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Controlled finite momentum pairing and spatially varying order parameter in proximitized HgTe quantum wells


Conventional s-wave superconductivity arises from singlet pairing of electrons with opposite Fermi momenta, forming Cooper pairs with zero net momentum. Recent studies have focused on coupling s-wave superconductors to systems with an unusual configuration of electronic spin and momentum at the Fermi surface, where the nature of the paired state can be modified and the system may even undergo a topological phase transition. Here we present measurements and theoretical calculations of HgTe quantum wells coupled to aluminium or niobium superconductors and subject to a magnetic field in the plane of the quantum well. We find that this magnetic field tunes the momentum of Cooper pairs in the quantum well, directly reflecting the response of the spin-dependent Fermi surfaces. In the high electron density regime, the induced superconductivity evolves with electron density in agreement with our model based on the Hamiltonian of Bernevig, Hughes and Zhang. This agreement provides a quantitative value for g ̃/vF, where g ̃ is the effective g-factor and vF is the Fermi velocity. Our new understanding of the interplay between spin physics and superconductivity introduces a way to spatially engineer the order parameter from singlet to triplet pairing, and in general allows investigation of electronic spin texture at the Fermi surface of materials.

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Figure 1: Experimental control of the order parameter and of pairing momentum.
Figure 2: Theoretical prediction for the spatially varying order parameter 〈Ψ(x, y)〉1 near a single superconducting lead, with Bz = 0.
Figure 3: Modelling Josephson interference between two superconducting leads.
Figure 4: The evolution of minimum differential resistance as density and parallel magnetic field Bx vary.


  1. Meissner, W. & Ochsenfeld, R. Ein neuer Effekt bei Eintritt der Supraleitfahigkeit. Naturwissenschaften 21, 787–788 (1933).

    Article  ADS  Google Scholar 

  2. Bardeen, J., Cooper, L. N. & Schrieffer, J. R. Theory of superconductivity. Phys. Rev. 108, 1175–1204 (1957).

    Article  ADS  MathSciNet  Google Scholar 

  3. Fulde, P. & Ferrell, R. A. Superconductivity in a strong spin-exchange field. Phys. Rev. 135, A550–A564 (1964).

    Article  ADS  Google Scholar 

  4. Larkin, A. I. & Ovchinnikov, Y. N. Inhomogeneous state of superconductors. Sov. Phys. JETP 20, 762–769 (1965).

    MathSciNet  Google Scholar 

  5. Kenzelmann, M. et al. Coupled superconducting and magnetic order in CeCoIn5 . Science 321, 1652–1654 (2008).

    Article  ADS  Google Scholar 

  6. Mayaffre, H. et al. Evidence of Andreev bound states as a hallmark of the FFLO phase in κ-(BEDT-TTF)2Cu(NCS)2 . Nat. Phys. 10, 928–932 (2014).

    Article  Google Scholar 

  7. Predrag Nikolic, T. D. & Tesanovic, Z. Fractional topological insulators of Cooper pairs induced by the proximity effect. Phys. Rev. Lett. 110, 176804 (2013).

    Article  ADS  Google Scholar 

  8. Reeg, C. R. & Maslov, D. L. Proximity-induced triplet superconductivity in Rashba materials. Phys. Rev. B 92, 134512 (2015).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. Sau, J. D., Lutchyn, R. M., Tewari, S. & Sarma, S. D. Generic new platform for topological quantum computation using semiconductor heterostructures. Phys. Rev. Lett. 104, 040502 (2010).

    Article  ADS  Google Scholar 

  11. Yokoyama, T., Eto, M. & Nazarov, Y. V. Anomalous Josephson effect induced by spin-orbit interaction and Zeeman effect in semiconductor nanowires. Phys. Rev. B 89, 195407 (2014).

    Article  ADS  Google Scholar 

  12. Dolcini, F., Houzet, M. & Meyer, J. S. Topological Josephson φ0 junctions. Phys. Rev. B 92, 035428 (2015).

    Article  ADS  Google Scholar 

  13. Buzdin, A. I., Bulaevskii, L. N. & Panyukov, S. V. Critical-current oscillations as a function of the exchange field and thickness of the ferromagnetic metal (F) in an S-F-S Josephson junction. Pis’ma Zh. Eksp. Teor. Fiz. 35, 147–148 (1982).

