Interaction between subbands in a quasi-one-dimensional superconductor

Yu. P. Chuburin   ; T. S. Tinyukova

Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 3, pp. 455-469

Résumé

In the framework of the Bogoliubov–de Gennes equation, we study the spinless $p$-wave superconductor in an infinite strip in the presence of some impurity. We analytically determine the wave functions of stable bound states with energies close to edge points of the energy gap. We prove that for a small impurity potential, the contribution of the nearest subbands to the wave functions in the case of energy values close to edge points is very small, and these energy levels are significantly closer to the gap edge than in the one-dimensional case. We also study the bound states with nearly zero energy values; in contrast to the one-dimensional case, they do not have the “particle–hole” symmetry. In the cases under study, in addition to the bound states, there also exit resonance states related to them.

Détail

Keywords: Bogoliubov–de Gennes Hamiltonian, superconducting gap, Andreev bound state, Majorana bound state, resonance state, subband.

Bibliographie

[1] 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

[2] F. von Oppen, Y. Peng, F. Pientka, “Topological superconducting phases in one dimension”, Topological Aspects of Condensed Matter Physics (École de Physique des Houches, Session CIII, 4–29 August, 2014), Lecture Notes of the Les Houches Summer School, 103, eds. C. Chamon, M. O. Goerbig, R. Moessner, L. F. Cugliandolo, Oxford Univ. Press, Oxford, 2017, 387–447 | DOI

[3] M. Sato, S. Fujimoto, “Majorana fermions and topology in superconductors”, J. Phys. Soc. Japan, 85:7 (2016), 072001, 31 pp. | DOI

[4] J. D. Sau, S. Tewari, R. M. Lutchyn, T. D. Stanescu, S. Das Sarma, “Non-Abelian quantum order in spin-orbit-coupled semiconductors: Search for topological Majorana particles in solid-state systems”, Phys. Rev. B, 82:21 (2010), 214509, 26 pp., arXiv: 1006.2829 | DOI

[5] Y. Oreg, G. Refael, F. von Oppen, “Helical liquids and Majorana bound states in quantum wires”, Phys. Rev. Lett., 105:17 (2010), 177002 | DOI

[6] 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, 336:6084 (2012), 1003–1007, arXiv: 1204.2792 | DOI

[7] 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”, Nature Phys., 8:12 (2012), 887–895, arXiv: 1205.7073 | DOI

[8] C.-X. Liu, J. D. Sau, T. D. Stanescu, S. Das 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, 96:7 (2017), 075161, 29 pp., arXiv: 1705.02035 | DOI

[9] C. Moore, C. Zeng, T. D. Stanescu, S. Tewari, “Quantized zero-bias conductance plateau in semiconductor-superconductor heterostructures without topological Majorana zero modes”, Phys. Rev. B, 98:15 (2018), 155314, 6 pp., arXiv: 1804.03164 | DOI

[10] D. B. Woods, S. Das Sarma, T. D. Stanescu, “Subband occupation in semiconductor-superconductor nanowires”, Phys. Rev. B, 101:4 (2020), 045405, 13 pp., arXiv: 1910.04362 | DOI

[11] T. D. Stanescu, R. M. Lutchyn, S. Das Sarma, “Majorana fermions in semiconductor nanowires, Majorana fermions in semiconductor nanowires”, Phys. Rev. B, 84:14 (2011), 144522, 29 pp., arXiv: 1106.3078 | DOI

[12] F. Pientka, G. Kells, A. Romito, P. W. Brouwer, F. von Oppen, “Enhanced zero-bias Majorana peak in the differential tunneling conductance of disordered multisubband quantum-wire/superconductor junctions”, Phys. Rev. Lett., 109:22 (2012), 227006, 5 pp., arXiv: 1206.0723 | DOI

[13] B. D. Woods, J. Chen, S. M. Frolov, T. D. Stanescu, “Zero-energy pinning of topologically trivial bound states in multiband semiconductor-superconductor nanowires”, Phys. Rev. B, 100:12 (2019), 125407, 17 pp., arXiv: 1902.02772 | DOI

[14] Z. Hou, J. Klinovaja, Zero-energy Andreev bound states in iron-based superconductor Fe(Te,Se), arXiv: 2109.08200

[15] 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., 105:22 (2010), 227003, 4 pp., arXiv: 1007.4569 | DOI

[16] Yu. P. Chuburin, T. S. Tinyukova, “Vzaimnyi perekhod andreevskikh i maioranovskikh lokalizovannykh sostoyanii v sverkhprovodyaschei scheli”, TMF, 205:3 (2020), 484–501 | DOI | DOI | MR

[17] Yu. P. Chuburin, T. S. Tinyukova, “Povedenie andreevskikh sostoyanii pri topologicheskom fazovom perekhode”, TMF, 208:1 (2021), 145–162 | DOI | DOI

[18] R. Aguado, “Majorana quasiparticles in condensed matter”, Riv. Nuovo Cimento, 40:11 (2017), 523–593, arXiv: 1711.00011 | DOI

[19] Dzh. Teilor, Teoriya rasseyaniya: kvantovaya teoriya nerelyativistskikh stolknovenii, Mir, M., 1985

[20] C. W. J. Beenakker, “Random-matrix theory of Majorana fermions and topological superconductors”, Rev. Modern Phys., 87:3 (2015), 1037–1066, arXiv: 1407.2131 | DOI | MR