Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Superconducting, insulating and anomalous metallic regimes in a gated two-dimensional semiconductor–superconductor array

Nature Physics volume 14, pages 1138–1144 (2018)Cite this article

Subjects

Abstract

The superconductor–insulator transition in two dimensions has been widely investigated as a paradigmatic quantum phase transition. The topic remains controversial because many experiments exhibit a metallic regime with saturating low-temperature resistance, which is at odds with conventional theory. Here, we explore this transition in a highly controllable system, a semiconductor heterostructure with epitaxial aluminium, patterned to form a regular array of superconducting islands connected by a gateable quantum well. Spanning nine orders of magnitude in resistance, the system exhibits regimes of superconducting, metallic and insulating behaviour, along with signatures of flux commensurability and vortex penetration. An in-plane magnetic field eliminates the metallic regime, restoring the direct superconductor–insulator transition; it also improves the scaling behaviour while strongly altering the scaling exponent.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it

$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Semiconductor/superconductor array.
Fig. 2: Voltage-controlled transitions.
Fig. 3: Experimental phase diagram.
Fig. 4: Temperature, magnetic field and nonlinear response.
Fig. 5: Flux effects in S, M* and I regimes.
Fig. 6: In-plane magnetic field effects.

References

  1. Jaeger, H. M., Haviland, D. B., Orr, B. G. & Goldman, A. M. Onset of superconductivity in ultrathin granular metal films. Phys. Rev. B 40, 182–196 (1989).

    Article  ADS  Google Scholar 

  2. Lee, S. J. & Ketterson, J. B. Critical sheet resistance for the suppression of superconductivity in thin Mo-C films. Phys. Rev. Lett. 64, 3078–3081 (1990).

    Article  ADS  Google Scholar 

  3. Goldman, A. M. Superconductor–insulator transitions. Int. J. Mod. Phys. B 24, 4081–4101 (2010).

    Article  ADS  Google Scholar 

  4. Gantmakher, V. F. & Dolgopolov, V. T. Superconductor–insulator quantum phase transition. Phys. Usp. 53, 1–49 (2010).

  5. Dobrosavljevic, V., Trivedi, N. & Valles, J. M. Jr Conductor Insulator Quantum Phase Transitions (Oxford Univ. Press, Oxford, 2012).

  6. Kapitulnik, A., Kivelson, S. A. & Spivak, B. Anomalous metals – failed superconductors. Preprint at https://arxiv.org/abs/1712.07215 (2017).

  7. Mason, N. & Kapitulnik, A. Dissipation effects on the superconductor–insulator transition in 2D superconductors. Phys. Rev. Lett. 82, 5341–5344 (1999).

    Article  ADS  Google Scholar 

  8. Yazdani, A. & Kapitulnik, A. Superconducting–insulating transition in two-dimensional a-MoGe thin films. Phys. Rev. Lett. 74, 3037–3040 (1995).

    Article  ADS  Google Scholar 

  9. Steiner, M. & Kapitulnik, A. Superconductivity in the insulating phase above the field-tuned superconductor–insulator transition in disordered indium oxide films. Physica C 422, 16–26 (2005).

    Article  ADS  Google Scholar 

  10. Bollinger, A. T. et al. Superconductor–insulator transition in La2−xSrxCuO4 at the pair quantum resistance. Nature 472, 458–460 (2011).

    Article  ADS  Google Scholar 

  11. Schneider, R., Zaitsev, A. G., Fuchs, D. & v. Löhneysen, H. Superconductor–insulator quantum phase transition in disordered FeSe thin films. Phys. Rev. Lett. 108, 257003 (2012).

    Article  ADS  Google Scholar 

  12. Allain, A., Han, Z. & Bouchiat, V. Electrical control of the superconducting-to-insulating transition in graphene-metal hybrids. Nat. Mater. 11, 590–594 (2012).

    Article  ADS  Google Scholar 

  13. Marković, N., Christiansen, C., Mack, A. M., Huber, W. H. & Goldman, A. M. Superconductor–insulator transition in two dimensions. Phys. Rev. B 60, 4320–4328 (1999).

    Article  ADS  Google Scholar 

  14. Park, S., Shin, J. & Kim, E. Scaling analysis of field-tuned superconductor–insulator transition in two-dimensional tantalum thin films. Sci. Rep. 7, 42969 (2017).

