOI

[13] Y. Matsui, “Nucleon-trinucleon scattering with Yamaguchi potential”, Progr. Theor. Phys., 104:5 (2000), 981–993 | DOI

[14] Yu. P. Chuburin, “Existence of Majorana bound states near impurities in the case of a small superconducting gap”, Physica E, 89 (2017), 130–133 | DOI

[15] D. Sticlet, B. Nijholt, A. Akhmerov, “Robustness of Majorana bound states in the short-junction limit”, Phys. Rev. B, 95:11 (2017), 115421, 13 pp., arXiv: 1609.00637 | DOI

[16] P. San-Jose, J. Cayao, E. Prada, R. Aguado, “Majorana bound states from exceptional points in non-topological superconductors”, Sci. Rep., 6 (2016), 21427, 13 pp. | DOI