- 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

Interaction-induced topological superconductivity in antiferromagnet-superconductor junctions

Senna S. Luntama, Päivi Törmä, and Jose L. Lado*

  • Department of Applied Physics, Aalto University, 00076 Aalto, Espoo, Finland

  • *jose.lado@aalto.fi
PDF

Phys. Rev. Research 3, L012021 – Published 5 March, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L012021

Abstract

We predict that junctions between an antiferromagnetic insulator and a superconductor provide a robust platform to create a one-dimensional topological superconducting state. Its emergence does not require the presence of intrinsic spin-orbit coupling nor noncollinear magnetism, but arises solely from repulsive electronic interactions on interfacial solitonic states. We demonstrate that a topological superconducting state is generated by repulsive interactions at arbitrarily small coupling strength, and that the size of the topological gap rapidly saturates to one of the parent trivial superconductor. Our results put forward antiferromagnetic insulators as a new platform for interaction-driven topological superconductivity.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (85)

  1. A. Yu. Kitaev, Unpaired Majorana fermions in quantum wires, Phys. Usp. 44, 131 (2001).
  2. J. Alicea, New directions in the pursuit of Majorana fermions in solid state systems, Rep. Prog. Phys. 75, 076501 (2012).
  3. C. W. J. Beenakker, Search for Majorana fermions in superconductors, Annu. Rev. Condens. Matter Phys. 4, 113 (2013).
  4. C. Beenakker and L. Kouwenhoven, A road to reality with topological superconductors, Nat. Phys. 12, 618 (2016).
  5. M. T. Deng, C. L. Yu, G. Y. Huang, M. Larsson, P. Caroff, and H. Q. Xu, Anomalous zero-bias conductance peak in a Nb–InSb nanowire–Nb hybrid device, Nano Lett. 12, 6414 (2012).
  6. 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).
  7. 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).
  8. J. Röntynen and T. Ojanen, Topological Superconductivity and High Chern Numbers in 2D Ferromagnetic Shiba Lattices, Phys. Rev. Lett. 114, 236803 (2015).
  9. P. Hosur, P. Ghaemi, R. S. K. Mong, and A. Vishwanath, Majorana Modes at the Ends of Superconductor Vortices in Doped Topological Insulators, Phys. Rev. Lett. 107, 097001 (2011).
  10. 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).
  11. J.-P. Xu, C. Liu, M.-X. Wang, J. Ge, Z.-L. Liu, X. Yang, Y. Chen, Y. Liu, Z.-A. Xu, C.-L. Gao, D. Qian, F.-C. Zhang, and J.-F. Jia, Artificial Topological Superconductor by the Proximity Effect, Phys. Rev. Lett. 112, 217001 (2014).
  12. G. Xu, B. Lian, P. Tang, X.-L. Qi, and S.-C. Zhang, Topological Superconductivity on the Surface of Fe-Based Superconductors, Phys. Rev. Lett. 117, 047001 (2016).
  13. Y. Asano and Y. Tanaka, Majorana fermions and odd-frequency cooper pairs in a normal-metal nanowire proximity-coupled to a topological superconductor, Phys. Rev. B 87, 104513 (2013).
  14. Q. L. He, L. Pan, A. L. Stern, E. C. Burks, X. Che, G. Yin, J. Wang, B. Lian, Q. Zhou, E. S. Choi, K. Murata, X. Kou, Z. Chen, T. Nie, Q. Shao, Y. Fan, S.-C. Zhang, K. Liu, J. Xia, and K. L. Wang, Chiral Majorana fermion modes in a quantum anomalous Hall insulator–superconductor structure, Science 357, 294 (2017).
  15. F. Finocchiaro, F. Guinea, and P. San-Jose, Topological π Junctions from Crossed Andreev Reflection in the Quantum Hall Regime, Phys. Rev. Lett. 120, 116801 (2018).
  16. M. Ruby, F. Pientka, Y. Peng, F. von Oppen, B. W. Heinrich, and K. J. Franke, End States and Subgap Structure in Proximity-Coupled Chains of Magnetic Adatoms, Phys. Rev. Lett. 115, 197204 (2015).
  17. S. Nadj-Perge, I. K. Drozdov, J. Li, H. Chen, S. Jeon, J. Seo, A. H. MacDonald, B. A. Bernevig, and A. Yazdani, Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor, Science 346, 602 (2014).
