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.
This is a preview of subscription content
Subscribe to Journal
Get full journal access for 1 year
only $8.25 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Meissner, W. & Ochsenfeld, R. Ein neuer Effekt bei Eintritt der Supraleitfahigkeit. Naturwissenschaften 21, 787–788 (1933).
Bardeen, J., Cooper, L. N. & Schrieffer, J. R. Theory of superconductivity. Phys. Rev. 108, 1175–1204 (1957).
Fulde, P. & Ferrell, R. A. Superconductivity in a strong spin-exchange field. Phys. Rev. 135, A550–A564 (1964).
Larkin, A. I. & Ovchinnikov, Y. N. Inhomogeneous state of superconductors. Sov. Phys. JETP 20, 762–769 (1965).
Kenzelmann, M. et al. Coupled superconducting and magnetic order in CeCoIn5 . Science 321, 1652–1654 (2008).
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).
Predrag Nikolic, T. D. & Tesanovic, Z. Fractional topological insulators of Cooper pairs induced by the proximity effect. Phys. Rev. Lett. 110, 176804 (2013).
Reeg, C. R. & Maslov, D. L. Proximity-induced triplet superconductivity in Rashba materials. Phys. Rev. B 92, 134512 (2015).
Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).
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).
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).
Dolcini, F., Houzet, M. & Meyer, J. S. Topological Josephson φ0 junctions. Phys. Rev. B 92, 035428 (2015).
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).
Demler, E. A., Arnold, G. B. & Beasley, M. R. Superconducting proximity effects in magnetic metals. Phys. Rev. B 55, 15174–15182 (1997).
Ryazanov, V. V. et al. Coupling of two superconductors through a ferromagnet: evidence for a π junction. Phys. Rev. Lett. 86, 2427–2430 (2001).
Kontos, T. et al. Josephson junction through a thin ferromagnetic layer: negative coupling. Phys. Rev. Lett. 89, 137007 (2002).
Sellier, H. et al. Temperature-induced crossover between 0 and π states in S/F/S junctions. Phys. Rev. B 68, 054531 (2003).
Frolov, S. M. et al. Measurement of the current-phase relation of superconductor/ ferromagnet/superconductor π Josephson junctions. Phys. Rev. B 70, 144505 (2004).
Oostinga, J. B. et al. Josephson supercurrent through the topological surface states of strained bulk HgTe. Phys. Rev. X 3, 021007 (2013).
Meservey, R. & Tedrow, P. M. Properties of very thin aluminum films. J. Appl. Phys. 42, 51–53 (1971).
Tinkham, M. Introduction to Superconductivity (Dover Publications, 2004).
Konig, M. et al. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007).
Hart, S. et al. Induced superconductivity in the quantum spin Hall edge. Nat. Phys. 10, 638–643 (2014).
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).
Rothe, D. G. et al. Fingerprint of different spin-orbit terms for spin transport in HgTe quantum wells. New J. Phys. 12, 065012 (2010).
Weithofer, L. & Recher, P. Chiral Majorana edge states in HgTe quantum wells. New J. Phys. 15, 085008 (2013).
Konig, M. et al. The quantum spin Hall effect: theory and experiment. J. Phys. Soc. Jpn 77, 031007 (2008).
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).
Dresselhaus, G. Spin-orbit coupling effects in zinc blende structures. Phys. Rev. 100, 580–586 (1955).
Dynes, R. C. & Fulton, T. A. Supercurrent density distribution in Josephson junctions. Phys. Rev. B 3, 3015–3023 (1971).
Gui, Y. S. et al. Giant spin-orbit splitting in a HgTe quantum well. Phys. Rev. B 70, 115328 (2004).
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’.
The authors declare no competing financial interests.
About this article
Cite this article
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). https://doi.org/10.1038/nphys3877
Nature Communications (2020)
Nature Communications (2019)
Topological Larkin-Ovchinnikov phase and Majorana zero mode chain in bilayer superconducting topological insulator films
Communications Physics (2019)