Abstract
Magic-angle twisted bilayer graphene (MATBG) hosts a number of correlated states of matter that can be tuned by electrostatic doping1,2,3,4. Transport5,6 and scanning-probe7,8,9 experiments have shown evidence for band, correlated and Chern insulators along with superconductivity. This variety of in situ tunable states has allowed for the realization of tunable Josephson junctions10,11,12. However, although phase-coherent phenomena have been measured10,11,12, no control of the phase difference of the superconducting condensates has been demonstrated so far. Here we build on previous gate-defined junction realizations and form a superconducting quantum interference device13 (SQUID) in MATBG, where the superconducting phase difference is controlled through the magnetic field. We observe magneto-oscillations of the critical current, demonstrating long-range coherence of superconducting charge carriers with an effective charge of 2e. We tune to both asymmetric and symmetric SQUID configurations by electrostatically controlling the critical currents through the junctions. This tunability allows us to study the inductances in the device, finding values of up to 2 μH. Furthermore, we directly probe the current–phase relation of one of the junctions of the device. Our results show that complex devices in MATBG can be realized and used to reveal the properties of the material. We envision our findings, together with the established history of applications SQUIDs have14,15,16, will foster the development of a wide range of devices such as phase-slip junctions17 or high kinetic inductance detectors18.
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Data availability
The data that support the findings of this study are available online through the ETH Research Collection at https://doi.org/10.3929/ethz-b-000563127. This includes analysis and plotting scripts for Figs. 1–3, Extended Data Figs. 2–9 and Supplementary Information Figs. 1–3. It also includes raw microscopy files for Extended Data Fig. 1.
Code availability
The code used for plotting the figures is available online through the ETH Research Collection at https://doi.org/10.3929/ethz-b-000563127.
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Acknowledgements
We thank P. Märki, L. Ginzburg, P. Tomić and the staff of the ETH cleanroom facility FIRST for technical support. We thank H. Pothier for helpful and detailed discussions on superconducting devices and O. Zilberberg, J. Cole and members of the quantum e-leaps consortium for comments on our data. We acknowledge financial support by the European Graphene Flagship, the ERC Synergy Grant Quantropy, the European Union’s Horizon 2020 research and innovation programme under grant agreement number 862660/QUANTUM E LEAPS and NCCR QSIT (Swiss National Science Foundation). K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan (grant number JPMXP0112101001) and JSPS KAKENHI (grant numbers 19H05790, 20H00354 and 21H05233). E.P. acknowledges support of a fellowship from ‘la Caixa’ Foundation (ID 100010434) under fellowship code LCF/BQ/EU19/11710062.
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E.P. fabricated the device. T.T. and K.W. supplied the hBN crystals. E.P. and F.K.d.V. performed the measurements and analysis of the data. E.P., F.K.d.V., S.I., G.Z. and P.R. discussed the data. F.K.d.V., T.I. and K.E. supervised the project. E.P. and F.K.d.V. wrote the manuscript with comments from all authors.
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Extended data
Extended Data Fig. 1 Device fabrication: Capture of the design file and optical images taken during the fabrication process.
a Optical image of the device after etching and evaporation of the gold contacts. The scale bar corresponds to a length of 1μm. b Optical image of the device after mesa etching. c Optical image of the device after the deposition of a layer of aluminium oxide and definition and evaporation of top gates. d Capture of the design file of the device. Contacts are depicted in yellow, etched areas in pink and top gates in white.
Extended Data Fig. 2 Density maps and angle extraction.
a Differential resistance maps across the device as a function of electron density in regions biased by only the back gate (global) or both back and top gates. The data in the left panel corresponds to VG1 being swept and gate 2 being fixed at VG2 = 10V. In the centre panel VG2 is swept while gate 1 is kept constant at VG1 = 10V. In the right panel both top gates are swept together. Densities are computed from the model described in the Methods section. Black dashed lines indicate the values at which we consider the flat bands to be fully filled. These values are then used to extract the twist angle of the device. b Extended range trace of the resistance as a function of the global density induced by the back gate, with each local top gate set to zero.
Extended Data Fig. 3 Resistance of the device as a function of density.
VG1 and VG2 are kept at zero volts. We plot the derivative of the measured voltage drop as a function of the current bias, which corresponds to the differential resistance R = dV/dIdc across the device. The red dashed line indicates the ’optimal density’ nopt = − 1.27 × 1012cm−2 at which we set the back gate when wanting to maximize the critical current through the device. The upper axis indicates the filling factors corresponding to the electron densities.
Extended Data Fig. 4 Differential resistance across each arm of the loop as a function of local densities.
The back gate is tuned to its optimal point nopt = − 1.27 × 1012cm−2. We step the local top gate of each arm and sweep the current bias. For a, the voltage bias of gate G2 is fixed at VG2 = 10V, to prevent any supercurrent from going through it, while we step G1. For b the configuration is the opposite, we have VG1 = 10V while we step VG2. The dashed lines correspond to the voltage of each top gate at the asymmetric (orange) and symmetric (red) regime measurements shown in Fig. 1d,e.
Extended Data Fig. 5 Critical field at each arm of the device.
The voltage of the back gate is set to the optimal point for every figure. a Differential resistance as a function of current bias and magnetic field when VG1 = 10V, preventing any supercurrent from flowing through arm 1 and VG2 = -0.5V maximizes the critical current of arm 2. We thus observe the resistance across arm 2 of the device as a function of current and magnetic field. b Same measurement as in a, this time with VG2 = 10V and VG1 = -0.37V.
Extended Data Fig. 6 Hysteresis and discontinuities in the critical current as a function of magnetic field.
Each line represents a CPR trace taken at the most asymmetric regime of the device. The magnetic field is swept from negative to positive in a small range, then the direction is reversed and the range increased. This procedure is repeated several times to obtain the data shown in the figure. Switches in the CPR traces and hysteresis appear as the range of the magnetic field sweep increases. We can not rule out a ferromagnetic part of the cryostat or the superconducting magnet to be at the origin of this phenomenon. Therefore, we do not highlight it in the main text.
Extended Data Fig. 7 Presence or absence of oscillations depending on the current sweep direction.
The device is in the most asymmetric configuration. The left panel of the figure is a zoom in of Fig. 1. We measure the voltage drop across the device as a function of magnetic field and current. We observe oscillations due to superconducting interference in the superconducting lobe or the switching current but no oscillations for the retrapping current. The current bias is swept from negative to positive values in the left panel and from positive to negative in the right panel.
Extended Data Fig. 8 Voltage drop over the device when biased above the critical current in the symmetric regime.
The curves show the voltage drop across the device as a function of magnetic field with a different current bias for each curve. Black dotted lines are guides to the eye plotted using equation (S1) fixing Ic at 2.25 nA.
Extended Data Fig. 9 Resistance across the device as a function of density and temperature.
The black dotted line highlights the superconducting lobe. The line is taken where the resistance is 50% of the normal state resistance.
Supplementary information
Supplementary Information
Supplementary Discussion and Figs. 1–3.
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Portolés, E., Iwakiri, S., Zheng, G. et al. A tunable monolithic SQUID in twisted bilayer graphene. Nat. Nanotechnol. 17, 1159–1164 (2022). https://doi.org/10.1038/s41565-022-01222-0
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DOI: https://doi.org/10.1038/s41565-022-01222-0
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