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# A tunable Fabry–Pérot quantum Hall interferometer in graphene

## 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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## Data availability

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

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## 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.

## Author information

Authors

### 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.

### Corresponding author

Correspondence to Benjamin Sacépé.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## 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.

## Supplementary information

### Supplementary Information

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

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Reprints and Permissions

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

• Accepted:

• Published:

• ### AharonovâBohm effect in graphene-based FabryâPÃ©rot quantum Hall interferometers

• Yuval Ronen
• , Thomas Werkmeister
• , Andrew T. Pierce
• , Laurel E. Anderson
• , Young Jae Shin
• , Si Young Lee
• , Young Hee Lee
• , Bobae Johnson
• , Kenji Watanabe
• , Takashi Taniguchi
• , Amir Yacoby
•  & Philip Kim

Nature Nanotechnology (2021)