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A tunable Fabry–Pérot quantum Hall interferometer in graphene

Nature Nanotechnology volume 16, pages 555–562 (2021)Cite this article

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Abstract

Electron interferometry with quantum Hall (QH) edge channels in semiconductor heterostructures can probe and harness the exchange statistics of anyonic excitations. However, the charging effects present in semiconductors often obscure the Aharonov–Bohm interference in QH interferometers and make advanced charge-screening strategies necessary. Here we show that high-mobility monolayer graphene constitutes an alternative material system, not affected by charging effects, for performing Fabry–Pérot QH interferometry in the integer QH regime. In devices equipped with gate-tunable quantum point contacts acting on the edge channels of the zeroth Landau level, we observe—in agreement with theory—high-visibility Aharonov–Bohm interference widely tunable through electrostatic gating or magnetic fields. A coherence length of 10 μm at a temperature of 0.02 K allows us to further achieve coherently coupled double Fabry–Pérot interferometry. In future, QH interferometry with graphene devices may enable investigations of anyonic excitations in fractional QH states.

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Fig. 1: Graphene QH FP interferometer.
Fig. 2: Gate-tunable quantum interference.
Fig. 3: Aharonov–Bohm effect and energy dependence.
Fig. 4: Coherently coupled double QH FP interferometer.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. van Wees, B. J. et al. Observation of zero-dimensional states in a one-dimensional electron interferometer. Phys. Rev. Lett. 62, 2523–2526 (1989).

    Article  Google Scholar 

  2. Ji, Y. et al. An electronic Mach–Zehnder interferometer. Nature 422, 415–418 (2003).

    Article  CAS  Google Scholar 

  3. Bäuerle, C. et al. Coherent control of single electrons: a review of current progress. Rep. Prog. Phys. 81, 056503 (2018).

    Article  Google Scholar 

  4. Chamon, C., Freed, D. E., Kivelson, S. A., Sondhi, S. L. & Wen, X. G. Two point-contact interferometer for quantum Hall systems. Phys. Rev. B 55, 2331–2343 (1997).

    Article  Google Scholar 

  5. Fradkin, E., Nayak, C., Tsvelik, A. & Wilczek, F. A Chern–Simons effective field theory for the Pfaffian quantum Hall state. Nucl. Phys. B 516, 704–718 (1998).

    Article  Google Scholar 

  6. Das Sarma, S., Freedman, M. & Nayak, C. Topologically protected qubits from a possible non-Abelian fractional quantum Hall state. Phys. Rev. Lett. 94, 166802 (2005).

    Article  Google Scholar 

  7. Bonderson, P., Kitaev, A. & Shtengel, K. Detecting non-Abelian statistics in the ν = 5/2 fractional quantum Hall state. Phys. Rev. Lett. 96, 016803 (2006).

    Article  Google Scholar 

  8. Chung, S. B. & Stone, M. Proposal for reading out anyon qubits in non-Abelian ν = 12/5 quantum Hall state. Phys. Rev. B 73, 245311 (2006).

    Article  Google Scholar 

  9. Stern, A. & Halperin, B. I. Proposed experiments to probe the non-Abelian ν = 5/2 quantum Hall state. Phys. Rev. Lett. 96, 016802 (2006).

    Article  Google Scholar 

  10. Feldman, D. E. & Kitaev, A. Detecting non-Abelian statistics with an electronic Mach–Zehnder interferometer. Phys. Rev. Lett. 97, 186803 (2006).

    Article  CAS  Google Scholar 

  11. Stern, A., Rosenow, B., Ilan, R. & Halperin, B. I. Interference, Coulomb blockade, and the identification of non-Abelian quantum Hall states. Phys. Rev. B 82, 085321 (2010).

    Article  Google Scholar 

  12. Camino, F. E., Zhou, W. & Goldman, V. J. e/3 Laughlin quasiparticle primary-filling ν = 1/3 interferometer. Phys. Rev. Lett. 98, 076805 (2007).

    Article  CAS  Google Scholar 

  13. Zhang, Y. et al. Distinct signatures for Coulomb blockade and Aharonov–Bohm interference in electronic Fabry–Perot interferometers. Phys. Rev. B 79, 241304 (2009).

    Article  Google Scholar 

  14. McClure, D. T. et al. Edge-state velocity and coherence in a quantum Hall Fabry–Pérot interferometer. Phys. Rev. Lett. 103, 206806 (2009).

    Article  CAS  Google Scholar 

  15. Ofek, N. et al. Role of interactions in an electronic Fabry–Perot interferometer operating in the quantum Hall effect regime. Proc. Natl Acad. Sci. USA 107, 5276–5281 (2010).

    Article  CAS  Google Scholar 

  16. McClure, D. T., Chang, W., Marcus, C. M., Pfeiffer, L. N. & West, K. W. Fabry–Perot interferometry with fractional charges. Phys. Rev. Lett. 108, 256804 (2012).

    Article  CAS  Google Scholar 

  17. Willett, R. L., Nayak, C., Shtengel, K., Pfeiffer, L. N. & West, K. W. Magnetic-field-tuned Aharonov–Bohm oscillations and evidence for non-Abelian anyons at ν = 5/2. Phys. Rev. Lett. 111, 186401 (2013).

    Article  CAS  Google Scholar 

  18. Choi, H. K. et al. Robust electron pairing in the integer quantum Hall effect regime. Nat. Commun. 6, 7435 (2015).

    Article  CAS  Google Scholar 

  19. Sivan, I. et al. Observation of interaction-induced modulations of a quantum Hall liquid’s area. Nat. Commun. 7, 12184 (2016).

    Article  CAS  Google Scholar 

  20. Rosenow, B. & Halperin, B. I. Influence of interactions on flux and back-gate period of quantum Hall interferometers. Phys. Rev. Lett. 98, 106801 (2007).

    Article  CAS  Google Scholar 

  21. Halperin, B. I., Stern, A., Neder, I. & Rosenow, B. Theory of the Fabry–Pérot quantum Hall interferometer. Phys. Rev. B 83, 155440 (2011).

    Article  Google Scholar 

  22. Ngo Dinh, S. & Bagrets, D. A. Influence of Coulomb interaction on the Aharonov–Bohm effect in an electronic Fabry–Pérot interferometer. Phys. Rev. B 85, 073403 (2012).

    Article  Google Scholar 

  23. Röösli, M. P. et al. Observation of quantum Hall interferometer phase jumps due to a change in the number of bulk quasiparticles. Phys. Rev. B 101, 125302 (2020).

    Article  Google Scholar 

  24. Nakamura, J. et al. Aharonov–Bohm interference of fractional quantum Hall edge modes. Nat. Phys. 15, 563–569 (2019).

    Article  CAS  Google Scholar 

  25. Nakamura, J., Liang, S., Gardner, G. C. & Manfra, M. J. Direct observation of anyonic braiding statistics. Nat. Phys. 16, 931–936 (2020).

    Article  CAS  Google Scholar 

  26. Bartolomei, H. et al. Fractional statistics in anyon collisions. Science 368, 173–177 (2020).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  28. Du, X., Skachko, I., Duerr, F., Luican, A. & Andrei, A. Y. Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene. Nature 462, 192–195 (2009).

    Article  CAS  Google Scholar 

  29. Bolotin, K. I., Ghahari, F., Shulman, M. D., Stormer, H. L. & Kim, P. Observation of the fractional quantum Hall effect in graphene. Nature 462, 196–199 (2009).

    Article  CAS  Google Scholar 

  30. Dean, C. R. et al. Multicomponent fractional quantum Hall effect in graphene. Nat. Phys. 7, 693–696 (2011).

    Article  CAS  Google Scholar 

  31. Kim, Y. et al. Even denominator fractional quantum Hall states in higher Landau levels of graphene. Nat. Phys. 15, 154–158 (2019).

    Article  CAS  Google Scholar 

  32. Zibrov, A. A. et al. Even-denominator fractional quantum Hall states at an isospin transition in monolayer graphene. Nat. Phys. 14, 930–935 (2018).

    Article  CAS  Google Scholar 

  33. Young, A. F. et al. Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state. Nature 505, 528–532 (2014).

    Article  CAS  Google Scholar 

  34. Veyrat, L. et al. Helical quantum Hall phase in graphene on SrTiO3. Science 367, 781–786 (2020).

    Article  CAS  Google Scholar 

  35. Yankowitz, M., Ma, Q., Jarillo-Herrero, P. & LeRoy, B. J. Van der Waals heterostructures combining graphene and hexagonal boron nitride. Nat. Rev. Phys. 1, 112–125 (2019).

    Article  CAS  Google Scholar 

  36. Nakaharai, S., Williams, J. R. & Marcus, C. M. Gate-defined graphene quantum point contact in the quantum Hall regime. Phys. Rev. Lett. 107, 036602 (2011).

    Article  CAS  Google Scholar 

  37. Veyrat, L. et al. Low-magnetic-field regime of a gate-defined constriction in high-mobility graphene. Nano Letters 19, 635–642 (2019).

    Article  Google Scholar 

  38. Wei, D. S. et al. Mach–Zehnder interferometry using spin- and valley-polarized quantum Hall edge states in graphene. Sci. Adv. 3, e1700600 (2017).

    Article  Google Scholar 

  39. Makk, P. et al. Coexistence of classical snake states and Aharonov–Bohm oscillations along graphene p–n junctions. Phys. Rev. B 98, 035413 (2018).

    Article  CAS  Google Scholar 

  40. Zhang, G. et al. Coulomb-dominated oscillations in a graphene quantum Hall Fabry–Pérot interferometer. Chin. Phys. B 28, 127203 (2019).

    Article  CAS  Google Scholar 

  41. Zimmermann, K. et al. Tunable transmission of quantum Hall edge channels with full degeneracy lifting in split-gated graphene devices. Nat. Commun. 8, 14983 (2017).

    Article  CAS  Google Scholar 

  42. Yamauchi, Y. et al. Universality of bias- and temperature-induced dephasing in ballistic electronic interferometers. Phys. Rev. B 79, 161306 (2009).

    Article  Google Scholar 

  43. Gurman, I., Sabo, R., Heiblum, M., Umansky, V. & Mahalu, D. Dephasing of an electronic two-path interferometer. Phys. Rev. B 93, 121412 (2016).

    Article  Google Scholar 

  44. Ronen, Y. et al. Aharonov–Bohm effect in graphene-based Fabry–Pérot quantum Hall interferometers. Nat. Nanotechnol. https://doi.org/10.1038/s41565-021-00861-z (2021).

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  47. Zhao, L. et al. Interference of chiral Andreev edge states. Nat. Phys. 16, 862–867 (2020).

    Article  CAS  Google Scholar 

  48. Huang, X. L. & Nazarov, Y. V. Interaction-induced supercurrent in quantum Hall setups. Phys. Rev. B 100, 155411 (2019).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank I. Aleiner for valuable discussions. We thank S. Dumont for the development of low-noise, high-stability voltage sources and F. Blondelle for his technical support. Samples were prepared at the Nanofab facility of Néel Institute. This work was supported by H2020 ERC grants QUEST number 637815 and SUPERGRAPH number 866365. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by MEXT, Japan, grant number JPMXP0112101001, JSPS KAKENHI grant number JP20H00354 and CREST (JPMJCR15F3), JST.

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Authors and Affiliations

  1. Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble, France

    Corentin Déprez, Louis Veyrat, Hadrien Vignaud, Goutham Nayak, Frédéric Gay, Hermann Sellier & Benjamin Sacépé

  2. Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan

    Kenji Watanabe

  3. International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan

    Takashi Taniguchi

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  1. Corentin Déprez
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Contributions

C.D., L.V., H.V. and G.N. performed the sample fabrication. C.D. performed the experiments under the supervision of B.S.; F.G. provided technical support on the experiments. K.W. and T.T. grew the hBN crystals. C.D., H.S. and B.S. analysed the data. C.D. and H.S. developed the theoretical aspects. B.S. conceived the project and wrote the paper with inputs from all coauthors.

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Correspondence to Benjamin Sacépé.

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Peer review information Nature Nanotechnology thanks G. Fève and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 QPC conductance maps at 14 T.

a,b,c, Diagonal conductance GD versus split-gate voltages, VQPC, and back-gate voltages, Vbg, for the three QPCs of the device presented in the main text. During a measurement, only one QPC is studied and the two other sets of split gates are kept floating. The slope of the diagonal stripes corresponds to the capacitance ratio between the QPC constriction and the back gate. This slope is about twice/three times smaller than the zero-field slope of the charge neutrality point under the split-gate electrodes for QPC2 and QPC3, but is only slightly smaller for QPC1 (due to the unintentional absence of gap between the two electrodes of this QPC).

Extended Data Fig. 2 QPC transmission curves at 14 T.

Evolution of the diagonal conductance GD as a function of split-gate voltages VQPC at fixed back-gate voltage Vbg. a,Vbg = 0.88 V. b,Vbg = 0.53 V.

Extended Data Fig. 3 Resistance oscillations at positive plunger-gate voltage.

a,b,c, Resistance oscillations as a function of plunger-gate voltage Vpg2 measured in the small interferometer for Vpg2 > 0. These data are the extension of the measurements performed in Fig. 2c of the main text to positive plunger-gate voltage, which corresponds to the accumulation of localized electron states beneath the plunger gate (see inset in Fig. 2d). a and b show zooms on smaller Vpg2 ranges of the resistance oscillations converted in visibility \((R-\bar{R})/\bar{R}\), where \(\bar{R}\) is the resistance background. d, Fourier amplitude of the resistance oscillations in c as a function of Vpg2 and plunger-gate voltage frequency fpg2.

Extended Data Fig. 4 Bias dependence of Aharonov–Bohm oscillations.

a,b,c, Amplitude of the Fourier transform of the oscillations at fixed voltage bias (blue dots) and fits with Suppl. Eq. (S12) (red line) and Suppl. Eq. (S13) (orange line). Fitting parameters are reported in Suppl. Table S3.

Extended Data Fig. 5 Phase coherence length Lϕ.

Evolution of the best visibilities \({\mathcal{V}}\) with the perimeter 2L of the interferometers obtained in experiments at base temperature with the outer (blue dots) and the inner (red dots) edge channel. The red solid line shows the thermal broadening contribution. The fit of the data (black dashed line) with Suppl. Eq. (S30) and discarding the inner edge channel experiment for the large interferometer, provides a coherence length of 10 μm at 0.02 K.

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Supplementary Information

Supplementary Sections I–XVII, Figs. 1–17 and Tables 1–3.

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Déprez, C., Veyrat, L., Vignaud, H. et al. A tunable Fabry–Pérot quantum Hall interferometer in graphene. Nat. Nanotechnol. 16, 555–562 (2021). https://doi.org/10.1038/s41565-021-00847-x

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