    Article  ADS  Google Scholar 

  15. Steiner, M. A., Breznay, N. P. & Kapitulnik, A. Approach to a superconductor-to-Bose-insulator transition in disordered films. Phys. Rev. B 77, 212501 (2008).

    Article  ADS  Google Scholar 

  16. Eley, S., Gopalakrishnan, S., Goldbart, P. M. & Mason, N. Approaching zero-temperature metallic states in mesoscopic superconductor–normal–superconductor arrays. Nat. Phys. 8, 59–62 (2012).

    Article  Google Scholar 

  17. Han, Z. et al. Collapse of superconductivity in a hybrid tin-graphene Josephson junction array. Nat. Phys. 10, 380–386 (2014).

    Article  Google Scholar 

  18. Feigel’man, M. & Larkin, A. Quantum superconductor–metal transition in a 2D proximity-coupled array. Chem. Phys. 235, 107–114 (1998).

    Article  Google Scholar 

  19. Spivak, B., Zyuzin, A. & Hruska, M. Quantum superconductor–metal transition. Phys. Rev. B 64, 132502 (2001).

    Article  ADS  Google Scholar 

  20. Spivak, B., Oreto, P. & Kivelson, S. A. Theory of quantum metal to superconductor transitions in highly conducting systems. Phys. Rev. B 77, 214523 (2008).

    Article  ADS  Google Scholar 

  21. Lee, D.-H., Kivelson, S. & Zhang, S.-C. Theory of the quantum-Hall liquid to insulator transition. Phys. Rev. Lett. 67, 3302–3305 (1991).

    Article  ADS  Google Scholar 

  22. Kivelson, S., Lee, D.-H. & Zhang, S.-C. Global phase diagram in the quantum Hall effect. Phys. Rev. B 46, 2223–2238 (1992).

    Article  ADS  Google Scholar 

  23. Phillips, P. & Dalidovich, D. The elusive Bose metal. Science 302, 243–247 (2003).

    Article  ADS  Google Scholar 

  24. Kapitulnik, A., Mason, N., Kivelson, S. A. & Chakravarty, S. Effects of dissipation on quantum phase transitions. Phys. Rev. B 63, 125322 (2001).

    Article  ADS  Google Scholar 

  25. Mulligan, M. & Raghu, S. Composite fermions and the field-tuned superconductor-insulator transition. Phys. Rev. B 93, 205116 (2016).

    Article  ADS  Google Scholar 

  26. Tamir, I. et al. Extreme sensitivity of the superconducting state in thin films. Preprint at https://arxiv.org/abs/1804.04648 (2018).

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

    Article  ADS  Google Scholar 

  28. Chalker, J. T. et al. Thermal metal in network models of a disordered two-dimensional superconductor. Phys. Rev. B 65, 012506 (2001).

    Article  ADS  Google Scholar 

  29. Dimitrova, O. & Feigel’man, M. V. Theory of a two-dimensional superconductor with broken inversion symmetry. Phys. Rev. B 76, 014522 (2007).

    Article  ADS  Google Scholar 

  30. Levine, Y., Haim, A. & Oreg, Y. Realizing topological superconductivity with superlattices. Phys. Rev. B 96, 165147 (2017).

    Article  ADS  Google Scholar 

  31. Chang, W. et al. Hard gap in epitaxial semiconductor–superconductor nanowires. Nat. Nanotech. 10, 232–236 (2015).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  33. Kjaergaard, M. et al. Transparent semiconductor–superconductor interface and induced gap in an epitaxial heterostructure Josephson junction. Phys. Rev. Appl. 7, 034029 (2017).

    Article  ADS  Google Scholar 

  34. Fisher, M. P. A. Quantum phase transitions in disordered two-dimensional superconductors. Phys. Rev. Lett. 65, 923–926 (1990).

    Article  ADS  Google Scholar 

  35. Biscaras, J. et al. Multiple quantum criticality in a two-dimensional superconductor. Nat. Mater. 12, 542–548 (2013).

    Article  ADS  Google Scholar 

  36. Breznay, N. P., Steiner, M. A., Kivelson, S. A. & Kapitulnik, A. Phase transition in granulated superconductors. Proc. Natl Acad. Sci. USA 113, 208–285 (2016).

    Article  Google Scholar 

  37. Shkovskii, B. I. & Efros, A. L. Electronic Properties of Doped Semiconductors (Springer, Berlin, 1984).

  38. Baturina, T. I., Mironov, A. Y., Vinokur, V. M., Baklanov, M. R. & Strunk, C. Localized superconductivity in the quantum-critical region of the disorder-driven superconductor–insulator transition in TiN thin films. Phys. Rev. Lett. 99, 39 (2007).

    Article  Google Scholar 

  39. Joung, D. & Khondaker, S. I. Efros–Shklovskii variable-range hopping in reduced graphene oxide sheets of varying carbon sp 2 fraction. Phys. Rev. B 86, 1964–1968 (2012).

    Article  Google Scholar 

  40. Sambandamurthy, G., Engel, L. W., Johansson, A. & Shahar, D. Superconductivity-related insulating behavior. Phys. Rev. Lett. 92, 107005 (2004).

    Article  ADS  Google Scholar 

  41. Fazio, R. & van der Zant, H. Quantum phase transitions and vortex dynamics in superconducting networks. Phys. Rep. 355, 235–334 (2001).

    Article  ADS  Google Scholar 

  42. Baelus, B. J. et al. Multivortex and giant vortex states near the expulsion and penetration fields in thin mesoscopic superconducting squares. Phys. Rev. B 73, 024514 (2006).

    Article  ADS  Google Scholar 

  43. Vinokur, V. M. et al. Superinsulator and quantum synchronization. Nature 452, 613–615 (2008).

    Article  ADS  Google Scholar 

  44. Wagenblast, K. H., vanOtterlo, A., Schön, G. & Zimanyi, G. T. New universality class at the superconductor–insulator transition. Phys. Rev. Lett. 78, 1779–1782 (1997).

    Article  ADS  Google Scholar 

  45. van der Zant, H. S. J., Elion, W. J., Geerligs, L. J. & Mooij, J. E. Quantum phase transitions in two dimensions: Experiments in Josephson-junction arrays. Phys. Rev. B 54, 10081–10093 (1996).

    Article  ADS  Google Scholar 

  46. Couëdo, F. et al. Dissipative phases across the superconductor-to-insulator transition. Sci. Rep. 6, 35834 (2016).

    Article  ADS  Google Scholar 

  47. Suominen, H. J. et al. Anomalous Fraunhofer interference in epitaxial superconductor-semiconductor Josephson junctions. Phys. Rev. B 95, 035307 (2017).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank A. Kapitulnik, S. Kivelson, K. Rasmussen, D. Shahar, B. Spivak, C. Strunk and V. Vinokur for useful discussion. Research was supported by Microsoft Station Q and the Danish National Research Foundation. C.M.M. acknowledges support from the Villum Foundation. F.N. acknowledges support from a Marie Curie Fellowship (no. 659653).

Author information

Author notes

  1. C. G. L. Bøttcher

    Present address: Harvard University, Cambridge, MA, USA

  2. M. Kjaergaard

    Present address: MIT, Cambridge, MA, USA

  3. J. Shabani

    Present address: NYU, New York, NY, USA

Authors and Affiliations

  1. Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

    C. G. L. Bøttcher, F. Nichele, M. Kjaergaard, H. J. Suominen & C. M. Marcus

  2. California NanoSystems Institute, University of California, Santa Barbara, CA, USA

    J. Shabani & C. J. Palmstrøm

  3. Department of Electrical Engineering, University of California, Santa Barbara, CA, USA

    C. J. Palmstrøm

  4. Materials Department, University of California, Santa Barbara, CA, USA

    C. J. Palmstrøm

Authors
  1. C. G. L. Bøttcher
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Nichele
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Kjaergaard
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. H. J. Suominen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. J. Shabani
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. C. J. Palmstrøm
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. C. M. Marcus
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

C.B., C.M. and F.N. conceived the experiments. C.P. and J.S. grew the wafer. C.B. and F.N. fabricated the samples and performed measurements. C.B., C.M. and F.N. analysed the data and wrote the manuscript with input from M.K. and H.S.

Corresponding author

Correspondence to C. M. Marcus.

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.

Supplementary information

Supplementary Material

Supplementary figures 1–8; Supplementary references 1–7

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Bøttcher, C.G.L., Nichele, F., Kjaergaard, M. et al. Superconducting, insulating and anomalous metallic regimes in a gated two-dimensional semiconductor–superconductor array. Nature Phys 14, 1138–1144 (2018). https://doi.org/10.1038/s41567-018-0259-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-018-0259-9

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing