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.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 /Â 30Â days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
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
Klapwijk, T. M. Proximity effect from an Andreev perspective. J. Supercond. 17, 593â611 (2004).
Beenakker, C. W. J. Random-matrix theory of Majorana fermions and topological superconductors. Rev. Mod. Phys. 87, 1037â1066 (2015).
Stern, A. & Lindner, N. H. Topological quantum computationâfrom basic concepts to first experiments. Science 339, 1179â1184 (2013).
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, 10938â10942 (2018).
Lutchyn, R. M. et al. Majorana zero modes in superconductorâsemiconductor heterostructures. Nat. Rev. Mater. 3, 52â68 (2018).
Mong, R. S. K. et al. Universal topological quantum computation from a superconductor-Abelian quantum Hall heterostructure. Phys. Rev. X 4, 011036 (2014).
Qi, X.-L., Hughes, T. L. & Zhang, S.-C. Chiral topological superconductor from the quantum Hall state. Phys. Rev. B 82, 184516 (2010).
Takagaki, Y. Transport properties of semiconductorâsuperconductor junctions in quantizing magnetic fields. Phys. Rev. B 57, 4009â4016 (1998).
Hoppe, H., Zülicke, U. & Schön, G. Andreev reflection in strong magnetic fields. Phys. Rev. Lett. 84, 1804â1807 (2000).
Khaymovich, I. M., Chtchelkatchev, N. M., Shereshevskii, I. A. & Melânikov, A. S. Andreev transport in two-dimensional normal-superconducting systems in strong magnetic fields. Europhys. Lett. 91, 17005 (2010).
Chamon, C., Jackiw, R., Nishida, Y., Pi, S.-Y. & Santos, L. Quantizing Majorana fermions in a superconductor. Phys. Rev. B 81, 224515 (2010).
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).
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).
Chaudhary, G. & MacDonald, A. H. Vortex-lattice structure and topological superconductivity in the quantum Hall regime. Phys. Rev. B 101, 024516 (2020).
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).
Batov, I. E., Schäpers, T., Chtchelkatchev, N. M., Hardtdegen, H. & Ustinov, A. V. Andreev reflection and strongly enhanced magnetoresistance oscillations in GaxIn1âââxAs/InP heterostructures with superconducting contacts. Phys. Rev. B 76, 115313 (2007).
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).
Rickhaus, P., Weiss, M., Marot, L. & Schönenberger, C. Quantum Hall effect in graphene with superconducting electrodes. Nano Lett. 12, 1942â1945 (2012).
Wan, Z. et al. Induced superconductivity in high-mobility two-dimensional electron gas in gallium arsenide heterostructures. Nat. Commun. 6, 7426 (2015).
Ben Shalom, M. et al. Quantum oscillations of the critical current and high-field superconducting proximity in ballistic graphene. Nat. Phys. 12, 318â322 (2016).
Calado, V. E. et al. Ballistic Josephson junctions in edge-contacted graphene. Nat. Nanotechnol. 10, 761â764 (2015).
Amet, F. et al. Supercurrent in the quantum Hall regime. Science 352, 966â969 (2016).
Seredinski, A. et al. Quantum Hall-based superconducting interference device. Sci. Adv. 5, eaaw8693 (2019).
Lee, G.-H. et al. Inducing superconducting correlation in quantum Hall edge states. Nat. Phys. 13, 693â698 (2017).
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).
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).
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).
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).
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).
Lian, B., Wang, J. & Zhang, S.-C. Edge-state-induced Andreev oscillation in quantum anomalous Hall insulatorâsuperconductor junctions. Phys. Rev. B 93, 161401 (2016).
Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614â617 (2013).
Borzenets, I. V. et al. Ballistic graphene Josephson junctions from the short to the long junction regimes. Phys. Rev. Lett. 117, 237002 (2016).
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).
PetkoviÄ, I. et al. Carrier drift velocity and edge magnetoplasmons in graphene. Phys. Rev. Lett. 110, 016801 (2013).
Akhmerov, A. R. & Beenakker, C. W. J. Detection of valley polarization in graphene by a superconducting contact. Phys. Rev. Lett. 98, 157003 (2007).
Beenakker, C. W. J. Annihilation of colliding Bogoliubov quasiparticles reveals their Majorana nature. Phys. Rev. Lett. 112, 070604 (2014).
Clarke, D. J., Alicea, J. & Shtengel, K. Exotic circuit elements from zero-modes in hybrid superconductorâquantum-Hall systems. Nat. Phys. 10, 877â882 (2014).
Hwang, S.-Y., Giazotto, F. & Sothmann, B. Phase-coherent heat circulator based on multiterminal Josephson junctions. Phys. Rev. Appl. 10, 044062 (2018).
Zhao, L. et al. Data and Codes for âInterference of Chiral Andreev Edge Statesâ (Zenodo, 2020); https://doi.org/10.5281/zenodo.3708374
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).
Author information
Authors and Affiliations
Contributions
L.Z. and A.S. characterized and fabricated the device. H.L. and F.A. made the grapheneâhBN 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
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Peer review information Nature Physics thanks Leonid Rokhinson and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Publisherâs note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Supplementary Information
Supplementary sections 1â7 and Figs. 1â15.
Rights and permissions
About this article
Cite this article
Zhao, L., Arnault, E.G., Bondarev, A. et al. Interference of chiral Andreev edge states. Nat. Phys. 16, 862â867 (2020). https://doi.org/10.1038/s41567-020-0898-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41567-020-0898-5
This article is cited by
-
Induced superconducting correlations in a quantum anomalous Hall insulator
Nature Physics (2024)
-
One-dimensional proximity superconductivity in the quantum Hall regime
Nature (2024)
-
Magnetically controllable multimode interference in topological photonic crystals
Light: Science & Applications (2024)
-
A way to cross the Andreev bridge
Nature Physics (2024)
-
Quantum-anomalous-Hall current patterns and interference in thin slabs of chiral topological superconductors
Scientific Reports (2023)