  18. 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).
  19. 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).
  20. 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).
  21. R. S. K. Mong, D. J. Clarke, J. Alicea, N. H. Lindner, P. Fendley, C. Nayak, Y. Oreg, A. Stern, E. Berg, K. Shtengel, and M. P. A. Fisher, Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure, Phys. Rev. X 4, 011036 (2014).
  22. 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).
  23. S. Kezilebieke, M. Nurul 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 designer ferromagnet-superconductor van der Waals heterostructure, Nature (London) 588, 424 (2020).
  24. Y. Oreg, G. Refael, and F. von Oppen, Helical Liquids and Majorana Bound States in Quantum Wires, Phys. Rev. Lett. 105, 177002 (2010).
  25. J. D. Sau, R. M. Lutchyn, S. Tewari, and S. Das Sarma, Generic New Platform for Topological Quantum Computation Using Semiconductor Heterostructures, Phys. Rev. Lett. 104, 040502 (2010).
  26. T. Jungwirth, X. Marti, P. Wadley, and J. Wunderlich, Antiferromagnetic spintronics, Nat. Nanotechnol. 11, 231 (2016).
  27. V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, and Y. Tserkovnyak, Antiferromagnetic spintronics, Rev. Mod. Phys. 90, 015005 (2018).
  28. D.-F. Shao, G. Gurung, S.-H. Zhang, and E. Y. Tsymbal, Dirac Nodal Line Metal for Topological Antiferromagnetic Spintronics, Phys. Rev. Lett. 122, 077203 (2019).
  29. W. Zhang, M. B. Jungfleisch, W. Jiang, J. E. Pearson, A. Hoffmann, F. Freimuth, and Y. Mokrousov, Spin Hall Effects in Metallic Antiferromagnets, Phys. Rev. Lett. 113, 196602 (2014).
  30. M. F. Jakobsen, K. B. Naess, P. Dutta, A. Brataas, and A. Qaiumzadeh, Electrical and thermal transport in antiferromagnet-superconductor junctions, Phys. Rev. B 102, 140504(R) (2020).
  31. M. M. Otrokov, I. I. Klimovskikh, H. Bentmann, D. Estyunin, A. Zeugner, Z. S. Aliev, S. Gaß, A. U. B. Wolter, A. V. Koroleva, A. M. Shikin, M. Blanco-Rey, M. Hoffmann, I. P. Rusinov, A. Yu. Vyazovskaya, S. V. Eremeev, Yu. M. Koroteev, V. M. Kuznetsov, F. Freyse, J. Sánchez-Barriga, I. R. Amiraslanov, M. B. Babanly, N. T. Mamedov, N. A. Abdullayev, V. N. Zverev, A. Alfonsov, V. Kataev, B. Büchner, E. F. Schwier, S. Kumar, A. Kimura, L. Petaccia, G. D. Santo, R. C. Vidal, S. Schatz, K. Kißner, M. Ünzelmann, C. H. Min, S. Moser, T. R. F. Peixoto, F. Reinert, A. Ernst, P. M. Echenique, A. Isaeva, and E. V. Chulkov, Prediction and observation of an antiferromagnetic topological insulator, Nature (London) 576, 416 (2019).
  32. C. Liu, Y. Wang, H. Li, Y. Wu, Y. Li, J. Li, K. He, Y. Xu, J. Zhang, and Y. Wang, Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator, Nat. Mater. 19, 522 (2020).
  33. C. Niu, H. Wang, N. Mao, B. Huang, Y. Mokrousov, and Y. Dai, Antiferromagnetic Topological Insulator with Nonsymmorphic Protection in Two Dimensions, Phys. Rev. Lett. 124, 066401 (2020).
  34. R. S. K. Mong, A. M. Essin, and J. E. Moore, Antiferromagnetic topological insulators, Phys. Rev. B 81, 245209 (2010).
  35. A. Heimes, P. Kotetes, and G. Schön, Majorana fermions from Shiba states in an antiferromagnetic chain on top of a superconductor, Phys. Rev. B 90, 060507(R) (2014).
  36. A. Tan, V. Labracherie, N. Kunchur, A. U. B. Wolter, J. Cornejo, J. Dufouleur, B. Büchner, A. Isaeva, and R. Giraud, Metamagnetism of Weakly Coupled Antiferromagnetic Topological Insulators, Phys. Rev. Lett. 124, 197201 (2020).
  37. P. M. Sass, J. Kim, D. Vanderbilt, J. Yan, and W. Wu, Robust a-Type Order and Spin-Flop Transition on the Surface of the Antiferromagnetic Topological Insulator MnBi2Te4, Phys. Rev. Lett. 125, 037201 (2020).
  38. K. Machida, K. Nokura, and T. Matsubara, Theory of antiferromagnetic superconductors, Phys. Rev. B 22, 2307 (1980).