    Google Scholar 

  14. Demler, E. A., Arnold, G. B. & Beasley, M. R. Superconducting proximity effects in magnetic metals. Phys. Rev. B 55, 15174–15182 (1997).

    Article  ADS  Google Scholar 

  15. Ryazanov, V. V. et al. Coupling of two superconductors through a ferromagnet: evidence for a π junction. Phys. Rev. Lett. 86, 2427–2430 (2001).

    Article  ADS  Google Scholar 

  16. Kontos, T. et al. Josephson junction through a thin ferromagnetic layer: negative coupling. Phys. Rev. Lett. 89, 137007 (2002).

    Article  ADS  Google Scholar 

  17. Sellier, H. et al. Temperature-induced crossover between 0 and π states in S/F/S junctions. Phys. Rev. B 68, 054531 (2003).

    Article  ADS  Google Scholar 

  18. Frolov, S. M. et al. Measurement of the current-phase relation of superconductor/ ferromagnet/superconductor π Josephson junctions. Phys. Rev. B 70, 144505 (2004).

    Article  ADS  Google Scholar 

  19. Oostinga, J. B. et al. Josephson supercurrent through the topological surface states of strained bulk HgTe. Phys. Rev. X 3, 021007 (2013).

    Google Scholar 

  20. Meservey, R. & Tedrow, P. M. Properties of very thin aluminum films. J. Appl. Phys. 42, 51–53 (1971).

    Article  ADS  Google Scholar 

  21. Tinkham, M. Introduction to Superconductivity (Dover Publications, 2004).

    Google Scholar 

  22. Konig, M. et al. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007).

    Article  ADS  Google Scholar 

  23. Hart, S. et al. Induced superconductivity in the quantum spin Hall edge. Nat. Phys. 10, 638–643 (2014).

    Article  Google Scholar 

  24. Bernevig, B. A., Hughes, T. L. & Zhang, S.-C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006).

    Article  ADS  Google Scholar 

  25. Rothe, D. G. et al. Fingerprint of different spin-orbit terms for spin transport in HgTe quantum wells. New J. Phys. 12, 065012 (2010).

    Article  ADS  Google Scholar 

  26. Weithofer, L. & Recher, P. Chiral Majorana edge states in HgTe quantum wells. New J. Phys. 15, 085008 (2013).

    Article  ADS  Google Scholar 

  27. Konig, M. et al. The quantum spin Hall effect: theory and experiment. J. Phys. Soc. Jpn 77, 031007 (2008).

    Article  ADS  Google Scholar 

  28. Bychkov, Y. A. & Rashba, E. I. Properties of a 2D electron gas with lifted spectral degeneracy. Pis’ma Zh. Eksp. Teor. Fiz. 39, 66–69 (1984).

    Google Scholar 

  29. Dresselhaus, G. Spin-orbit coupling effects in zinc blende structures. Phys. Rev. 100, 580–586 (1955).

    Article  ADS  Google Scholar 

  30. Dynes, R. C. & Fulton, T. A. Supercurrent density distribution in Josephson junctions. Phys. Rev. B 3, 3015–3023 (1971).

    Article  ADS  Google Scholar 

  31. Gui, Y. S. et al. Giant spin-orbit splitting in a HgTe quantum well. Phys. Rev. B 70, 115328 (2004).

    Article  ADS  Google Scholar 

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We acknowledge E. M. Hankiewicz and G. Tkachov for theoretical discussions. This work was supported by the NSF DMR-1206016, by the STC Center for Integrated Quantum Materials under NSF Grant No. DMR-1231319, by the NSF GRFP under Grant DGE1144152, and by Microsoft Corporation Project Q. We acknowledge additional financial support from the German Research Foundation (The Leibniz Program, Sonderforschungsbereich 1170 ‘Tocotronics’ and Schwerpunktprogramm 1666), the EU ERC-AG program (Project 3-TOP) and the Elitenetzwerk Bayern IDK ‘Topologische Isolatoren’.

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The experiment is a collaboration between the Harvard and Würzburg experimental groups. S.H., H.R., M.K., G.B.-S., B.I.H. and A.Y. carried out the theoretical modelling and analysis.

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Correspondence to Amir Yacoby.

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The authors declare no competing financial interests.

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Hart, S., Ren, H., Kosowsky, M. et al. Controlled finite momentum pairing and spatially varying order parameter in proximitized HgTe quantum wells. Nature Phys 13, 87–93 (2017).

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