Spin-resolved Andreev levels and parity crossings in hybrid superconductor–semiconductor nanostructures

Abstract

The physics and operating principles of hybrid superconductor–semiconductor devices rest ultimately on the magnetic properties of their elementary subgap excitations, usually called Andreev levels. Here we report a direct measurement of the Zeeman effect on the Andreev levels of a semiconductor quantum dot with large electron g-factor, strongly coupled to a conventional superconductor with a large critical magnetic field. This material combination allows spin degeneracy to be lifted without destroying superconductivity. We show that a spin-split Andreev level crossing the Fermi energy results in a quantum phase transition to a spin-polarized state, which implies a change in the fermionic parity of the system. This crossing manifests itself as a zero-bias conductance anomaly at finite magnetic field with properties that resemble those expected for Majorana modes in a topological superconductor. Although this resemblance is understood without evoking topological superconductivity, the observed parity transitions could be regarded as precursors of Majorana modes in the long-wire limit.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Andreev levels in a hybrid N–QD–S system and device description.
Figure 2: Andreev levels in different coupling regimes and their magnetic-field dependence.
Figure 3: Magnetic-field evolution of the Andreev levels at fixed gate voltage and the level-repulsion effect.
Figure 4: Magnetic-field induced QPT and angle anisotropy.

References

  1. 1

    De Franceschi, S., Kouwenhoven, L. P., Schönenberger, C. & Wernsdorfer, W. Hybrid superconductor–quantum dot devices. Nature Nanotechnol. 5, 703–711 (2010).

  2. 2

    Hofstetter, L., Csonka, S., Nygård, J. & Schönenberger, C. Cooper pair splitter realized in a two-quantum-dot Y-junction. Nature 461, 960–963 (2009).

  3. 3

    Herrmann, L. G. et al. Carbon nanotubes as Cooper pair splitters. Phys. Rev. Lett. 104, 026801 (2010).

  4. 4

    Das, A. et al. High-efficiency Cooper pair splitting demonstrated by two-particle conductance resonance and positive noise cross-correlation. Nature Commun. 3, 1165 (2012).

  5. 5

    Cleuziou, J., Wernsdorfer, W., Bouchiat, V., Ondarcuhu, T. & Monthioux, M. Carbon nanotube superconducting quantum interference device. Nature Nanotechnol. 1, 53–59 (2006).

  6. 6

    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).

  7. 7

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

  8. 8

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

  9. 9

    van Dam, J. A., Nazarov, Y. V., Bakkers, E. P. A. M., De Franceschi, S. & Kouwenhoven, L. P. Supercurrent reversal in quantum dots. Nature 442, 667–670 (2006).

  10. 10

    Buitelaar, M. R., Nussbaumer, T. & Schönenberger, C. Quantum dot in the Kondo regime coupled to superconductors. Phys. Rev. Lett. 89, 256801 (2002).

  11. 11

    Jorgensen, H. I., Novotny, T., Grove-Rasmussen, K., Flensberg, K. & Lindelof, P. E. Critical current 0–π transition in designed Josephson quantum dot junctions. Nano Lett. 7, 2441–2445 (2007).

  12. 12

    Maurand, R. et al. First-order 0–π quantum phase transition in the Kondo regime of a superconducting carbon nanotube quantum dot. Phys. Rev. X 2, 011009 (2012).

  13. 13

    Doh, Y. J., De Franceschi, S., Bakkers, E. P. A. M. & Kouwenhoven, L. P. Andreev reflection versus Coulomb blockade in hybrid semiconductor nanowire devices. Nano Lett. 8, 4098–4102 (2008).

  14. 14

    Yamada, Y., Tanaka, Y. & Kawakami, N. Interplay of Kondo and superconducting correlations in the nonequilibrium Andreev transport through a quantum dot. Phys. Rev. B 84, 075484 (2011).

  15. 15

    Glazman, L. I. & Matveev, K. Resonant Josephson current through Kondo impurities in a tunnel barrier. JETP Lett. 49, 659 (1989).

  16. 16

    Rozhkov, A. V. & Arovas, D. P. Josephson coupling through a magnetic impurity. Phys. Rev. Lett. 82, 2788–2791 (1999).

  17. 17

    Vecino, E., Martín-Rodero, A. & Yeyati, A. L. Josephson current through a correlated quantum level: Andreev states and π junction behavior. Phys. Rev. B 68, 035105 (2003).

  18. 18

    Oguri, A., Tanaka, Y. & Hewson, A. C. Quantum phase transition in a minimal model for the Kondo effect in a Josephson junction. J. Phys. Soc. Jpn 73, 2494–2504 (2004).

  19. 19

    Bauer, J., Oguri, A. & Hewson, A. C. Spectral properties of locally correlated electrons in a Bardeen–Cooper–Schrieffer superconductor. J. Phys. Condens. Matter 19, 486211 (2007).

  20. 20

    Choi, M. S., Lee, M., Kang, K. & Belzig, W. Kondo effect and Josephson current through a quantum dot between two superconductors. Phys. Rev. B 70, 020502(R) (2004).

  21. 21

    Meng, T., Florens, S. & Simon, P. Self-consistent description of Andreev bound states in Josephson quantum dot devices. Phys. Rev. B 79, 224521 (2009).

  22. 22

    Domański, T., Donabidowicz, A. & Wysokiński, K. I. Meservey–Tedrow–Fulde effect in a quantum dot embedded between metallic and superconducting electrodes. Phys. Rev. B 78, 144515 (2008).

  23. 23

    Futterer, D., Swieboddzinski, J., Governale, M. & König, J. Renormalization effects in interacting quantum dots coupled to superconducting leads. Phys. Rev. B 87, 014509 (2013).

  24. 24

    Kanai, Y. et al. Electrical control of Kondo effect and superconducting transport in a side-gated InAs quantum dot Josephson junction. Phys. Rev. B 82, 054512 (2010).

  25. 25

    Sand-Jespersen, T. et al. Kondo-enhanced Andreev tunneling in InAs nanowire quantum dots. Phys. Rev. Lett. 99, 126603 (2007).

  26. 26

    Eichler, A. et al. Even–odd effect in Andreev transport through a carbon nanotube quantum dot. Phys. Rev. Lett. 99, 126602 (2007).

  27. 27

    Pillet, J. D. et al. Andreev bound states in supercurrent-carrying carbon nanotubes revealed. Nature Phys. 6, 965–969 (2010).

  28. 28

    Deacon, R. S. et al. Tunneling spectroscopy of Andreev energy levels in a quantum dot coupled to a superconductor. Phys. Rev. Lett. 104, 076805 (2010).

  29. 29

    Dirks, T. et al. Transport through Andreev bound states in a graphene quantum dot. Nature Phys. 7, 386–390 (2011).

  30. 30

    Lee, E. J. H. et al. Zero-bias anomaly in a nanowire quantum dot coupled to superconductors. Phys. Rev. Lett. 109, 186802 (2012).

  31. 31

    Chang, W., Manucharyan, V. E., Jespersen, T. S., Nygåard, J. & Marcus, C. M. Tunneling spectroscopy of quasiparticle bound states in a spinful Josephson junction. Phys. Rev. Lett. 110, 217005 (2013).

  32. 32

    Pillet, J. D., Joyez, P., Zitko, R. & Goffman, M. F. Tunneling spectroscopy of a single quantum dot coupled to a superconductor: from Kondo ridge to Andreev bound states. Phys. Rev. B 88, 045101 (2013).

  33. 33

    Kumar, A. et al. Temperature dependence of Andreev spectra in a superconducting carbon nanotube quantum dot. Preprint at http://lanl.arXiv.org/1308.1020v1 (2013).

  34. 34

    Giazotto, F. et al. A Josephson quantum electron pump. Nature Phys. 7, 857–861 (2011).

  35. 35

    Prada, E., San-Jose, P. & Aguado, R. Transport spectroscopy of N–S nanowire junctions with Majorana fermions. Phys. Rev. B 86, 180503(R) (2012).

  36. 36

    Rainis, D., Klinovaja, J. & Loss, D. Towards a realistic transport modeling in a superconducting nanowire with Majorana fermions. Phys. Rev. B 87, 024515 (2013).

  37. 37

    Sarma, S. D., Sau, J. D. & Stanescu, T. D. Splitting of the zero-bias conductance peak as smoking gun evidence for the existence of the Majorana mode in a superconductor–semiconductor nanowire. Phys. Rev. B 86, 220506(R) (2012).

  38. 38

    Liu, J., Potter, A. C., Law, K. T. & Lee, P. A. Zero-bias peaks in the tunneling conductance of spin-orbit-coupled superconducting wires with and without Majorana end-states. Phys. Rev. Lett. 109, 267002 (2012).

  39. 39

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

  40. 40

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

  41. 41

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

  42. 42

    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 (2012).

  43. 43

    Churchill, H. O. H. et al. Superconductor-nanowire devices from tunnelling to multi-channel regime: zero-bias oscillations and magnetoconductance crossover. Phys. Rev. B 87, 242401(R) (2013).

  44. 44

    Stanescu, T. D., Lutchyn, R. M. & Sarma, S. D. Dimensional crossover in spin-orbit-coupled semiconductor nanowires with induced superconducting pairing. Phys. Rev. B 87, 094518 (2013).

  45. 45

    Nadj-Perge, S., Drozdov, I. K., Bernevig, B. A. & Yazdani, A. Proposal for realizing Majorana fermions in chains of magnetic atoms on a superconductor. Phys. Rev. B 88, 020407(R) (2013).

  46. 46

    Klinovaja, J., Stano, P., Yazdani, A. & Loss, D. Topological superconductivity and Majorana fermions in RKKY systems. Phys. Rev. Lett. 111, 186805 (2013).

  47. 47

    Vazifeh, M. M. & Franz, M. Self-organized topological state with Majorana fermions. Phys. Rev. Lett. 111, 206802 (2013).

  48. 48

    Braunecker, B. & Simon, P. Interplay between classical magnetic moments and superconductivity in quantum one-dimensional conductors: towards a self-sustained topological Majorana phase. Phys. Rev. Lett. 111, 147202 (2013).

  49. 49

    Pientka, F., Glazman, L. & von Oppen, F. Topological superconducting phase in helical Shiba chains. Phys. Rev. B 88, 155420 (2013).

  50. 50

    Jiang, X., Xiong, Q., Qian, F., Li, Y. & Lieber, C. M. InAs/InP radial nanowire heterostructures as high electron mobility devices. Nano Lett. 7, 3214–3218 (2007).

Download references

Acknowledgements

This work was supported by the European Research Council (ERC Grant agreement no. 280043-HybridNano) and by the Agence Nationale de la Recherche (ANR-08-JCJC-0010). R.A. acknowledges support from the Spanish Ministry of Economy and Innovation through grants FIS2009-08744 and FIS2012-33521. The authors thank J-D. Pillet for useful discussions.

Author information

Affiliations

Authors

Contributions

E.J.H.L. and S.D.F. conceived the experiment. X.J. grew the semiconductor NWs under C.M.L.'s supervision. E.J.H.L. fabricated the devices and performed all the measurements under S.D.F.'s supervision. R.A. performed the Hartree–Fock calculations, and M.H. carried out the analytical study of the level-repulsion effect. E.J.H.L., S.D.F., R.A. and M.H. analysed and interpreted the results. All authors co-wrote the manuscript.

Corresponding author

Correspondence to Silvano De Franceschi.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 1239 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Lee, E., Jiang, X., Houzet, M. et al. Spin-resolved Andreev levels and parity crossings in hybrid superconductor–semiconductor nanostructures. Nature Nanotech 9, 79–84 (2014). https://doi.org/10.1038/nnano.2013.267

Download citation

Further reading