  39. M. Weides, M. Disch, H. Kohlstedt, and D. E. Bürgler, Observation of Josephson coupling through an interlayer of antiferromagnetically ordered chromium, Phys. Rev. B 80, 064508 (2009).
  40. J. W. A. Robinson, G. B. Halász, and M. G. Blamire, Crossover Induced by Spin-Density-Wave Interference in the Coherence of Singlet Electron Pairs in Cr, Phys. Rev. Lett. 103, 207002 (2009).
  41. C. Bell, E. J. Tarte, G. Burnell, C. W. Leung, D.-J. Kang, and M. G. Blamire, Proximity and Josephson effects in superconductor/antiferromagnetic Nb/γ−Fe50Mn50 heterostructures, Phys. Rev. B 68, 144517 (2003).
  42. M. J. Nass, K. Levin, and G. S. Grest, Bardeen-Cooper-Schrieffer Pairing in Antiferromagnetic Superconductors, Phys. Rev. Lett. 46, 614 (1981).
  43. M. H. Fischer, M. Sigrist, and D. F. Agterberg, Superconductivity Without Inversion and Time-Reversal Symmetries, Phys. Rev. Lett. 121, 157003 (2018).
  44. S. Coh, M. L. Cohen, and S. G Louie, Large electron–phonon interactions from FeSe phonons in a monolayer, New J. Phys. 17, 073027 (2015).
  45. Z. F. Wang, H. Zhang, D. Liu, C. Liu, C. Tang, C. Song, Y. Zhong, J. Peng, F. Li, C. Nie, L. Wang, X. J. Zhou, X. Ma, Q. K. Xue, and F. Liu, Topological edge states in a high-temperature superconductor FeSe/SrTiO3(001) film, Nat. Mater. 15, 968 (2016).
  46. Taking a smooth transition between the superconductor and antiferromagnet does not impact the results qualitatively.
  47. Charge renormalization is reabsorbed in Eq. (2).
  48. M. P. L. Sancho, J. M. L. Sancho, J. M. L. Sancho, and J. Rubio, Highly convergent schemes for the calculation of bulk and surface green functions, J. Phys. F 15, 851 (1985).
  49. R. Jackiw and C. Rebbi, Solitons with fermion number, Phys. Rev. D 13, 3398 (1976).
  50. P. San-Jose, J. L. Lado, R. Aguado, F. Guinea, and J. Fernández-Rossier, Majorana Zero Modes in Graphene, Phys. Rev. X 5, 041042 (2015).
  51. J. L. Lado and M. Sigrist, Two-Dimensional Topological Superconductivity With Antiferromagnetic Insulators, Phys. Rev. Lett. 121, 037002 (2018).
  52. A. L. R. Manesco, G. Weber, and D. Rodrigues, Effective model for Majorana modes in graphene, Phys. Rev. B 100, 125411 (2019).
  53. J. L. Lado and M. Sigrist, Solitonic in-gap modes in a superconductor-quantum antiferromagnet interface, Phys. Rev. Research 2, 023347 (2020).
  54. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81, 109 (2009).
  55. J. C. Budich and E. Ardonne, Equivalent topological invariants for one-dimensional Majorana wires in symmetry class d, Phys. Rev. B 88, 075419 (2013).
  56. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L012021 for details on the microscopic mean field.
  57. Z. Qiao, S. A. Yang, W. Feng, W.-K. Tse, J. Ding, Y. Yao, J. Wang, and Q. Niu, Quantum anomalous Hall effect in graphene from Rashba and exchange effects, Phys. Rev. B 82, 161414(R) (2010).
  58. C. L. Kane and E. J. Mele, Quantum Spin Hall Effect in Graphene, Phys. Rev. Lett. 95, 226801 (2005).
  59. C. Popovici, C. S. Fischer, and L. von Smekal, Fermi velocity renormalization and dynamical gap generation in graphene, Phys. Rev. B 88, 205429 (2013).
  60. T. Stauber, P. Parida, M. Trushin, M. V. Ulybyshev, D. L. Boyda, and J. Schliemann, Interacting Electrons in Graphene: Fermi Velocity Renormalization and Optical Response, Phys. Rev. Lett. 118, 266801 (2017).
  61. The term in HMF creating the gap opening shows a similar exponential dependence.
  62. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108, 1175 (1957).
  63. A. M. Lobos, R. M. Lutchyn, and S. Das Sarma, Interplay of Disorder and Interaction in Majorana Quantum Wires, Phys. Rev. Lett. 109, 146403 (2012).
  64. N. M. Gergs, L. Fritz, and D. Schuricht, Topological order in the Kitaev/Majorana chain in the presence of disorder and interactions, Phys. Rev. B 93, 075129 (2016).
