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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.

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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.

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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.

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Correspondence to Lingfei Zhao or Gleb Finkelstein.

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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 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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