- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Magnon-mediated topological superconductivity in a quantum wire

Florinda Viñas Boström1,2,* and Emil Viñas Boström3,4,†

  • *florinda.vinas_bostrom@ftf.lth.se
  • †emil.bostrom@mpsd.mpg.de
PDF

Phys. Rev. Research 6, L022042 – Published 16 May, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L022042

Abstract

Many emergent phases of matter stem from the intertwined dynamics of quasiparticles. Here we show that a topological superconducting phase emerges as the result of interactions between electrons and magnons in a quantum wire and a helical magnet. The magnon-mediated interaction favors triplet superconductivity over a large magnetic phase space region, and stabilizes topological superconductivity over an extended region of chemical potentials. The superconducting gap depends exponentially on the spin-electron coupling, allowing it to be enhanced through material engineering techniques.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (65)

  1. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108, 1175 (1957).
  2. W. Eerenstein, N. D. Mathur, and J. F. Scott, Multiferroic and magnetoelectric materials, Nature (London) 442, 759 (2006).
  3. X. Li, T. Qiu, J. Zhang, E. Baldini, J. Lu, A. M. Rappe, and K. A. Nelson, Terahertz field-induced ferroelectricity in quantum paraelectric SrTiO3, Science 364, 1079 (2019).
  4. D. Werdehausen, T. Takayama, M. Höppner, G. Albrecht, A. W. Rost, Y. Lu, D. Manske, H. Takagi, and S. Kaiser, Coherent order parameter oscillations in the ground state of the excitonic insulator Ta2NiSe5, Sci. Adv. 4, eaap8652 (2018).
  5. G. Mazza, M. Rösner, L. Windgätter, S. Latini, H. Hübener, A. J. Millis, A. Rubio, and A. Georges, Nature of symmetry breaking at the excitonic insulator transition: Ta2NiSe5, Phys. Rev. Lett. 124, 197601 (2020).
  6. R. B. Laughlin, Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations, Phys. Rev. Lett. 50, 1395 (1983).
  7. X. G. Wen and Q. Niu, Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces, Phys. Rev. B 41, 9377 (1990).
  8. A. Yu. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. (NY) 303, 2 (2003).
  9. C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys. 80, 1083 (2008).
  10. D. Arovas, J. R. Schrieffer, and F. Wilczek, Fractional statistics and the quantum Hall effect, Phys. Rev. Lett. 53, 722 (1984).
  11. A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Phys. (NY) 321, 2 (2006).
  12. L. Savary and L. Balents, Quantum spin liquids: A review, Rep. Prog. Phys. 80, 016502 (2017).
  13. H. Bartolomei, M. Kumar, R. Bisognin, A. Marguerite, J.-M. Berroir, E. Bocquillon, B. Plaçais, A. Cavanna, Q. Dong, U. Gennser et al., Fractional statistics in anyon collisions, Science 368, 173 (2020).
  14. J. Nakamura, S. Liang, G. C. Gardner, and M. J. Manfra, Direct observation of anyonic braiding statistics, Nat. Phys. 16, 931 (2020).
  15. J. M. Leinaas and J. Myrheim, On the theory of identical particles, Il Nuovo Cim. B 37, 1 (1977).
  16. F. Wilczek, Quantum mechanics of fractional-spin particles, Phys. Rev. Lett. 49, 957 (1982).
  17. L. Fu and C. L. Kane, Superconducting proximity effect and Majorana fermions at the surface of a topological insulator, Phys. Rev. Lett. 100, 096407 (2008).
  18. S. Nakosai, Y. Tanaka, and N. Nagaosa, Two-dimensional p-wave superconducting states with magnetic moments on a conventional s-wave superconductor, Phys. Rev. B 88, 180503(R) (2013).
  19. H.-H. Sun, K.-W. Zhang, L.-H. Hu, C. Li, G.-Y. Wang, H.-Y. Ma, Z.-A. Xu, C.-L. Gao, D.-D. Guan, Y.-Y. Li, C. Liu, D. Qian, Y. Zhou, L. Fu, S.-C. Li, F.-C. Zhang, and J.-F. Jia, Majorana zero mode detected with spin selective Andreev reflection in the vortex of a topological superconductor, Phys. Rev. Lett. 116, 257003 (2016).
  20. G. C. Ménard, S. Guissart, C. Brun, R. T. Leriche, M. Trif, F. Debontridder, D. Demaille, D. Roditchev, P. Simon, and T. Cren, Two-dimensional topological superconductivity in Pb/Co/Si(111), Nat. Commun. 8, 2040 (2017).
  21. A. Palacio-Morales, E. Mascot, S. Cocklin, H. Kim, S. Rachel, D. K. Morr, and R. Wiesendanger, Atomic-scale interface engineering of Majorana edge modes in a 2D magnet-superconductor hybrid system, Sci. Adv. 5, eaav6600 (2019).
  22. Z. Wang, J. O. Rodriguez, L. Jiao, S. Howard, M. Graham, G. D. Gu, T. L. Hughes, D. K. Morr, and V. Madhavan, Evidence for dispersing 1D Majorana channels in an iron-based superconductor, Science 367, 104 (2020).
  23. S. Kezilebieke, M. N. Huda, V. Vaňo, M. Aapro, S. C. Ganguli, O. J. Silveira, S. Głodzik, A. S. Foster, T. Ojanen, and P. Liljeroth, Topological superconductivity in a van der Waals heterostructure, Nature (London) 588, 424 (2020).
  24. K. Flensberg, Tunneling characteristics of a chain of Majorana bound states, Phys. Rev. B 82, 180516(R) (2010).
  25. Y. Oreg, G. Refael, and F. von Oppen, Helical liquids and Majorana bound states in quantum wires, Phys. Rev. Lett. 105, 177002 (2010).
  26. R. M. Lutchyn, J. D. Sau, and S. Das Sarma, Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures, Phys. Rev. Lett. 105, 077001 (2010).
  27. R. M. Lutchyn, E. P. A. M. Bakkers, L. P. Kouwenhoven, P. Krogstrup, C. M. Marcus, and Y. Oreg, Majorana zero modes in superconductor-semiconductor heterostructures, Nat. Rev. Mater. 3, 52 (2018).
  28. K. T. Law, P. A. Lee, and T. K. Ng, Majorana fermion induced resonant Andreev reflection, Phys. Rev. Lett. 103, 237001 (2009).
  29. T. D. Stanescu, R. M. Lutchyn, and S. Das Sarma, Majorana fermions in semiconductor nanowires, Phys. Rev. B 84, 144522 (2011).
  30. J. Alicea, Y. Oreg, G. Refael, F. von Oppen, and M. P. A. Fisher, Non-Abelian statistics and topological quantum information processing in 1D wire networks, Nat. Phys. 7, 412 (2011).
  31. V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, and L. P. Kouwenhoven, Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices, Science 336, 1003 (2012).
  32. A. Das, Y. Ronen, Y. Most, Y. Oreg, M. Heiblum, and H. Shtrikman, Zero-bias peaks and splitting in an Al-InAs nanowire topological superconductor as a signature of Majorana fermions, Nat. Phys. 8, 887 (2012).
  33. A. D. K. Finck, D. J. Van Harlingen, P. K. Mohseni, K. Jung, and X. Li, Anomalous modulation of a zero-bias peak in a hybrid nanowire-superconductor device, Phys. Rev. Lett. 110, 126406 (2013).
  34. S. M. Albrecht, A. P. Higginbotham, M. Madsen, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup, and C. M. Marcus, Exponential protection of zero modes in Majorana islands, Nature (London) 531, 206 (2016).
  35. M. T. Deng, S. Vaitiekėnas, E. B. Hansen, J. Danon, M. Leijnse, K. Flensberg, J. Nygård, P. Krogstrup, and C. M. Marcus, Majorana bound state in a coupled quantum-dot hybrid-nanowire system, Science 354, 1557 (2016).
  36. F. Nichele, A. C. C. Drachmann, A. M. Whiticar, E. C. T. O'Farrell, H. J. Suominen, A. Fornieri, T. Wang, G. C. Gardner, C. Thomas, A. T. Hatke, P. Krogstrup, M. J. Manfra, K. Flensberg, and C. M. Marcus, Scaling of Majorana zero-bias conductance peaks, Phys. Rev. Lett. 119, 136803 (2017).
  37. H. Zhang, D. E. Liu, M. Wimmer, and L. P. Kouwenhoven, Next steps of quantum transport in Majorana nanowire devices, Nat. Commun. 10, 5128 (2019).
  38. E. Prada, P. San-Jose, M. W. A. de Moor, A. Geresdi, E. J. H. Lee, J. Klinovaja, D. Loss, J. Nygård, R. Aguado, and L. P. Kouwenhoven, From Andreev to Majorana bound states in hybrid superconductor-semiconductor nanowires, Nat. Rev. Phys. 2, 575 (2020).
  39. M. Aghaee et al. (Microsoft Quantum), InAs-Al hybrid devices passing the topological gap protocol, Phys. Rev. B 107, 245423 (2023).
  40. K. Mæland and A. Sudbø, Quantum topological phase transitions in skyrmion crystals, Phys. Rev. Res. 4, L032025 (2022).
  41. K. Mæland and A. Sudbø, Topological superconductivity mediated by skyrmionic magnons, Phys. Rev. Lett. 130, 156002 (2023).
  42. K. Mæland, S. Abnar, J. Benestad, and A. Sudbø, Topological superconductivity mediated by magnons of helical magnetic states, Phys. Rev. B 108, 224515 (2023).
  43. A. Altland and M. R. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures, Phys. Rev. B 55, 1142 (1997).
  44. A. Y. Kitaev, Unpaired Majorana fermions in quantum wires, Phys.-Usp. 44, 131 (2001).
  45. C.-K. Chiu, J. C. Y. Teo, A. P. Schnyder, and S. Ryu, Classification of topological quantum matter with symmetries, Rev. Mod. Phys. 88, 035005 (2016).
  46. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L022042 for additional details on the diagonalization of the magnon and electron sub-systems, the derivation of the electron-magnon interaction, the derivation of the effective electron-electron interaction, the derivation of the gap equation, and an extended discussion of the Z2 topological invariant of the superconducting system.
  47. E. Viñas Boström, F. G. Eich, and A. Rubio, Magnon frequency renormalization by the electronic geometrical spin torque in itinerant magnets, arXiv:2112.06547.
  48. S. Nadj-Perge, I. K. Drozdov, B. A. Bernevig, and A. Yazdani, Proposal for realizing Majorana fermions in chains of magnetic atoms on a superconductor, Phys. Rev. B 88, 020407(R) (2013).
  49. P. B. Allen and B. Mitrović, Theory of superconducting tc, in Solid State Physics (Elsevier, New York, 1983), pp. 1–92.
  50. F. Loder, A. P. Kampf, and T. Kopp, Superconducting state with a finite-momentum pairing mechanism in zero external magnetic field, Phys. Rev. B 81, 020511(R) (2010).
  51. M. Nilsson, F. Viñas Boström, S. Lehmann, K. A. Dick, M. Leijnse, and C. Thelander, Tuning the two-electron hybridization and spin states in parallel-coupled InAs quantum dots, Phys. Rev. Lett. 121, 156802 (2018).
  52. R. Debbarma, M. Aspegren, F. Viñas Boström, S. Lehmann, K. Dick, and C. Thelander, Josephson current via spin and orbital states of a tunable double quantum dot, Phys. Rev. B 106, L180507 (2022).
  53. N. Nagaosa and Y. Tokura, Topological properties and dynamics of magnetic skyrmions, Nat. Nanotechnol. 8, 899 (2013).
  54. Q. Song, C. A. Occhialini, E. Ergeçen, B. Ilyas, D. Amoroso, P. Barone, J. Kapeghian, K. Watanabe, T. Taniguchi, A. S. Botana, S. Picozzi, N. Gedik, and R. Comin, Evidence for a single-layer van der Waals multiferroic, Nature (London) 602, 601 (2022).
  55. Z. Qiao, W. Ren, H. Chen, L. Bellaiche, Z. Zhang, A. H. MacDonald, and Q. Niu, Quantum anomalous Hall effect in graphene proximity coupled to an antiferromagnetic insulator, Phys. Rev. Lett. 112, 116404 (2014).
  56. T. Norden, C. Zhao, P. Zhang, R. Sabirianov, A. Petrou, and H. Zeng, Giant valley splitting in monolayer WS2 by magnetic proximity effect, Nat. Commun. 10, 4163 (2019).
  57. K. Mæland, H. I. Røst, J. W. Wells, and A. Sudbø, Electron-magnon coupling and quasiparticle lifetimes on the surface of a topological insulator, Phys. Rev. B 104, 125125 (2021).
  58. C. Cardoso, A. T. Costa, A. H. MacDonald, and J. Fernández-Rossier, Strong magnetic proximity effect in van der Waals heterostructures driven by direct hybridization, Phys. Rev. B 108, 184423 (2023).
  59. J. Schlappa, K. Wohlfeld, K. J. Zhou, M. Mourigal, M. W. Haverkort, V. N. Strocov, L. Hozoi, C. Monney, S. Nishimoto, S. Singh et al., Spin-orbital separation in the quasi-one-dimensional Mott insulator Sr2CuO3, Nature (London) 485, 82 (2012).
  60. D. M. Kennes, L. Xian, M. Claassen, and A. Rubio, One-dimensional flat bands in twisted bilayer germanium selenide, Nat. Commun. 11, 1124 (2020).
  61. P. J. W. Moll, Focused ion beam microstructuring of quantum matter, Annu. Rev. Condens. Matter Phys. 9, 147 (2018).
  62. M. A. Sentef, M. Ruggenthaler, and A. Rubio, Cavity quantum-electrodynamical polaritonically enhanced electron-phonon coupling and its influence on superconductivity, Sci. Adv. 4, aau6969 (2018).
  63. E. Barrigón, M. Heurlin, Z. Bi, B. Monemar, and L. Samuelson, Synthesis and applications of III-V nanowires, Chem. Rev. 119, 9170 (2019).
  64. E. Viñas Boström, A. Sriram, M. Claassen, and A. Rubio, Controlling the magnetic state of the proximate quantum spin liquid α−RuCl3 with an optical cavity, npj Comput. Mater. 9, 202 (2023).
  65. S. Das Sarma, In search of Majorana, Nat. Phys. 19, 165 (2023).

Outline

Information

Phys. Rev. Research 6, L022042– Published 16 May, 2024
  • Received 5 December 2023
  • Revised 28 March 2024
  • Accepted 2 May 2024
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation