Interference of chiral Andreev edge states

Abstract

The search for topological excitations such as Majorana fermions has spurred interest in the boundaries between distinct quantum states. Here, we explore an interface between two prototypical phases of electrons with conceptually different ground states: the integer quantum Hall insulator and the s-wave superconductor. We find clear signatures of hybridized electron and hole states similar to chiral Majorana fermions, which we refer to as chiral Andreev edge states (CAESs). These propagate along the interface in the direction determined by the magnetic field and their interference can turn an incoming electron into an outgoing electron or hole, depending on the phase accumulated by the CAESs along their path. Our results demonstrate that these excitations can propagate and interfere over a significant length, opening future possibilities for their coherent manipulation.

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Fig. 1: Andreev reflection in the quantum Hall regime.
Fig. 2: The interference of CAESs on various quantum Hall plateaux and its magnetic field dependence.
Fig. 3: The bias dependence of the interference effect.

Data availability

Source data for figures (including the supplementary figures) are available in the public repository Zenodo (https://doi.org/10.5281/zenodo.3708374)39. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

The codes used for the analysis and simulations are available in the public repository Zenodo (https://doi.org/10.5281/zenodo.3708374)39.

References

  1. 1.

    Klapwijk, T. M. Proximity effect from an Andreev perspective. J. Supercond. 17, 593–611 (2004).

    ADS  Article  Google Scholar 

  2. 2.

    Beenakker, C. W. J. Random-matrix theory of Majorana fermions and topological superconductors. Rev. Mod. Phys. 87, 1037–1066 (2015).

    ADS  MathSciNet  Article  Google Scholar 

  3. 3.

    Stern, A. & Lindner, N. H. Topological quantum computation—from basic concepts to first experiments. Science 339, 1179–1184 (2013).

    ADS  Article  Google Scholar 

  4. 4.

    Lian, B., Sun, X.-Q., Vaezi, A., Qi, X.-L. & Zhang, S.-C. Topological quantum computation based on chiral Majorana fermions. Proc. Natl Acad. Sci. USA 115, 10938–10942 (2018).

    ADS  MathSciNet  Article  Google Scholar 

  5. 5.

    Lutchyn, R. M. et al. Majorana zero modes in superconductor–semiconductor heterostructures. Nat. Rev. Mater. 3, 52–68 (2018).

    ADS  Article  Google Scholar 

  6. 6.

    Mong, R. S. K. et al. Universal topological quantum computation from a superconductor-Abelian quantum Hall heterostructure. Phys. Rev. X 4, 011036 (2014).

    Google Scholar 

  7. 7.

    Qi, X.-L., Hughes, T. L. & Zhang, S.-C. Chiral topological superconductor from the quantum Hall state. Phys. Rev. B 82, 184516 (2010).

    ADS  Article  Google Scholar 

  8. 8.

    Takagaki, Y. Transport properties of semiconductor–superconductor junctions in quantizing magnetic fields. Phys. Rev. B 57, 4009–4016 (1998).

    ADS  Article  Google Scholar 

  9. 9.

    Hoppe, H., Zülicke, U. & Schön, G. Andreev reflection in strong magnetic fields. Phys. Rev. Lett. 84, 1804–1807 (2000).

    ADS  Article  Google Scholar 

  10. 10.

    Khaymovich, I. M., Chtchelkatchev, N. M., Shereshevskii, I. A. & Mel’nikov, A. S. Andreev transport in two-dimensional normal-superconducting systems in strong magnetic fields. Europhys. Lett. 91, 17005 (2010).

    ADS  Article  Google Scholar 

  11. 11.

    Chamon, C., Jackiw, R., Nishida, Y., Pi, S.-Y. & Santos, L. Quantizing Majorana fermions in a superconductor. Phys. Rev. B 81, 224515 (2010).

    ADS  Article  Google Scholar 

  12. 12.

    Tiwari, R. P., Zülicke, U. & Bruder, C. Majorana fermions from Landau quantization in a superconductor and topological-insulator hybrid structure. Phys. Rev. Lett. 110, 186805 (2013).

    ADS  Article  Google Scholar 

  13. 13.

    Gamayun, O., Hutasoit, J. A. & Cheianov, V. V. Two-terminal transport along a proximity-induced superconducting quantum Hall edge. Phys. Rev. B 96, 241104 (2017).

    ADS  Article  Google Scholar 

  14. 14.

    Chaudhary, G. & MacDonald, A. H. Vortex-lattice structure and topological superconductivity in the quantum Hall regime. Phys. Rev. B 101, 024516 (2020).

    ADS  Article  Google Scholar 

  15. 15.

    Eroms, J., Weiss, D., Boeck, J. D., Borghs, G. & Zülicke, U. Andreev reflection at high magnetic fields: evidence for electron and hole transport in edge states. Phys. Rev. Lett. 95, 107001 (2005).

    ADS  Article  Google Scholar 

  16. 16.

    Batov, I. E., Schäpers, T., Chtchelkatchev, N. M., Hardtdegen, H. & Ustinov, A. V. Andreev reflection and strongly enhanced magnetoresistance oscillations in GaxIn1 − xAs/InP heterostructures with superconducting contacts. Phys. Rev. B 76, 115313 (2007).

    ADS  Article  Google Scholar 

  17. 17.

    Komatsu, K., Li, C., Autier-Laurent, S., Bouchiat, H. & Guéron, S. Superconducting proximity effect in long superconductor/graphene/superconductor junctions: from specular Andreev reflection at zero field to the quantum Hall regime. Phys. Rev. B 86, 115412 (2012).

    ADS  Article  Google Scholar 

  18. 18.

    Rickhaus, P., Weiss, M., Marot, L. & Schönenberger, C. Quantum Hall effect in graphene with superconducting electrodes. Nano Lett. 12, 1942–1945 (2012).

    ADS  Article  Google Scholar 

  19. 19.

    Wan, Z. et al. Induced superconductivity in high-mobility two-dimensional electron gas in gallium arsenide heterostructures. Nat. Commun. 6, 7426 (2015).

    ADS  Article  Google Scholar 

  20. 20.

    Ben Shalom, M. et al. Quantum oscillations of the critical current and high-field superconducting proximity in ballistic graphene. Nat. Phys. 12, 318–322 (2016).

    Article  Google Scholar 

  21. 21.

    Calado, V. E. et al. Ballistic Josephson junctions in edge-contacted graphene. Nat. Nanotechnol. 10, 761–764 (2015).

    ADS  Article  Google Scholar 

  22. 22.

    Amet, F. et al. Supercurrent in the quantum Hall regime. Science 352, 966–969 (2016).

    ADS  MathSciNet  Article  Google Scholar 

  23. 23.

    Seredinski, A. et al. Quantum Hall-based superconducting interference device. Sci. Adv. 5, eaaw8693 (2019).

    ADS  Article  Google Scholar 

  24. 24.

    Lee, G.-H. et al. Inducing superconducting correlation in quantum Hall edge states. Nat. Phys. 13, 693–698 (2017).

    Article  Google Scholar 

  25. 25.

    Sahu, M. R. et al. Inter-Landau-level Andreev reflection at the Dirac point in a graphene quantum Hall state coupled to a NbSe2 superconductor. Phys. Rev. Lett. 121, 086809 (2018).

    ADS  Article  Google Scholar 

  26. 26.

    Park, G.-H., Kim, M., Watanabe, K., Taniguchi, T. & Lee, H.-J. Propagation of superconducting coherence via chiral quantum-Hall edge channels. Sci. Rep. 7, 10953 (2017).

    ADS  Article  Google Scholar 

  27. 27.

    Kozuka, Y., Sakaguchi, A., Falson, J., Tsukazaki, A. & Kawasaki, M. Andreev reflection at the interface with an oxide in the quantum Hall regime. J. Phys. Soc. Jpn 87, 124712 (2018).

    ADS  Article  Google Scholar 

  28. 28.

    Matsuo, S. et al. Equal-spin Andreev reflection on junctions of spin-resolved quantum Hall bulk state and spin-singlet superconductor. Sci. Rep. 8, 3454 (2018).

    ADS  Article  Google Scholar 

  29. 29.

    van Ostaay, J. A. M., Akhmerov, A. R. & Beenakker, C. W. J. Spin-triplet supercurrent carried by quantum Hall edge states through a Josephson junction. Phys. Rev. B 83, 195441 (2011).

    ADS  Article  Google Scholar 

  30. 30.

    Lian, B., Wang, J. & Zhang, S.-C. Edge-state-induced Andreev oscillation in quantum anomalous Hall insulator–superconductor junctions. Phys. Rev. B 93, 161401 (2016).

    ADS  Article  Google Scholar 

  31. 31.

    Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).

    ADS  Article  Google Scholar 

  32. 32.

    Borzenets, I. V. et al. Ballistic graphene Josephson junctions from the short to the long junction regimes. Phys. Rev. Lett. 117, 237002 (2016).

    ADS  Article  Google Scholar 

  33. 33.

    Roulleau, P. et al. Direct measurement of the coherence length of edge states in the integer quantum Hall regime. Phys. Rev. Lett. 100, 126802 (2008).

    ADS  Article  Google Scholar 

  34. 34.

    Petković, I. et al. Carrier drift velocity and edge magnetoplasmons in graphene. Phys. Rev. Lett. 110, 016801 (2013).

    ADS  Article  Google Scholar 

  35. 35.

    Akhmerov, A. R. & Beenakker, C. W. J. Detection of valley polarization in graphene by a superconducting contact. Phys. Rev. Lett. 98, 157003 (2007).

    ADS  Article  Google Scholar 

  36. 36.

    Beenakker, C. W. J. Annihilation of colliding Bogoliubov quasiparticles reveals their Majorana nature. Phys. Rev. Lett. 112, 070604 (2014).

    ADS  Article  Google Scholar 

  37. 37.

    Clarke, D. J., Alicea, J. & Shtengel, K. Exotic circuit elements from zero-modes in hybrid superconductor–quantum-Hall systems. Nat. Phys. 10, 877–882 (2014).

    Article  Google Scholar 

  38. 38.

    Hwang, S.-Y., Giazotto, F. & Sothmann, B. Phase-coherent heat circulator based on multiterminal Josephson junctions. Phys. Rev. Appl. 10, 044062 (2018).

    ADS  Article  Google Scholar 

  39. 39.

    Zhao, L. et al. Data and Codes for ‘Interference of Chiral Andreev Edge States’ (Zenodo, 2020); https://doi.org/10.5281/zenodo.3708374

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Acknowledgements

We greatly appreciate stimulating discussion with A. Chang, M. Gilbert, B. Lian, Y. Oreg, K. Shtengel and A. Stern. Transport measurements conducted by L.Z., E.G.A. and A.S. were supported by the Division of Materials Sciences and Engineering, Office of Basic Energy Sciences, US Department of Energy, under award no. DE-SC0002765. Lithographic fabrication and characterization of the samples was performed by L.Z. and A.S. with the support of NSF awards ECCS-1610213 and DMR-1743907. The measurement set-up was developed by A.W.D., T.F.Q.L. and G.F. with the support of ARO award W911NF-16-1-0122. Numerical simulations conducted by A.B. and H.U.B. were supported by the Division of Materials Sciences and Engineering, Office of Basic Energy Sciences, US Department of Energy, under award no. DE-SC0005237. H.L. and F.A. acknowledge support from ARO (award W911NF-16-1-0132). K.W. and T.T. acknowledge support from JSPS KAKENHI grant no. JP15K21722 and the Elemental Strategy Initiative conducted by the MEXT, Japan. T.T. acknowledges support from JSPS Grant-in-Aid for Scientific Research A (no. 26248061) and JSPS Innovative Areas Nano Informatics (no. 25106006). Sample fabrication was performed in part at the Duke University Shared Materials Instrumentation Facility (SMIF), a member of the North Carolina Research Triangle Nanotechnology Network (RTNN), which is supported by the National Science Foundation (grant no. ECCS-1542015) as part of the National Nanotechnology Coordinated Infrastructure (NNCI).

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Contributions

L.Z. and A.S. characterized and fabricated the device. H.L. and F.A. made the graphene–hBN heterostructure. T.T. and K.W. provided the hBN crystals. L.Z., E.G.A. and A.S. performed the measurements. A.W.D., T.F.Q.L. and G.F. developed the measurement set-up. A.B. and H.U.B. conducted the numerical calculations. L.Z. and G.F. analysed the data and wrote the manuscript. H.U.B., F.A. and G.F. supervised the project.

Corresponding authors

Correspondence to Lingfei Zhao or Gleb Finkelstein.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Leonid Rokhinson and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information

Supplementary sections 1–7 and Figs. 1–15.

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Zhao, L., Arnault, E.G., Bondarev, A. et al. Interference of chiral Andreev edge states. Nat. Phys. 16, 862–867 (2020). https://doi.org/10.1038/s41567-020-0898-5

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