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.


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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’.

Author information

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.

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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