  65. İ. Adagideli, M. Wimmer, and A. Teker, Effects of electron scattering on the topological properties of nanowires: Majorana fermions from disorder and superlattices, Phys. Rev. B 89, 144506 (2014).
  66. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L012021 for details on the role of Anderson disorder and different interfaces.
  67. Although square lattice models can have antiferromagnetism, their low energy model is usually not of the Dirac form.
  68. M. McGuire, Crystal and magnetic structures in layered, transition metal dihalides and trihalides, Crystals 7, 121 (2017).
  69. L. Webster and J.-A. Yan, Strain-tunable magnetic anisotropy in monolayer CrCl3, CrBr3, and CrI3, Phys. Rev. B 98, 144411 (2018).
  70. Z. Wu, J. Yu, and S. Yuan, Strain-tunable magnetic and electronic properties of monolayer CrI3, Phys. Chem. Chem. Phys. 21, 7750 (2019).
  71. A. Möller, U. Löw, T. Taetz, M. Kriener, G. André, F. Damay, O. Heyer, M. Braden, and J. A. Mydosh, Structural domain and finite-size effects of the antiferromagnetic S=1/2 honeycomb lattice in InCu2/3V1/3O3, Phys. Rev. B 78, 024420 (2008).
  72. A. A. Tsirlin, O. Janson, and H. Rosner, β-Cu2V2O7: A spin-12 honeycomb lattice system, Phys. Rev. B 82, 144416 (2010).
  73. T. O. Wehling, A. M. Black-Schaffer, and A. V. Balatsky, Dirac materials, Adv. Phys. 63, 1 (2014).
  74. P. Seth, P. Hansmann, A. van Roekeghem, L. Vaugier, and S. Biermann, Towards a First-Principles Determination of Effective Coulomb Interactions in Correlated Electron Materials: Role of Intershell Interactions, Phys. Rev. Lett. 119, 056401 (2017).
  75. M. Schüler, M. Rösner, T. O. Wehling, A. I. Lichtenstein, and M. I. Katsnelson, Optimal Hubbard Models for Materials with Nonlocal Coulomb Interactions: Graphene, Silicene, and Benzene, Phys. Rev. Lett. 111, 036601 (2013).
  76. I. Timrov, N. Marzari, and M. Cococcioni, Hubbard parameters from density-functional perturbation theory, Phys. Rev. B 98, 085127 (2018).
  77. I. Timrov, N. Marzari, and M. Cococcioni, Self-consistent Hubbard parameters from density-functional perturbation theory in the ultrasoft and projector-augmented wave formulations, Phys. Rev. B 103, 045141 (2021).
  78. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L012021 for a discussion on the V2 values in two-dimensional materials.
  79. P. Törmä and K. Sengstock, Quantum Gas Experiments—Exploring Many-Body States (Imperial College Press, London, 2015).
  80. G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, Experimental realization of the topological Haldane model with ultracold fermions, Nature (London) 515, 237 (2014).
  81. A. Mazurenko, C. S. Chiu, G. Ji, M. F. Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, A cold-atom Fermi–Hubbard antiferromagnet, Nature (London) 545, 462 (2017).
  82. S. Baier, M. J. Mark, D. Petter, K. Aikawa, L. Chomaz, Z. Cai, M. Baranov, P. Zoller, and F. Ferlaino, Extended Bose-Hubbard models with ultracold magnetic atoms, Science 352, 201 (2016).
  83. E. Guardado-Sanchez, B. M. Spar, P. Schauss, R. Belyansky, J. T. Young, P. Bienias, A. V. Gorshkov, T. Iadecola, and W. S. Bakr, Quench dynamics of a Fermi gas with strong long-range interactions, arXiv:2010.05871.
  84. B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. A. Hazzard, A. M. Rey, D. S. Jin, and J. Ye, Observation of dipolar spin-exchange interactions with lattice-confined polar molecules, Nature (London) 501, 521 (2013).
  85. D. Mitra, P. T. Brown, E. Guardado-Sanchez, S. S. Kondov, T. Devakul, D. A. Huse, P. Schauß, and W. S. Bakr, Quantum gas microscopy of an attractive Fermi–Hubbard system, Nat. Phys. 14, 173 (2017).

Outline

Information

Phys. Rev. Research 3, L012021– Published 5 March, 2021
  • Received 14 November 2020
  • Revised 26 January 2021
  • Accepted 8 February 2021
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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation