Topological superconductivity in hybrid devices

Abstract

Topological superconductivity can emerge from the combination of conventional superconductivity in a metal and strong spin–orbit coupling in a semiconductor when they are made into a hybrid device. The most exciting manifestation of topological superconductivity is the Majorana zero modes that are predicted to exist at the ends of the proximatized nanowires. In this Perspective, we review the evidence for the existence of Majorana zero modes that has accumulated in numerous experiments and the remaining uncertainties, and discuss what additional evidence is desirable. One very important factor for future development is the quality of the interface between the superconductor and semiconductor; we sketch out where further progress in the materials science of these interfaces can take us. We then discuss the path towards applying these modes in topologically protected quantum computing and observing more exotic kinds of superconductivity based on the same materials platform, and how to make connections to high-energy physics.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: The concept of topological superconductivity using a spinless superconductor primer.
Fig. 2: Zero-bias conductance peaks can appear due to MZMs or due to trivial ABSs.
Fig. 3: Materials considerations for superconductor/semiconductor hybrid systems.
Fig. 4: Future exotic topologically superconducting phases.

References

  1. 1.

    Read, N. & Green, D. 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, 10267–10297 (2000).

    ADS  Google Scholar 

  2. 2.

    Ivanov, D. A. Non-abelian statistics of half-quantum vortices in p-wave superconductors. Phys. Rev. Lett. 86, 268–271 (2001).

    ADS  Google Scholar 

  3. 3.

    Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003).

    ADS  MathSciNet  MATH  Google Scholar 

  4. 4.

    Volovik, G. E. Fermion zero modes on vortices in chiral superconductors. J. Exp. Theor. Phys. Lett. 70, 609–614 (1999).

    Google Scholar 

  5. 5.

    Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).

    ADS  Google Scholar 

  6. 6.

    Lutchyn, R. M., Sau, J. D. & Das Sarma, S. Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures. Phys. Rev. Lett. 105, 077001 (2010).

    ADS  Google Scholar 

  7. 7.

    Oreg, Y., Refael, G. & von Oppen, F. Helical liquids and Majorana bound states in quantum wires. Phys. Rev. Lett. 105, 177002 (2010).

    ADS  Google Scholar 

  8. 8.

    Kitaev, A. Y. Unpaired Majorana fermions in quantum wires. Phys. -Uspekhi 44, 131–136 (2001).

    ADS  Google Scholar 

  9. 9.

    Sengupta, K., Žutić, I., Kwon, H.-J., Yakovenko, V. M. & Das Sarma, S. Midgap edge states and pairing symmetry of quasi-one-dimensional organic superconductors. Phys. Rev. B 63, 144531 (2001).

    ADS  Google Scholar 

  10. 10.

    Liu, C.-X., Cole, W. S. & Sau, J. D. Proposal for measuring the parity anomaly in a topological superconductor ring. Phys. Rev. Lett. 122, 117001 (2019).

    ADS  Google Scholar 

  11. 11.

    Krogstrup, P. et al. Epitaxy of semiconductor–superconductor nanowires. Nat. Mater. 14, 400–406 (2015).

    ADS  Google Scholar 

  12. 12.

    Shabani, J. et al. Two-dimensional epitaxial superconductor-semiconductor heterostructures: A platform for topological superconducting networks. Phys. Rev. B 93, 155402 (2016).

    ADS  Google Scholar 

  13. 13.

    Gazibegovic, S. et al. Epitaxy of advanced nanowire quantum devices. Nature 548, 434–438 (2017).

    ADS  Google Scholar 

  14. 14.

    Sugaya, T., Okada, Y. & Kawabe, M. Selective growth of GaAs by molecular beam epitaxy. Jpn. J. Appl. Phys. 31, L713 (1992).

    ADS  Google Scholar 

  15. 15.

    Nishinaga, T. & Bacchin, G. Selective area MBE of GaAs, AlAs and their alloys by periodic supply epitaxy. Thin Solid Films 367, 6–12 (2000).

    ADS  Google Scholar 

  16. 16.

    Mourik, V. et al. Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices. Science 336, 1003–1007 (2012).

    ADS  Google Scholar 

  17. 17.

    Das, A. et al. Zero-bias peaks and splitting in an Al-InAs nanowire topological superconductor as a signature of Majorana fermions. Nat. Phys. 8, 887–895 (2012).

    Google Scholar 

  18. 18.

    Deng, M. et al. Anomalous zero-bias conductance peak in a Nb–InSb nanowire–Nb hybrid device. Nano. Lett. 12, 6414–6419 (2012).

    ADS  Google Scholar 

  19. 19.

    Finck, A. D. K., Van Harlingen, D. J., Mohseni, P. K., Jung, K. & Li, X. Anomalous modulation of a zero-bias peak in a hybrid nanowire-superconductor device. Phys. Rev. Lett. 110, 126406 (2013).

    ADS  Google Scholar 

  20. 20.

    Churchill, H. O. H. et al. Superconductor-nanowire devices from tunneling to the multichannel regime: Zero-bias oscillations and magnetoconductance crossover. Phys. Rev. B 87, 241401 (2013).

    ADS  Google Scholar 

  21. 21.

    Lee, E. J. H. et al. Spin-resolved andreev levels and parity crossings in hybrid superconductor-semiconductor nanostructures. Nat. Nanotechnol. 9, 79–84 (2014).

    ADS  Google Scholar 

  22. 22.

    Liu, C.-X., Sau, J. D., Stanescu, T. D. & Das Sarma, S. 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, 075161 (2017).

    ADS  Google Scholar 

  23. 23.

    Vuik, A., Nijholt, B., Akhmerov, A. R. & Wimmer, M. Reproducing topological properties with quasi-Majorana states. SciPost Phys. 7, 061 (2019).

    ADS  Google Scholar 

  24. 24.

    Kells, Meidan, G. D. & Brouwer, P. W. Near-zero-energy end states in topologically trivial spin-orbit coupled superconducting nanowires with a smooth confinement. Phys. Rev. B 86, 100503 (2012).

    ADS  Google Scholar 

  25. 25.

    Pan, H., Cole, W. S., Sau, J. D. & Das Sarma, S. Generic quantized zero-bias conductance peaks in superconductor-semiconductor hybrid structures. Phys. Rev. B 101, 024506 (2020).

    ADS  Google Scholar 

  26. 26.

    Brouwer, P. W. & Beenakker, C. W. J. Insensitivity to time-reversal symmetry breaking of universal conductance fluctuations with Andreev reflection. Phys. Rev. B 52, 16772 (1995).

    ADS  Google Scholar 

  27. 27.

    Altland, A. & Zirnbauer, M. R. Random matrix theory of a chaotic andreev quantum dot. Phys. Rev. Lett. 76, 3420–3423 (1996).

    ADS  Google Scholar 

  28. 28.

    Albrecht, S. M. et al. Exponential protection of zero modes in Majorana islands. Nature 531, 206–209 (2016).

    ADS  Google Scholar 

  29. 29.

    Deng, M. T. et al. Majorana bound state in a coupled quantum-dot hybrid-nanowire system. Science 354, 1557–1562 (2016).

    ADS  Google Scholar 

  30. 30.

    Chen, J. et al. Experimental phase diagram of zero-bias conductance peaks in superconductor/semiconductor nanowire devices. Sci. Adv. 3, e1701476 (2017).

    ADS  Google Scholar 

  31. 31.

    Nichele, F. et al. Scaling of Majorana zero-bias conductance peaks. Phys. Rev. Lett. 119, 136803 (2017).

    ADS  Google Scholar 

  32. 32.

    Kjaergaard, M. et al. Quantized conductance doubling and hard gap in a two-dimensional semiconductor–superconductor heterostructure. Nat. Commun. 7, 12841 (2016).

    ADS  Google Scholar 

  33. 33.

    Grivnin, A., Bor, E., Heiblum, M., Oreg, Y. & Shtrikman, H. Concomitant opening of a bulk-gap with an emerging possible majorana zero mode. Nat. Commun. 10, 1940 (2019).

    ADS  Google Scholar 

  34. 34.

    Chen, J. et al. Ubiquitous non-Majorana zero-bias conductance peaks in nanowire devices. Phys. Rev. Lett. 123, 107703 (2019).

    ADS  Google Scholar 

  35. 35.

    Rokhinson, L. P., Liu, X. & Furdyna, J. K. The fractional a.c. Josephson effect in a semiconductor–superconductor nanowire as a signature of Majorana particles. Nat. Phys. 8, 795–799 (2012).

    Google Scholar 

  36. 36.

    Houzet, M., Meyer, J. S., Badiane, D. M. & Glazman, L. I. Dynamics of majorana states in a topological Josephson junction. Phys. Rev. Lett. 111, 046401 (2013).

    ADS  Google Scholar 

  37. 37.

    Billangeon, P.-M., Pierre, F., Bouchiat, H. & Deblock, R. Ac Josephson effect and resonant Cooper pair tunneling emission of a single Cooper pair transistor. Phys. Rev. Lett. 98, 216802 (2007).

    ADS  Google Scholar 

  38. 38.

    Anselmetti, G. L. R. et al. End-to-end correlated subgap states in hybrid nanowires. Preprint at https://arxiv.org/abs/1908.05549 (2019).

  39. 39.

    Yu, P. et al. Non-majorana states yield nearly quantized conductance in superconductor-semiconductor nanowire devices. Preprint at https://arxiv.org/abs/2004.08583 (2020).

  40. 40.

    Akhmerov, A. R., Dahlhaus, J. P., Hassler, F., Wimmer, M. & Beenakker, C. W. J. Quantized conductance at the Majorana phase transition in a disordered superconducting wire. Phys. Rev. Lett. 106, 057001 (2011).

    ADS  Google Scholar 

  41. 41.

    Rosdahl, T. Ö., Vuik, A., Kjaergaard, M. & Akhmerov, A. R. Andreev rectifier: a nonlocal conductance signature of topological phase transitions. Phys. Rev. B 97, 045421 (2018).

    ADS  Google Scholar 

  42. 42.

    Fu., L. Electron teleportation via Majorana bound states in a mesoscopic superconductor. Phys. Rev. Lett. 104, 056402 (2010).

    ADS  Google Scholar 

  43. 43.

    Michaeli, K., Landau, L. A., Sela, E. & Fu, L. Electron teleportation and statistical transmutation in multiterminal Majorana islands. Phys. Rev. B 96, 205403 (2017).

    ADS  Google Scholar 

  44. 44.

    Motrunich, O., Damle, K. & Huse, D. A. Griffiths effects and quantum critical points in dirty superconductors without spin-rotation invariance: one-dimensional examples. Phys. Rev. B 63, 224204 (2001).

    ADS  Google Scholar 

  45. 45.

    Ren, H. et al. Topological superconductivity in a phase-controlled Josephson junction. Nature 569, 93–98 (2019).

    ADS  Google Scholar 

  46. 46.

    Fornieri, A. et al. Evidence of topological superconductivity in planar Josephson junctions. Nature 569, 89–92 (2019).

    Google Scholar 

  47. 47.

    Alicea, J., Oreg, Y., Refael, G., von Oppen, F. & Fisher, M. P. A. Non-abelian statistics and topological quantum information processing in 1D wire networks. Nat. Phys. 7, 412–417 (2011).

    Google Scholar 

  48. 48.

    Van Heck, B., Akhmerov, A. R., Hassler, F., Burrello, M. & Beenakker, C. W. J. Coulomb-assisted braiding of Majorana fermions in a Josephson junction array. New. J. Phys. 14, 035019 (2012).

    Google Scholar 

  49. 49.

    Karzig, T. et al. Scalable designs for quasiparticle-poisoning-protected topological quantum computation with Majorana zero modes. Phys. Rev. B 95, 235305 (2017).

    ADS  Google Scholar 

  50. 50.

    Stenger, J. P. T., Hatridge, M., Frolov, S. M. & Pekker, D. Braiding quantum circuit based on the 4π Josephson effect. Phys. Rev. D. 99, 035307 (2019).

    ADS  Google Scholar 

  51. 51.

    Krizek, F. et al. Field effect enhancement in buffered quantum nanowire networks. Phys. Rev. Mater. 2, 093401 (2018).

    Google Scholar 

  52. 52.

    Aseev, P. et al. Selectivity map for molecular beam epitaxy of advanced III–V quantum nanowire networks. Nano Lett. 19, 218–227 (2018).

    ADS  Google Scholar 

  53. 53.

    Lee, J. S. et al. Selective-area chemical beam epitaxy of in-plane InAs one-dimensional channels grown on InP (001), InP (111) B, and InP (011) surfaces. Phys. Rev. Mater. 3, 084606 (2019).

    Google Scholar 

  54. 54.

    Friedl, M. et al. Template-assisted scalable nanowire networks. Nano Lett. 18, 2666–2671 (2018).

    ADS  Google Scholar 

  55. 55.

    Rainis, D. & Loss, D. Majorana qubit decoherence by quasiparticle poisoning. Phys. Rev. B 85, 174533 (2012).

    ADS  Google Scholar 

  56. 56.

    Lafarge, P., Joyez, P., Esteve, D., Urbina, C. & Devoret, M. H. Measurement of the even-odd free-energy difference of an isolated superconductor. Phys. Rev. Lett. 70, 994–997 (1993).

    ADS  Google Scholar 

  57. 57.

    Pendharkar, M. et al. Parity-preserving and magnetic field resilient superconductivity in indium antimonide nanowires with tin shells. Preprint at https://arxiv.org/abs/1912.06071 (2019).

  58. 58.

    Bjergfelt, M. et al. Superconducting vanadium/indium-arsenide hybrid nanowires. Nanotechnology 30, 294005 (2019).

    Google Scholar 

  59. 59.

    Carrad, D. J. et al. Shadow lithography for in-situ growth of generic semiconductor/superconductor devices. Preprint at https://arxiv.org/abs/1911.00460 (2019).

  60. 60.

    Barkeshli, M. & Sau, J. D. Physical architecture for a universal topological quantum computer based on a network of Majorana nanowires. Preprint at https://arxiv.org/abs/1509.07135 (2015).

  61. 61.

    Ebisu, H., Sagi, E. & Oreg, Y. Supersymmetry in the insulating phase of a chain of majorana cooper pair boxes. Phys. Rev. Lett. 123, 026401 (2019).

    ADS  Google Scholar 

  62. 62.

    Chew, A., Essin, A. & Alicea, J. Approximating the Sachdev-Ye-Kitaev model with Majorana wires. Phys. Rev. B 96, 121119 (2017).

    ADS  Google Scholar 

  63. 63.

    Clarke, D. J., Alicea, J. & Shtengel, K. Exotic non-abelian anyons from conventional fractional quantum Hall states. Nat. Commun. 4, 1348 (2013).

    ADS  Google Scholar 

  64. 64.

    Lindner, N. H., Berg, E., Refael, G. & Stern, A. Fractionalizing majorana fermions: Non-abelian statistics on the edges of abelian quantum hall states. Phys. Rev. X 2, 041002 (2012).

    Google Scholar 

  65. 65.

    Cheng, M. Superconducting proximity effect on the edge of fractional topological insulators. Phys. Rev. B 86, 195126 (2012).

    ADS  Google Scholar 

  66. 66.

    Amet, F. et al. Supercurrent in the quantum Hall regime. Science 352, 966–969 (2016).

    ADS  MathSciNet  MATH  Google Scholar 

  67. 67.

    Moore, G. & Read, N. Nonabelions in the fractional quantum Hall effect. Nucl. Phys. B 360, 362–396 (1991).

    ADS  MathSciNet  Google Scholar 

  68. 68.

    Kitaev, A. Anyons in an exactly solved model and beyond. Ann. Phys. 321, 2–111 (2006).

    ADS  MathSciNet  MATH  Google Scholar 

  69. 69.

    Yao, H. & Kivelson, S. A. Exact chiral spin liquid with non-abelian anyons. Phys. Rev. Lett. 99, 247203 (2007).

    ADS  Google Scholar 

  70. 70.

    Wess, J. & Bagger, J. Supersymmetry and supergravity (Princeton Univ. Press, 1992).

  71. 71.

    Friedan, D., Qiu, Z. & Shenker, S. H. Conformal invariance, unitarity and two-dimensional critical exponents. Phys. Rev. Lett. 52, 1575–1578 (1984).

    ADS  MathSciNet  MATH  Google Scholar 

  72. 72.

    Sachdev, S. & Ye, J. Gapless spin-fluid ground state in a random quantum Heisenberg magnet. Phys. Rev. Lett. 70, 3339–3342 (1993).

    ADS  Google Scholar 

  73. 73.

    Kitaev, A. A Simple Model Of Quantum Holography (Part 1) http://online.kitp.ucsb.edu/online/entangled15/kitaev/ (UC Santa Barbara, 2015).

  74. 74.

    Kitaev, A. A Simple Model Of Quantum Holography (Part 2) http://online.kitp.ucsb.edu/online/entangled15/kitaev2/ (UC Santa Barbara, 2015).

  75. 75.

    Maldacena, J., Shenker, S. H. & Stanford, D. A bound on chaos. J. High. Energy Phys. 2016, 106 (2016).

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

We thank S. Das Sarma for comments. S.M.F. is supported by NSF DMR-1906325, NSF PIRE-1743717, ONR and ARO. M.J.M is supported by Microsoft Quantum. J.S. is supported by the NSF-DMR1555135 and helpful discussions at the KITP under Grant no. NSF PHY-1748958.

Author information

Affiliations

Authors

Corresponding author

Correspondence to S. M. Frolov.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Frolov, S.M., Manfra, M.J. & Sau, J.D. Topological superconductivity in hybrid devices. Nat. Phys. 16, 718–724 (2020). https://doi.org/10.1038/s41567-020-0925-6

Download citation